# Operasi Hitung Bilangan Cacah dan Pecahan untuk Persiapan Ujian SD > Lima bagian latihan untuk siswa kelas 6 yang bersiap menghadapi tes kompetensi. Dimulai dari urutan operasi bilangan cacah dengan aturan kabataku dan strategi berhitung cepat, lalu bentuk pecahan biasa, pecahan campuran, desimal, dan persen, cara membandingkan dan mengurutkan nilainya, serta penjumlahan, pengurangan, perkalian, dan pembagian pecahan, termasuk dengan bilangan asli. Setiap langkah dituliskan satu per satu dan digambarkan dengan pita, kotak, dan garis bilangan, lalu ditutup dengan soal cerita seperti yang muncul di ujian. - Canonical watch page: [Operasi Hitung Bilangan Cacah dan Pecahan untuk Persiapan Ujian SD](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd) - Publisher: [Academa, Inc.](https://academa.ai) - Subject: Mathematics - Published: 2026-09-03T00:51:21.032Z - Updated: 2026-09-03T00:51:21.032Z - Duration: PT1009S (16 minutes 49 seconds) - Chapters: 5 - Views: 2 - Language: en-US - Access: Free - Video stream: [HLS content](https://academa.ai/media/l/01M1JA4VKK6H0JA7FVN0PT5VZ7/0/dark/master.m3u8) - Embed: [Player](https://academa.ai/embed/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd) - Audiovisual record: [Semantic JSON](https://academa.ai/media/l/01M1JA4VKK6H0JA7FVN0PT5VZ7/0/semantic.json) - Thumbnail: [Image](https://academa.ai/media/l/01M1JA4VKK6H0JA7FVN0PT5VZ7/0/dark/poster.jpg) ## Description Latihan lengkap operasi bilangan cacah, urutan kabataku, bentuk pecahan, desimal, persen, serta operasi pecahan untuk ujian SD. ## Chapters - [00:00–04:16.953 · Urutan Operasi Bilangan Cacah](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=0) - [04:16.953–07:25.318 · Bentuk Pecahan, Desimal, dan Persen](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=256.9528958333333) - [07:25.318–09:32.246 · Membandingkan dan Mengurutkan](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=445.31804166666655) - [09:32.246–12:56.332 · Menjumlahkan dan Mengurangkan Pecahan](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=572.2464374999998) - [12:56.332–16:49 · Perkalian dan Pembagian Pecahan](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=776.3323958333332) ## Transcript ### [00:00 · Urutan Operasi Bilangan Cacah](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=0) Selamat datang. Kita akan berlatih operasi hitung bilangan cacah dan pecahan, supaya kamu siap menghadapi ujian. Mari mulai dari sebuah soal. Dua puluh, ditambah empat kali enam, dikurangi tiga puluh enam dibagi sembilan. Coba pikirkan sebentar. Bagian mana yang dikerjakan lebih dahulu? Ada dua cara yang mungkin kamu pikirkan. Cara pertama, kerjakan semuanya urut dari kiri ke kanan, seperti membaca. Dua puluh ditambah empat sama dengan dua puluh empat. Lalu dua puluh empat dikali enam menjadi seratus empat puluh empat. Kurangi tiga puluh enam, sisanya seratus delapan. Bagi sembilan, hasil akhirnya dua belas. Tetapi hasil dua belas itu salah. Dalam matematika, tambah dan kurang tidak boleh dikerjakan sebelum kali dan bagi. Cara kedua memakai aturan yang benar. Kali dan bagi dikerjakan lebih dahulu. Empat kali enam sama dengan dua puluh empat. Tiga puluh enam dibagi sembilan sama dengan empat. Baru sesudah itu kita tambah dan kurang: dua puluh ditambah dua puluh empat dikurangi empat, hasilnya empat puluh. Empat puluh, bukan dua belas. Jadi urutan mengerjakan operasi sungguh menentukan jawaban, dan karena itu kita perlu aturannya. Aturan urutan operasi punya tiga langkah, dan urutannya tidak boleh ditukar. Langkah pertama, kerjakan hitungan di dalam kurung. Apa pun isinya, kurung selalu didahulukan. Langkah kedua, kerjakan kali dan bagi. Keduanya setara, jadi yang lebih dahulu bertemu dari sebelah kiri dikerjakan lebih dahulu. Langkah ketiga, baru tambah dan kurang, juga dari kiri ke kanan. Supaya mudah diingat, urutan itu disingkat kabataku. Sekarang kita tulis pengerjaannya rapi, satu langkah satu baris. Tidak ada kurung di soal ini, jadi kita cari kali dan bagi lebih dahulu. Empat kali enam sama dengan dua puluh empat. Bagian itu kita ganti nilainya, bagian lain dibiarkan seperti semula. Berikutnya tiga puluh enam dibagi sembilan sama dengan empat. Sekarang tinggal tambah dan kurang, urut dari kiri. Dua puluh ditambah dua puluh empat sama dengan empat puluh empat. Lalu empat puluh empat dikurangi empat sama dengan empat puluh. Nilai empat puluh itulah jawaban yang benar untuk soal tadi. Bagaimana kalau ada tanda kurung? Perhatikan soal berikut: empat puluh lima kurang lima belas, di dalam kurung, dibagi enam, ditambah tujuh kali empat. Karena ada kurung, isinya dikerjakan paling dahulu. Empat puluh lima kurang lima belas sama dengan tiga puluh. Sesudah itu kali dan bagi. Tiga puluh dibagi enam sama dengan lima, dan tujuh kali empat sama dengan dua puluh delapan. Terakhir dijumlahkan: lima ditambah dua puluh delapan sama dengan tiga puluh tiga. Itu jawabannya. Tanpa kurung, hasilnya akan berbeda. Terakhir, satu strategi supaya berhitung lebih cepat. Berapa dua puluh lima kali empat puluh delapan? Angkanya besar, tetapi bisa dipecah. Empat puluh delapan sama dengan empat puluh ditambah delapan. Gambarnya seperti ini: sebuah persegi panjang bertinggi dua puluh lima, dengan lebar empat puluh pada bagian biru dan delapan pada bagian hijau. Luas bagian biru dua puluh lima kali empat puluh, yaitu seribu. Luas bagian hijau dua puluh lima kali delapan, yaitu dua ratus. Sekarang kedua luas itu dijumlahkan. Seribu ditambah dua ratus sama dengan seribu dua ratus. Jadi dua puluh lima kali empat puluh delapan sama dengan seribu dua ratus, tanpa perkalian bersusun sama sekali. Memecah bilangan seperti ini sangat berguna di ujian, karena bisa dihitung di kepala. Sekarang kita lanjut ke pecahan. ### [04:16.953 · Bentuk Pecahan, Desimal, dan Persen](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=256.9528958333333) Sekarang kita masuk ke pecahan. Satu nilai yang sama bisa ditulis dalam beberapa bentuk, dan pada soal ujian bentuknya sering dicampur. Bayangkan sebuah pita yang dibagi menjadi empat bagian sama besar. Tiga bagian di antaranya diwarnai hijau. Nilai bagian yang diwarnai adalah tiga per empat. Angka tiga di atas disebut pembilang, dan angka empat di bawah disebut penyebut. Bentuk kedua adalah desimal. Tiga per empat berarti tiga dibagi empat, dan hasil pembagiannya nol koma tujuh lima. Bentuk ketiga adalah persen. Persen artinya per seratus. Tiga per empat sama nilainya dengan tujuh puluh lima per seratus, jadi tujuh puluh lima persen. Ketiganya bernilai sama, hanya bentuknya berbeda. Bentuk seperti ini sangat sering muncul di soal ujian, jadi hafalkan hubungannya. Ada satu bentuk lagi yang sering keluar, yaitu pecahan campuran. Dua dan tiga per lima berarti dua utuh, ditambah tiga per lima. Pada garis bilangan, nilainya ada di antara dua dan tiga. Dari angka dua kita maju tiga langkah, dan satu langkah bernilai seperlima. Untuk mengubahnya menjadi pecahan biasa, kalikan bilangan bulatnya dengan penyebut, lalu tambahkan pembilangnya. Dua kali lima sama dengan sepuluh, ditambah tiga menjadi tiga belas. Penyebutnya tetap lima, sehingga hasilnya tiga belas per lima. Titik pada garis bilangan tidak berpindah, hanya namanya yang berganti. Sebaliknya, tujuh belas per empat bisa diubah menjadi pecahan campuran. Bagilah tujuh belas dengan empat: hasilnya empat, sisanya satu. Sisa satu menjadi pembilang, penyebutnya tetap empat. Jadi tujuh belas per empat sama dengan empat dan satu per empat. Bagaimana cara cepat mengubah bentuk? Kalau penyebutnya bisa dijadikan sepuluh atau seratus, pekerjaannya mudah. Ambil dua per lima. Kalikan pembilang dan penyebut dengan dua, maka penyebutnya menjadi sepuluh, dan pecahannya empat per sepuluh. Empat per sepuluh dibaca nol koma empat. Kalau dikalikan sepuluh lagi, kita mendapat empat puluh per seratus, artinya empat puluh persen. Beberapa nilai sebaiknya dihafal karena hampir selalu keluar. Nilai setengah sama dengan nol koma lima, atau lima puluh persen. Nilai seperempat sama dengan nol koma dua puluh lima, atau dua puluh lima persen. Nilai tiga per empat sama dengan nol koma tujuh lima. Nilai seperlima sama dengan dua puluh persen, dan sepersepuluh sama dengan sepuluh persen. Kalau ketiga bentuk itu sudah lancar, membandingkan pecahan menjadi jauh lebih mudah. Itu langkah kita berikutnya. ### [07:25.318 · Membandingkan dan Mengurutkan](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=445.31804166666655) Di ujian kamu sering diminta membandingkan dua pecahan. Mana yang lebih besar, tiga per lima atau dua per tiga? Dua pita ini sama panjang. Pita atas dibagi lima bagian, tiga di antaranya biru. Pita bawah dibagi tiga bagian, dua di antaranya hijau. Bagian berwarna pada pita bawah berakhir sedikit lebih ke kanan. Jadi dua per tiga tampak lebih besar. Tetapi mata bisa keliru, maka kita buktikan dengan hitungan. Caranya, samakan dulu penyebutnya. Kelipatan persekutuan terkecil dari lima dan tiga adalah lima belas. Tiga per lima dikalikan tiga, di atas dan di bawah, menjadi sembilan per lima belas. Dua per tiga dikalikan lima, di atas dan di bawah, menjadi sepuluh per lima belas. Sekarang penyebutnya sama, jadi cukup bandingkan pembilangnya: sembilan lebih kecil daripada sepuluh. Berarti tiga per lima memang lebih kecil daripada dua per tiga. Hitungan dan gambar memberi jawaban yang sama. Bagaimana kalau bentuknya bercampur? Misalnya tiga per lima, nol koma enam lima, dua per tiga, dan tujuh puluh persen. Cara paling aman adalah mengubah semuanya menjadi persen. Tiga per lima sama dengan enam puluh per seratus, yaitu enam puluh persen. Nol koma enam lima berarti enam puluh lima per seratus, yaitu enam puluh lima persen. Dua per tiga tidak bulat, tetapi nilainya kira kira enam puluh enam koma tujuh persen, sedikit di atas enam puluh lima. Dan tujuh puluh persen sudah berbentuk persen, letaknya paling kanan. Sekarang urutannya terlihat jelas pada garis bilangan, dari nilai terkecil sampai terbesar, dan itulah jawaban yang diminta soal. Jadi kalau bentuknya bercampur, jangan langsung dibandingkan. Ubah dulu ke bentuk yang sama, baru urutkan. Sesudah ini kita berhitung dengan pecahan. ### [09:32.246 · Menjumlahkan dan Mengurangkan Pecahan](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=572.2464374999998) Sekarang kita berhitung dengan pecahan, mulai dari penjumlahan. Keadaan paling mudah adalah kalau penyebutnya sudah sama. Sebuah kue dibagi menjadi tujuh bagian sama besar. Dua bagian diambil Ani, dan tiga bagian diambil Budi. Dua per tujuh ditambah tiga per tujuh. Karena penyebutnya sama, kita cukup menjumlahkan pembilangnya: dua ditambah tiga sama dengan lima. Penyebutnya tetap tujuh, jadi hasilnya lima per tujuh. Pada gambar, lima bagian dari tujuh sudah berwarna. Ingatlah, penyebutnya tidak ikut dijumlahkan. Hasil lima per empat belas itu keliru, karena tujuh ditambah tujuh tidak ada dalam aturan. Bagaimana kalau penyebutnya berbeda? Misalnya setengah ditambah sepertiga. Pita pertama dibagi dua, satu bagian diwarnai, itulah setengah. Pita kedua dibagi tiga, satu bagian diwarnai, itulah sepertiga. Keduanya tidak bisa langsung dijumlahkan, karena ukuran bagiannya tidak sama. Kita perlu satu ukuran yang cocok untuk keduanya. Kelipatan persekutuan terkecil dari dua dan tiga adalah enam. Jadi kita pakai pita yang dibagi enam. Setengah sama dengan tiga per enam, yaitu tiga kotak biru. Dan sepertiga sama dengan dua per enam, yaitu dua kotak hijau. Sekarang penyebutnya sudah sama, jadi pembilangnya tinggal dijumlahkan: tiga ditambah dua sama dengan lima. Hasilnya lima per enam, dan pada gambar memang ada lima kotak yang berwarna dari enam kotak. Sekarang pengurangan, dan kali ini dengan pecahan campuran. Tiga satu per empat dikurangi satu setengah. Langkah pertama, ubah keduanya menjadi pecahan biasa. Tiga satu per empat menjadi tiga belas per empat, dan satu setengah menjadi tiga per dua. Penyebutnya belum sama, jadi ubah tiga per dua menjadi enam per empat. Sekarang kurangkan pembilangnya: tiga belas dikurangi enam sama dengan tujuh, jadi hasilnya tujuh per empat. Tujuh per empat sama dengan satu tiga per empat. Perhatikan titiknya bergeser ke kiri, lalu berhenti tepat di satu tiga per empat. Kalau ada pecahan campuran, ubahlah dahulu ke pecahan biasa. Itu cara yang paling jarang membuat keliru. Sekarang satu soal cerita seperti di ujian. Ibu punya tiga per empat kilogram gula. Setengah kilogram dipakai untuk membuat kue. Berapa kilogram gula yang tersisa? Gula ibu digambarkan sebagai tiga dari empat bagian. Setengah kilogram sama dengan dua dari empat bagian, jadi dua bagian itu diambil. Tinggal satu bagian dari empat. Mari kita periksa dengan hitungan: tiga per empat dikurangi setengah, dan setengah sama dengan dua per empat. Tiga per empat dikurangi dua per empat sama dengan satu per empat. Jadi sisa gula ibu satu per empat kilogram, sesuai gambar. Untuk penjumlahan dan pengurangan, kuncinya satu: penyebut harus sama dahulu. Sesudah itu pekerjaannya mudah. Berikutnya kita belajar perkalian dan pembagian pecahan. ### [12:56.332 · Perkalian dan Pembagian Pecahan](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=776.3323958333332) Sekarang perkalian pecahan, dan ini justru lebih mudah daripada penjumlahan, karena penyebutnya tidak perlu disamakan. Bayangkan sebuah persegi. Sisi datarnya dibagi empat dan sisi tegaknya dibagi tiga, sehingga ada dua belas kotak kecil. Tiga per empat diambil ke arah datar, dan dua per tiga ke arah tegak. Daerah yang bertumpang berisi enam kotak. Enam dari dua belas kotak. Aturannya memang begitu: pembilang dikali pembilang, dan penyebut dikali penyebut. Tiga kali dua sama dengan enam, empat kali tiga sama dengan dua belas. Jadi hasilnya enam per dua belas. Enam per dua belas masih bisa disederhanakan: bagi keduanya dengan enam, hasilnya setengah. Aturan ini singkat, dan berlaku untuk semua perkalian pecahan. Perkalian pecahan dengan bilangan asli caranya sama. Dari dua puluh soal, tiga per empat bagian sudah dikerjakan. Berapa soal itu? Tulis dua puluh sebagai dua puluh per satu, lalu kalikan seperti biasa. Tiga kali dua puluh sama dengan enam puluh, dan empat kali satu sama dengan empat. Enam puluh per empat sama dengan lima belas. Jadi lima belas soal sudah dikerjakan, dan pada garis bilangan letaknya di sini, tiga per empat dari dua puluh. Sekarang pembagian, bagian yang paling sering ditanyakan. Pertanyaannya begini: ada berapa bagian setengah di dalam tiga per empat? Pita atas menunjukkan tiga per empat. Kotak hijau di bawahnya panjangnya setengah pita utuh. Kotak hijau pertama masuk seluruhnya. Kotak kedua hanya terisi separuh. Jadi jawabannya satu setengah. Dengan hitungan, membagi dengan setengah sama dengan mengalikan dengan dua per satu, yaitu kebalikannya. Tiga per empat kali dua per satu sama dengan enam per empat, dan enam per empat sama dengan satu setengah, tepat seperti gambar. Kalau pembaginya bilangan asli, caranya juga sama. Dua per tiga dibagi empat berarti dua per tiga kali seperempat, hasilnya dua per dua belas, atau seperenam. Ingat kalimatnya: bagi berubah menjadi kali, dan pecahan pembaginya dibalik. Satu soal cerita lagi. Pita sepanjang empat per lima meter dipotong menjadi bagian sepanjang satu per sepuluh meter. Berapa potong yang didapat? Ini pembagian: empat per lima dibagi satu per sepuluh. Ubahlah menjadi perkalian dengan kebalikannya, yaitu sepuluh per satu. Empat kali sepuluh sama dengan empat puluh, dan lima kali satu sama dengan lima. Empat puluh per lima sama dengan delapan. Jadi didapat delapan potong pita. Hitung kotaknya: satu, dua, tiga, empat, lima, enam, tujuh, delapan. Delapan potong. Kalau soalnya menanyakan berapa banyak potongan, itu tandanya pembagian, bukan perkalian. Mari kita ingat kembali semuanya. Ada lima hal penting. Satu, pada bilangan cacah: kurung dahulu, lalu kali dan bagi, baru tambah dan kurang. Dua, satu nilai bisa ditulis sebagai pecahan, desimal, atau persen. Tiga, untuk membandingkan pecahan, samakan penyebutnya atau ubah ke persen. Empat, untuk tambah dan kurang pecahan, samakan penyebutnya lebih dahulu. Lima, untuk kali, pembilang dikali pembilang, dan untuk bagi, kalikan dengan kebalikannya. Kerjakan setiap soal langkah demi langkah, dan tulis barisnya dengan rapi. Kalau kamu sudah terbiasa, soal ujian akan terasa jauh lebih ringan. Semangat berlatih! ## About Academa, Inc. Academa makes technical knowledge easier to understand through visual lectures and lets learners request new lecture videos on the topics they need. ## Complete audiovisual record Immutable source: [semantic.json](https://academa.ai/media/l/01M1JA4VKK6H0JA7FVN0PT5VZ7/0/semantic.json) Record version: 1. Render attempt: 0. ### How to read this timeline Each scene owns its object identifiers. A beat's board is the complete board when listed, empty when marked empty, and unchanged from the nearest earlier listed board in the same scene when marked unchanged. Action times are absolute positions in the published video. ### Scene 1: [Urutan Operasi Bilangan Cacah](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=0) Span: 00:00–04:16.953 (0s–256.9528958333333s). #### Objects - aturan: a Block \[text\] that says "Kerjakan hitungan di dalam kurung lebih dahulu. Kerjakan kali dan bagi, urut dari kiri ke kanan. Kerjakan tambah dan kurang, urut dari kiri ke kanan." - cap\_aturan: a Tex \[text\] that says "Pakai aturan" - cap\_kiri: a Tex \[text\] that says "Urut dari kiri" - catatan: a Text \[text\] that says "Kabataku: kali, bagi, tambah, kurang. Kurung selalu paling dahulu." - cepat: a Derivation \[text\] that says "$25 times 48 &= 25 times (40 + 8) \\ &= 1000 + 200 \\ &= 1200$" - head\_aturan: a Heading that says "Aturan Kabataku" - head\_cepat: a Heading that says "Strategi Berhitung Cepat" - head\_dua: a Heading that says "Dua Cara, Dua Hasil" - head\_kerja: a Heading that says "Mengerjakan Soalnya" - head\_kurung: a Heading that says "Kalau Ada Tanda Kurung" - kerja: a Derivation \[text\] that says "$&= 20 + 24 - 36 : 9 \\ &= 20 + 24 - 4 \\ &= 44 - 4 \\ &= 40$" - kotak: a Figure (x\_range=(0.0, 5.6), y\_range=(0.0, 3.8), aspect=(5.6, 3.8)) - kurung: a Derivation \[text\] that says "$&= 30 : 6 + 7 times 4 \\ &= 5 + 28 \\ &= 33$" - kurung\_soal: a Math \[text\] that says "$(45 - 15) : 6 + 7 times 4 = ?$" - luas\_biru: a Math \[text\] that says "$25 times 40 = 1000$" drawn in kotak - luas\_hijau: a Math \[text\] that says "$25 times 8 = 200$" drawn in kotak - petak\_biru: a Polygon \[blue\] drawn in kotak (vertices=((0.6, 0.5), (4.6, 0.5), (4.6, 3.0), (0.6, 3.0)), fill\_opacity=0.25, side\_labels=('40', None, None, '25')) - petak\_hijau: a Polygon \[green\] drawn in kotak (vertices=((4.6, 0.5), (5.4, 0.5), (5.4, 3.0), (4.6, 3.0)), fill\_opacity=0.25, side\_labels=('8', None, None, None)) - s0: a Math \[gray\] that says "$20 + 4 = 24$" - s1: a Math \[gray\] that says "$24 times 6 = 144$" - s2: a Math \[gray\] that says "$144 - 36 = 108$" - s3: a Math \[gray\] that says "$108 : 9 = 12$" - soal: a Panel that says "Berapa hasil dari $20 + 4 times 6 - 36 : 9$ ?" - soal\_math: a Math \[text\] that says "$20 + 4 times 6 - 36 : 9 = ?$" - t0: a Math \[text\] that says "$4 times 6 = 24$" - t1: a Math \[text\] that says "$36 : 9 = 4$" - t2: a Math \[text\] that says "$20 + 24 - 4 = 40$" #### Beats ##### [00:00](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=0) Narration: Selamat datang. Kita akan berlatih operasi hitung bilangan cacah dan pecahan, supaya kamu siap menghadapi ujian. Mari mulai dari sebuah soal. Board: Empty. Actions: - [00:8.452](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=8.452): soal is shown on the screen, written out. ##### [00:9.713](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=9.7135) Narration: Dua puluh, ditambah empat kali enam, dikurangi tiga puluh enam dibagi sembilan. Coba pikirkan sebentar. Bagian mana yang dikerjakan lebih dahulu? Board: soal — a Panel that says "Berapa hasil dari $20 + 4 times 6 - 36 : 9$ ?" Actions: - [00:19.71](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=19.71): soal is hidden from the screen — left the board. ##### [00:20.91](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=20.909999999999997) Narration: Ada dua cara yang mungkin kamu pikirkan. Cara pertama, kerjakan semuanya urut dari kiri ke kanan, seperti membaca. Dua puluh ditambah empat sama dengan dua puluh empat. Board: Empty. Actions: - [00:20.91](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=20.909999999999997): head\_dua is shown on the screen, written out. - [00:23.917](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=23.916999999999998): cap\_kiri is shown on the screen, written out. - [00:31.022](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=31.022): s0 is shown on the screen, written out. ##### [00:33.387](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=33.387) Narration: Lalu dua puluh empat dikali enam menjadi seratus empat puluh empat. Kurangi tiga puluh enam, sisanya seratus delapan. Bagi sembilan, hasil akhirnya dua belas. Board: cap\_kiri — a Tex \[text\] that says "Urut dari kiri"; s0 — a Math \[gray\] that says "$20 + 4 = 24$"; head\_dua — a Heading that says "Dua Cara, Dua Hasil" Actions: - [00:34.943](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=34.943): s1 is shown on the screen, written out. - [00:40.783](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=40.783): s2 is shown on the screen, written out. - [00:42.327](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=42.327): s3 is shown on the screen, written out. ##### [00:45.585](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=45.585499999999996) Narration: Tetapi hasil dua belas itu salah. Dalam matematika, tambah dan kurang tidak boleh dikerjakan sebelum kali dan bagi. Board: cap\_kiri — a Tex \[text\] that says "Urut dari kiri"; s0 — a Math \[gray\] that says "$20 + 4 = 24$"; s1 — a Math \[gray\] that says "$24 times 6 = 144$"; s2 — a Math \[gray\] that says "$144 - 36 = 108$"; s3 — a Math \[gray\] that says "$108 : 9 = 12$"; head\_dua — a Heading that says "Dua Cara, Dua Hasil" Actions: - [00:47.536](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=47.535999999999994): s3 (the "12" part) is struck through — it is ruled out. ##### [00:54.069](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=54.068999999999996) Narration: Cara kedua memakai aturan yang benar. Kali dan bagi dikerjakan lebih dahulu. Empat kali enam sama dengan dua puluh empat. Board: Unchanged from the preceding beat in this scene. Actions: - [00:54.626](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=54.626): cap\_aturan is shown on the screen, written out. - [01:1.348](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=61.348): t0 is shown on the screen, written out. ##### [01:3.231](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=63.2315) Narration: Tiga puluh enam dibagi sembilan sama dengan empat. Baru sesudah itu kita tambah dan kurang: dua puluh ditambah dua puluh empat dikurangi empat, hasilnya empat puluh. Board: cap\_kiri — a Tex \[text\] that says "Urut dari kiri"; s0 — a Math \[gray\] that says "$20 + 4 = 24$"; s1 — a Math \[gray\] that says "$24 times 6 = 144$"; s2 — a Math \[gray\] that says "$144 - 36 = 108$"; s3 — a Math \[gray\] that says "$108 : 9 = 12$"; cap\_aturan — a Tex \[text\] that says "Pakai aturan"; t0 — a Math \[text\] that says "$4 times 6 = 24$"; head\_dua — a Heading that says "Dua Cara, Dua Hasil" Actions: - [01:4.851](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=64.851): t1 is shown on the screen, written out. - [01:13.407](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=73.40700000000001): t2 is shown on the screen, written out. ##### [01:15.609](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=75.6095) Narration: Empat puluh, bukan dua belas. Jadi urutan mengerjakan operasi sungguh menentukan jawaban, dan karena itu kita perlu aturannya. Board: cap\_kiri — a Tex \[text\] that says "Urut dari kiri"; s0 — a Math \[gray\] that says "$20 + 4 = 24$"; s1 — a Math \[gray\] that says "$24 times 6 = 144$"; s2 — a Math \[gray\] that says "$144 - 36 = 108$"; s3 — a Math \[gray\] that says "$108 : 9 = 12$"; cap\_aturan — a Tex \[text\] that says "Pakai aturan"; t0 — a Math \[text\] that says "$4 times 6 = 24$"; t1 — a Math \[text\] that says "$36 : 9 = 4$"; t2 — a Math \[text\] that says "$20 + 24 - 4 = 40$"; head\_dua — a Heading that says "Dua Cara, Dua Hasil" Actions: - [01:16.863](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=76.863): A box is drawn around t2. - [01:24.862](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=84.8625): cap\_aturan is hidden from the screen — left the board. - [01:24.862](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=84.8625): cap\_kiri is hidden from the screen — left the board. - [01:24.862](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=84.8625): head\_dua is hidden from the screen — left the board. - [01:24.862](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=84.8625): s0 is hidden from the screen — left the board. - [01:24.862](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=84.8625): s1 is hidden from the screen — left the board. - [01:24.862](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=84.8625): s2 is hidden from the screen — left the board. - [01:24.862](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=84.8625): s3 is hidden from the screen — left the board. - [01:24.862](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=84.8625): t0 is hidden from the screen — left the board. - [01:24.862](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=84.8625): t1 is hidden from the screen — left the board. - [01:24.862](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=84.8625): t2 is hidden from the screen — left the board. ##### [01:26.063](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=86.0625) Narration: Aturan urutan operasi punya tiga langkah, dan urutannya tidak boleh ditukar. Board: Empty. Actions: - [01:26.063](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=86.0625): head\_aturan is shown on the screen, written out. - [01:28.141](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=88.141): aturan is shown on the screen, written out. ##### [01:32.293](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=92.2935) Narration: Langkah pertama, kerjakan hitungan di dalam kurung. Apa pun isinya, kurung selalu didahulukan. Board: aturan — a Block \[text\] that says "Kerjakan hitungan di dalam kurung lebih dahulu. Kerjakan kali dan bagi, urut dari kiri ke kanan. Kerjakan tambah dan kurang, urut dari kiri ke kanan."; head\_aturan — a Heading that says "Aturan Kabataku" Actions: - [01:35.324](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=95.324): aturan (the "di dalam kurung" part) is emphasized. ##### [01:40.242](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=100.24249999999999) Narration: Langkah kedua, kerjakan kali dan bagi. Keduanya setara, jadi yang lebih dahulu bertemu dari sebelah kiri dikerjakan lebih dahulu. Board: Unchanged from the preceding beat in this scene. Actions: - [01:40.962](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=100.96199999999999): aturan (the "di dalam kurung" part) is no longer emphasized. - [01:40.962](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=100.96199999999999): aturan (the "kali dan bagi" part) is emphasized. ##### [01:49.434](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=109.43449999999999) Narration: Langkah ketiga, baru tambah dan kurang, juga dari kiri ke kanan. Supaya mudah diingat, urutan itu disingkat kabataku. Board: Unchanged from the preceding beat in this scene. Actions: - [01:50.073](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=110.073): aturan (the "kali dan bagi" part) is no longer emphasized. - [01:50.073](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=110.073): aturan (the "tambah dan kurang" part) is emphasized. - [01:54.125](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=114.12499999999999): catatan is shown on the screen, written out. - [01:55.483](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=115.48299999999999): aturan (the "tambah dan kurang" part) is no longer emphasized. - [01:57.746](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=117.74649999999998): aturan is hidden from the screen — left the board. - [01:57.746](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=117.74649999999998): catatan is hidden from the screen — left the board. - [01:57.746](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=117.74649999999998): head\_aturan is hidden from the screen — left the board. ##### [01:58.946](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=118.94649999999999) Narration: Sekarang kita tulis pengerjaannya rapi, satu langkah satu baris. Tidak ada kurung di soal ini, jadi kita cari kali dan bagi lebih dahulu. Board: Empty. Actions: - [01:58.946](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=118.94649999999999): head\_kerja is shown on the screen, written out. - [02:0.746](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=120.746): soal\_math is shown on the screen, written out. ##### [02:8.318](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=128.31799999999998) Narration: Empat kali enam sama dengan dua puluh empat. Bagian itu kita ganti nilainya, bagian lain dibiarkan seperti semula. Board: soal\_math — a Math \[text\] that says "$20 + 4 times 6 - 36 : 9 = ?$"; head\_kerja — a Heading that says "Mengerjakan Soalnya" Actions: - [02:12.515](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=132.515): kerja is shown on the screen, written out. ##### [02:16.586](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=136.58599999999998) Narration: Berikutnya tiga puluh enam dibagi sembilan sama dengan empat. Board: Unchanged from the preceding beat in this scene. Actions: - [02:19.535](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=139.535): kerja is shown on the screen, written out. ##### [02:20.738](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=140.7385) Narration: Sekarang tinggal tambah dan kurang, urut dari kiri. Dua puluh ditambah dua puluh empat sama dengan empat puluh empat. Board: Unchanged from the preceding beat in this scene. Actions: - [02:25.87](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=145.87): kerja is shown on the screen, written out. ##### [02:28.264](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=148.2645) Narration: Lalu empat puluh empat dikurangi empat sama dengan empat puluh. Nilai empat puluh itulah jawaban yang benar untuk soal tadi. Board: Unchanged from the preceding beat in this scene. Actions: - [02:29.593](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=149.59300000000002): kerja is shown on the screen, written out. - [02:33.343](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=153.34300000000002): A box is drawn around kerja. - [02:35.654](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=155.6535): head\_kerja is hidden from the screen — left the board. - [02:35.654](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=155.6535): kerja is hidden from the screen — left the board. - [02:35.654](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=155.6535): soal\_math is hidden from the screen — left the board. ##### [02:36.853](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=156.8535) Narration: Bagaimana kalau ada tanda kurung? Perhatikan soal berikut: empat puluh lima kurang lima belas, di dalam kurung, dibagi enam, ditambah tujuh kali empat. Board: Empty. Actions: - [02:36.853](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=156.8535): head\_kurung is shown on the screen, written out. - [02:40.453](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=160.453): kurung\_soal is shown on the screen, written out. ##### [02:48.959](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=168.9595) Narration: Karena ada kurung, isinya dikerjakan paling dahulu. Empat puluh lima kurang lima belas sama dengan tiga puluh. Board: kurung\_soal — a Math \[text\] that says "$(45 - 15) : 6 + 7 times 4 = ?$"; head\_kurung — a Heading that says "Kalau Ada Tanda Kurung" Actions: - [02:54.393](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=174.393): kurung is shown on the screen, written out. ##### [02:56.548](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=176.5485) Narration: Sesudah itu kali dan bagi. Tiga puluh dibagi enam sama dengan lima, dan tujuh kali empat sama dengan dua puluh delapan. Board: Unchanged from the preceding beat in this scene. Actions: - [03:3.898](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=183.898): kurung is shown on the screen, written out. ##### [03:5.333](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=185.3335) Narration: Terakhir dijumlahkan: lima ditambah dua puluh delapan sama dengan tiga puluh tiga. Itu jawabannya. Tanpa kurung, hasilnya akan berbeda. Board: Unchanged from the preceding beat in this scene. Actions: - [03:10.163](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=190.163): kurung is shown on the screen, written out. - [03:13.948](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=193.948): A box is drawn around kurung. - [03:15.666](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=195.66649999999998): head\_kurung is hidden from the screen — left the board. - [03:15.666](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=195.66649999999998): kurung is hidden from the screen — left the board. - [03:15.666](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=195.66649999999998): kurung\_soal is hidden from the screen — left the board. ##### [03:16.866](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=196.86649999999997) Narration: Terakhir, satu strategi supaya berhitung lebih cepat. Berapa dua puluh lima kali empat puluh delapan? Angkanya besar, tetapi bisa dipecah. Board: Empty. Actions: - [03:16.866](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=196.86649999999997): head\_cepat is shown on the screen, written out. - [03:26.387](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=206.387): cepat is shown on the screen, written out. ##### [03:27.927](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=207.92699999999996) Narration: Empat puluh delapan sama dengan empat puluh ditambah delapan. Gambarnya seperti ini: sebuah persegi panjang bertinggi dua puluh lima, dengan lebar empat puluh pada bagian biru dan delapan pada bagian hijau. Board: head\_cepat — a Heading that says "Strategi Berhitung Cepat" Actions: - [03:32.652](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=212.652): kotak is shown on the screen, written out. - [03:39.212](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=219.212): petak\_biru is shown on the screen, written out. - [03:40.988](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=220.988): petak\_hijau is shown on the screen, written out. ##### [03:42.447](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=222.44699999999997) Narration: Luas bagian biru dua puluh lima kali empat puluh, yaitu seribu. Board: kotak — a Figure (x\_range=(0.0, 5.6), y\_range=(0.0, 3.8), aspect=(5.6, 3.8)); head\_cepat — a Heading that says "Strategi Berhitung Cepat"; petak\_biru — a Polygon \[blue\] drawn in kotak (vertices=((0.6, 0.5), (4.6, 0.5), (4.6, 3.0), (0.6, 3.0)), fill\_opacity=0.25, side\_labels=('40', None, None, '25')); petak\_hijau — a Polygon \[green\] drawn in kotak (vertices=((4.6, 0.5), (5.4, 0.5), (5.4, 3.0), (4.6, 3.0)), fill\_opacity=0.25, side\_labels=('8', None, None, None)) Actions: - [03:46.522](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=226.52200000000002): luas\_biru is shown on the screen, written out. ##### [03:47.958](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=227.95799999999997) Narration: Luas bagian hijau dua puluh lima kali delapan, yaitu dua ratus. Sekarang kedua luas itu dijumlahkan. Board: kotak — a Figure (x\_range=(0.0, 5.6), y\_range=(0.0, 3.8), aspect=(5.6, 3.8)); head\_cepat — a Heading that says "Strategi Berhitung Cepat"; petak\_biru — a Polygon \[blue\] drawn in kotak (vertices=((0.6, 0.5), (4.6, 0.5), (4.6, 3.0), (0.6, 3.0)), fill\_opacity=0.25, side\_labels=('40', None, None, '25')); petak\_hijau — a Polygon \[green\] drawn in kotak (vertices=((4.6, 0.5), (5.4, 0.5), (5.4, 3.0), (4.6, 3.0)), fill\_opacity=0.25, side\_labels=('8', None, None, None)); luas\_biru — a Math \[text\] that says "$25 times 40 = 1000$" drawn in kotak Actions: - [03:51.615](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=231.615): luas\_hijau is shown on the screen, written out. - [03:54.111](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=234.11100000000002): cepat is shown on the screen, written out. ##### [03:55.907](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=235.90749999999997) Narration: Seribu ditambah dua ratus sama dengan seribu dua ratus. Jadi dua puluh lima kali empat puluh delapan sama dengan seribu dua ratus, tanpa perkalian bersusun sama sekali. Board: kotak — a Figure (x\_range=(0.0, 5.6), y\_range=(0.0, 3.8), aspect=(5.6, 3.8)); head\_cepat — a Heading that says "Strategi Berhitung Cepat"; petak\_biru — a Polygon \[blue\] drawn in kotak (vertices=((0.6, 0.5), (4.6, 0.5), (4.6, 3.0), (0.6, 3.0)), fill\_opacity=0.25, side\_labels=('40', None, None, '25')); petak\_hijau — a Polygon \[green\] drawn in kotak (vertices=((4.6, 0.5), (5.4, 0.5), (5.4, 3.0), (4.6, 3.0)), fill\_opacity=0.25, side\_labels=('8', None, None, None)); luas\_biru — a Math \[text\] that says "$25 times 40 = 1000$" drawn in kotak; luas\_hijau — a Math \[text\] that says "$25 times 8 = 200$" drawn in kotak Actions: - [03:57.683](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=237.68300000000002): cepat is shown on the screen, written out. - [04:4.394](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=244.394): A box is drawn around cepat. ##### [04:7.548](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=247.54799999999997) Narration: Memecah bilangan seperti ini sangat berguna di ujian, karena bisa dihitung di kepala. Sekarang kita lanjut ke pecahan. Board: Unchanged from the preceding beat in this scene. Actions: - [04:8.953](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=248.953): petak\_biru is indicated — a transient flash. - [04:8.953](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=248.953): petak\_hijau is indicated — a transient flash. - [04:15.911](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=255.91122916666663): cepat is hidden from the screen — left the board. - [04:15.911](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=255.91122916666663): head\_cepat is hidden from the screen — left the board. - [04:15.911](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=255.91122916666663): kotak is hidden from the screen — left the board. - [04:15.911](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=255.91122916666663): petak\_biru is hidden from the screen — kotak left the board. - [04:15.911](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=255.91122916666663): petak\_hijau is hidden from the screen — kotak left the board. - [04:15.911](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=255.91122916666663): luas\_biru is hidden from the screen — kotak left the board. - [04:15.911](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=255.91122916666663): luas\_hijau is hidden from the screen — kotak left the board. ### Scene 2: [Bentuk Pecahan, Desimal, dan Persen](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=256.9528958333333) Span: 04:16.953–07:25.318 (256.9528958333333s–445.31804166666655s). #### Objects - biasa: a Derivation \[text\] that says "$17 : 4 &= 4 thin upright("sisa") thin 1 \\ frac(17, 4) &= 4 frac(1, 4)$" - campuran: a Derivation \[text\] that says "$2 frac(3, 5) &= frac(2 times 5 + 3, 5) \\ &= frac(13, 5)$" - f1: a Math \[text\] that says "$frac(3, 4)$" - f2: a Math \[text\] that says "$3 : 4 = upright("0,75")$" - f3: a Math \[text\] that says "$frac(3, 4) = frac(75, 100) = 75%$" - garis: a NumberLine (x\_range=(0.0, 3.0), ticks\_every=0.2) - head\_campuran: a Heading that says "Pecahan Campuran" - head\_ubah: a Heading that says "Mengubah Bentuk dengan Cepat" - head\_wajah: a Heading that says "Satu Nilai, Tiga Bentuk" - papan: a Figure (x\_range=(0.0, 4.0), y\_range=(-0.2, 1.6), aspect=(4.0, 1.8)) - petak: a Polygon \[green\] drawn in papan (vertices=((0, 0.2), (1, 0.2), (1, 1.2), (0, 1.2)), fill\_opacity=0.45) - petak\_2: a Polygon \[green\] drawn in papan (vertices=((1, 0.2), (2, 0.2), (2, 1.2), (1, 1.2)), fill\_opacity=0.45) - petak\_3: a Polygon \[green\] drawn in papan (vertices=((2, 0.2), (3, 0.2), (3, 1.2), (2, 1.2)), fill\_opacity=0.45) - petak\_4: a Polygon \[gray\] drawn in papan (vertices=((3, 0.2), (4, 0.2), (4, 1.2), (3, 1.2)), filled=False, fill\_opacity=0.45) - ringkas: a Math \[text\] that says "$frac(3, 4) = upright("0,75") = 75%$" - tabel: a Table \[text\] that says "Pecahan Desimal Persen $frac(1, 2)$ $upright("0,5")$ $50%$ $frac(1, 4)$ $upright("0,25")$ $25%$ $frac(3, 4)$ $upright("0,75")$ $75%$ $frac(1, 5)$ $upright("0,2")$ $20%$ $frac(1, 10)$ $upright("0,1")$ $10%$" (rows=(('Pecahan', 'Desimal', 'Persen'), ('$frac(1, 2)$', '$upright("…, header=True) - tanda: a Point \[gray\] labelled "0" drawn in garis - tanda\_2: a Point \[gray\] labelled "1" drawn in garis (location=(1.0, 0.0)) - tanda\_3: a Point \[gray\] labelled "2" drawn in garis (location=(2.0, 0.0)) - tanda\_4: a Point \[gray\] labelled "3" drawn in garis (location=(3.0, 0.0)) - titik: a Point \[yellow\] labelled "2 frac(3, 5)" drawn in garis (location=(2.6, 0.0)) - ubah: a Derivation \[text\] that says "$frac(2, 5) &= frac(2 times 2, 5 times 2) = frac(4, 10) \\ &= upright("0,4") \\ &= frac(40, 100) = 40%$" #### Beats ##### [04:16.953](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=256.9528958333333) Narration: Sekarang kita masuk ke pecahan. Satu nilai yang sama bisa ditulis dalam beberapa bentuk, dan pada soal ujian bentuknya sering dicampur. Board: Empty. Actions: - [04:16.953](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=256.9528958333333): head\_wajah is shown on the screen, written out. - [04:16.953](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=256.9528958333333): papan is shown on the screen, written out. ##### [04:26.794](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=266.7943958333333) Narration: Bayangkan sebuah pita yang dibagi menjadi empat bagian sama besar. Tiga bagian di antaranya diwarnai hijau. Board: papan — a Figure (x\_range=(0.0, 4.0), y\_range=(-0.2, 1.6), aspect=(4.0, 1.8)); head\_wajah — a Heading that says "Satu Nilai, Tiga Bentuk" Actions: - [04:29.581](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=269.5808958333333): petak is shown on the screen, written out. - [04:29.721](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=269.72116117860185): petak\_2 is shown on the screen, written out. - [04:29.861](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=269.86142652387036): petak\_3 is shown on the screen, written out. - [04:30.026](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=270.0261567028985): petak\_4 is shown on the screen, written out. - [04:34.097](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=274.0968958333333): petak is indicated — a transient flash. - [04:34.097](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=274.0968958333333): petak\_2 is indicated — a transient flash. - [04:34.097](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=274.0968958333333): petak\_3 is indicated — a transient flash. ##### [04:35.66](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=275.66039583333327) Narration: Nilai bagian yang diwarnai adalah tiga per empat. Angka tiga di atas disebut pembilang, dan angka empat di bawah disebut penyebut. Board: papan — a Figure (x\_range=(0.0, 4.0), y\_range=(-0.2, 1.6), aspect=(4.0, 1.8)); head\_wajah — a Heading that says "Satu Nilai, Tiga Bentuk"; petak — a Polygon \[green\] drawn in papan (vertices=((0, 0.2), (1, 0.2), (1, 1.2), (0, 1.2)), fill\_opacity=0.45); petak\_2 — a Polygon \[green\] drawn in papan (vertices=((1, 0.2), (2, 0.2), (2, 1.2), (1, 1.2)), fill\_opacity=0.45); petak\_3 — a Polygon \[green\] drawn in papan (vertices=((2, 0.2), (3, 0.2), (3, 1.2), (2, 1.2)), fill\_opacity=0.45); petak\_4 — a Polygon \[gray\] drawn in papan (vertices=((3, 0.2), (4, 0.2), (4, 1.2), (3, 1.2)), filled=False, fill\_opacity=0.45) Actions: - [04:37.924](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=277.9238958333333): papan moves to a new place on the board. - [04:37.924](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=277.9238958333333): f1 is shown on the screen, written out. - [04:41.047](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=281.0468958333333): f1 (the "3" part) is indicated — a transient flash. - [04:43.718](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=283.7178958333333): f1 (the "4" part) is indicated — a transient flash. ##### [04:45.258](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=285.2578958333333) Narration: Bentuk kedua adalah desimal. Tiga per empat berarti tiga dibagi empat, dan hasil pembagiannya nol koma tujuh lima. Board: f1 — a Math \[text\] that says "$frac(3, 4)$"; papan — a Figure (x\_range=(0.0, 4.0), y\_range=(-0.2, 1.6), aspect=(4.0, 1.8)); head\_wajah — a Heading that says "Satu Nilai, Tiga Bentuk"; petak — a Polygon \[green\] drawn in papan (vertices=((0, 0.2), (1, 0.2), (1, 1.2), (0, 1.2)), fill\_opacity=0.45); petak\_2 — a Polygon \[green\] drawn in papan (vertices=((1, 0.2), (2, 0.2), (2, 1.2), (1, 1.2)), fill\_opacity=0.45); petak\_3 — a Polygon \[green\] drawn in papan (vertices=((2, 0.2), (3, 0.2), (3, 1.2), (2, 1.2)), fill\_opacity=0.45); petak\_4 — a Polygon \[gray\] drawn in papan (vertices=((3, 0.2), (4, 0.2), (4, 1.2), (3, 1.2)), filled=False, fill\_opacity=0.45) Actions: - [04:49.635](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=289.6348958333333): f2 is shown on the screen, written out. ##### [04:54.821](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=294.8208958333333) Narration: Bentuk ketiga adalah persen. Persen artinya per seratus. Tiga per empat sama nilainya dengan tujuh puluh lima per seratus, jadi tujuh puluh lima persen. Board: f1 — a Math \[text\] that says "$frac(3, 4)$"; f2 — a Math \[text\] that says "$3 : 4 = upright("0,75")$"; papan — a Figure (x\_range=(0.0, 4.0), y\_range=(-0.2, 1.6), aspect=(4.0, 1.8)); head\_wajah — a Heading that says "Satu Nilai, Tiga Bentuk"; petak — a Polygon \[green\] drawn in papan (vertices=((0, 0.2), (1, 0.2), (1, 1.2), (0, 1.2)), fill\_opacity=0.45); petak\_2 — a Polygon \[green\] drawn in papan (vertices=((1, 0.2), (2, 0.2), (2, 1.2), (1, 1.2)), fill\_opacity=0.45); petak\_3 — a Polygon \[green\] drawn in papan (vertices=((2, 0.2), (3, 0.2), (3, 1.2), (2, 1.2)), fill\_opacity=0.45); petak\_4 — a Polygon \[gray\] drawn in papan (vertices=((3, 0.2), (4, 0.2), (4, 1.2), (3, 1.2)), filled=False, fill\_opacity=0.45) Actions: - [04:58.014](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=298.01389583333327): f3 is shown on the screen, written out. - [05:4.655](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=304.6548958333333): f3 (the "75%" part) is indicated — a transient flash. ##### [05:6.287](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=306.2873958333333) Narration: Ketiganya bernilai sama, hanya bentuknya berbeda. Bentuk seperti ini sangat sering muncul di soal ujian, jadi hafalkan hubungannya. Board: f1 — a Math \[text\] that says "$frac(3, 4)$"; f2 — a Math \[text\] that says "$3 : 4 = upright("0,75")$"; f3 — a Math \[text\] that says "$frac(3, 4) = frac(75, 100) = 75%$"; papan — a Figure (x\_range=(0.0, 4.0), y\_range=(-0.2, 1.6), aspect=(4.0, 1.8)); head\_wajah — a Heading that says "Satu Nilai, Tiga Bentuk"; petak — a Polygon \[green\] drawn in papan (vertices=((0, 0.2), (1, 0.2), (1, 1.2), (0, 1.2)), fill\_opacity=0.45); petak\_2 — a Polygon \[green\] drawn in papan (vertices=((1, 0.2), (2, 0.2), (2, 1.2), (1, 1.2)), fill\_opacity=0.45); petak\_3 — a Polygon \[green\] drawn in papan (vertices=((2, 0.2), (3, 0.2), (3, 1.2), (2, 1.2)), fill\_opacity=0.45); petak\_4 — a Polygon \[gray\] drawn in papan (vertices=((3, 0.2), (4, 0.2), (4, 1.2), (3, 1.2)), filled=False, fill\_opacity=0.45) Actions: - [05:8.773](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=308.7728958333333): ringkas is shown on the screen, written out. - [05:12.499](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=312.4988958333333): A box is drawn around ringkas. - [05:15.332](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=315.3323958333333): f1 is hidden from the screen — left the board. - [05:15.332](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=315.3323958333333): f2 is hidden from the screen — left the board. - [05:15.332](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=315.3323958333333): f3 is hidden from the screen — left the board. - [05:15.332](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=315.3323958333333): head\_wajah is hidden from the screen — left the board. - [05:15.332](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=315.3323958333333): papan is hidden from the screen — left the board. - [05:15.332](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=315.3323958333333): petak is hidden from the screen — papan left the board. - [05:15.332](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=315.3323958333333): petak\_2 is hidden from the screen — papan left the board. - [05:15.332](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=315.3323958333333): petak\_3 is hidden from the screen — papan left the board. - [05:15.332](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=315.3323958333333): petak\_4 is hidden from the screen — papan left the board. - [05:15.332](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=315.3323958333333): ringkas is hidden from the screen — left the board. ##### [05:16.532](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=316.5323958333333) Narration: Ada satu bentuk lagi yang sering keluar, yaitu pecahan campuran. Dua dan tiga per lima berarti dua utuh, ditambah tiga per lima. Board: Empty. Actions: - [05:16.532](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=316.5323958333333): head\_campuran is shown on the screen, written out. - [05:16.532](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=316.5323958333333): garis is shown on the screen, written out. - [05:20.015](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=320.0148958333333): tanda is shown on the screen, written out. - [05:20.364](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=320.36368256065464): tanda\_2 is shown on the screen, written out. - [05:20.712](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=320.71246928797603): tanda\_3 is shown on the screen, written out. - [05:21.061](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=321.0612560152974): tanda\_4 is shown on the screen, written out. - [05:22.987](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=322.9868958333333): titik is shown on the screen, written out. ##### [05:27.372](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=327.37189583333327) Narration: Pada garis bilangan, nilainya ada di antara dua dan tiga. Dari angka dua kita maju tiga langkah, dan satu langkah bernilai seperlima. Board: garis — a NumberLine (x\_range=(0.0, 3.0), ticks\_every=0.2); head\_campuran — a Heading that says "Pecahan Campuran"; tanda — a Point \[gray\] labelled "0" drawn in garis; tanda\_2 — a Point \[gray\] labelled "1" drawn in garis (location=(1.0, 0.0)); tanda\_3 — a Point \[gray\] labelled "2" drawn in garis (location=(2.0, 0.0)); tanda\_4 — a Point \[gray\] labelled "3" drawn in garis (location=(3.0, 0.0)); titik — a Point \[yellow\] labelled "2 frac(3, 5)" drawn in garis (location=(2.6, 0.0)) Actions: - [05:33.503](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=333.50289583333324): The segment (2.0, 0.0) to (2.6, 0.0) in garis is lit up. - [05:36.962](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=336.9623958333333): garis: retire a lit segment (unemphasize\_line). ##### [05:37.562](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=337.56239583333326) Narration: Untuk mengubahnya menjadi pecahan biasa, kalikan bilangan bulatnya dengan penyebut, lalu tambahkan pembilangnya. Dua kali lima sama dengan sepuluh, ditambah tiga menjadi tiga belas. Board: Unchanged from the preceding beat in this scene. Actions: - [05:40.72](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=340.7198958333332): garis moves to a new place on the board. - [05:40.72](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=340.7198958333332): campuran is shown on the screen, written out. ##### [05:50.585](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=350.5853958333333) Narration: Penyebutnya tetap lima, sehingga hasilnya tiga belas per lima. Titik pada garis bilangan tidak berpindah, hanya namanya yang berganti. Board: Unchanged from the preceding beat in this scene. Actions: - [05:51.456](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=351.4558958333333): campuran is shown on the screen, written out. - [05:58.55](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=358.54989583333327): titik: one name gives way to another over the same drawing (label\_becomes). ##### [06:0.195](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=360.19539583333324) Narration: Sebaliknya, tujuh belas per empat bisa diubah menjadi pecahan campuran. Bagilah tujuh belas dengan empat: hasilnya empat, sisanya satu. Board: Unchanged from the preceding beat in this scene. Actions: - [06:8.938](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=368.93789583333324): biasa is shown on the screen, written out. ##### [06:10.814](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=370.81439583333326) Narration: Sisa satu menjadi pembilang, penyebutnya tetap empat. Jadi tujuh belas per empat sama dengan empat dan satu per empat. Board: Unchanged from the preceding beat in this scene. Actions: - [06:13.497](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=373.49689583333327): biasa is shown on the screen, written out. - [06:19.243](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=379.24339583333324): biasa is hidden from the screen — left the board. - [06:19.243](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=379.24339583333324): campuran is hidden from the screen — left the board. - [06:19.243](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=379.24339583333324): garis is hidden from the screen — left the board. - [06:19.243](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=379.24339583333324): tanda is hidden from the screen — garis left the board. - [06:19.243](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=379.24339583333324): tanda\_2 is hidden from the screen — garis left the board. - [06:19.243](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=379.24339583333324): tanda\_3 is hidden from the screen — garis left the board. - [06:19.243](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=379.24339583333324): tanda\_4 is hidden from the screen — garis left the board. - [06:19.243](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=379.24339583333324): titik is hidden from the screen — garis left the board. - [06:19.243](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=379.24339583333324): head\_campuran is hidden from the screen — left the board. ##### [06:20.443](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=380.4433958333333) Narration: Bagaimana cara cepat mengubah bentuk? Kalau penyebutnya bisa dijadikan sepuluh atau seratus, pekerjaannya mudah. Board: Empty. Actions: - [06:20.443](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=380.4433958333333): head\_ubah is shown on the screen, written out. ##### [06:28.868](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=388.86839583333324) Narration: Ambil dua per lima. Kalikan pembilang dan penyebut dengan dua, maka penyebutnya menjadi sepuluh, dan pecahannya empat per sepuluh. Board: head\_ubah — a Heading that says "Mengubah Bentuk dengan Cepat" Actions: - [06:34.43](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=394.42989583333326): ubah is shown on the screen, written out. ##### [06:38.837](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=398.8373958333333) Narration: Empat per sepuluh dibaca nol koma empat. Kalau dikalikan sepuluh lagi, kita mendapat empat puluh per seratus, artinya empat puluh persen. Board: Unchanged from the preceding beat in this scene. Actions: - [06:40.208](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=400.2078958333333): ubah is shown on the screen, written out. - [06:45.862](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=405.8618958333333): ubah is shown on the screen, written out. ##### [06:49.422](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=409.4218958333332) Narration: Beberapa nilai sebaiknya dihafal karena hampir selalu keluar. Nilai setengah sama dengan nol koma lima, atau lima puluh persen. Nilai seperempat sama dengan nol koma dua puluh lima, atau dua puluh lima persen. Board: Unchanged from the preceding beat in this scene. Actions: - [06:51.524](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=411.5238958333332): tabel is shown on the screen, written out. - [06:54.798](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=414.7978958333332): tabel is shown on the screen, written out. - [06:59.894](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=419.8938958333332): tabel is shown on the screen, written out. ##### [07:5.405](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=425.4053958333333) Narration: Nilai tiga per empat sama dengan nol koma tujuh lima. Nilai seperlima sama dengan dua puluh persen, dan sepersepuluh sama dengan sepuluh persen. Board: Unchanged from the preceding beat in this scene. Actions: - [07:6.16](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=426.1598958333332): tabel is shown on the screen, written out. - [07:11.767](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=431.76689583333325): tabel is shown on the screen, written out. - [07:14.705](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=434.70489583333324): tabel is shown on the screen, written out. ##### [07:16.57](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=436.57039583333324) Narration: Kalau ketiga bentuk itu sudah lancar, membandingkan pecahan menjadi jauh lebih mudah. Itu langkah kita berikutnya. Board: Unchanged from the preceding beat in this scene. Actions: - [07:18.451](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=438.4508958333332): tabel (the "column=3" part) is emphasized. - [07:23.165](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=443.1648958333332): tabel (the "column=3" part) is no longer emphasized. - [07:24.276](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=444.2763749999999): head\_ubah is hidden from the screen — left the board. - [07:24.276](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=444.2763749999999): tabel is hidden from the screen — left the board. - [07:24.276](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=444.2763749999999): ubah is hidden from the screen — left the board. ### Scene 3: [Membandingkan dan Mengurutkan](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=445.31804166666655) Span: 07:25.318–09:32.246 (445.31804166666655s–572.2464374999998s). #### Objects - banding: a Figure (x\_range=(0.0, 4.8), y\_range=(0.0, 1.9), aspect=(4.8, 1.9)) - garis\_persen: a NumberLine labelled "%" (x\_range=(55.0, 75.0), include\_numbers=True, ticks\_every=5.0) - head\_banding: a Heading that says "Mana yang Lebih Besar?" - head\_urut: a Heading that says "Mengurutkan Bentuk yang Bercampur" - hitung: a Derivation \[text\] that says "$frac(3, 5) &= frac(3 times 3, 5 times 3) = frac(9, 15) \\ frac(2, 3) &= frac(2 times 5, 3 times 5) = frac(10, 15) \\ frac(9, 15) &\< frac(10, 15) \\ frac(3, 5) &\< frac(2, 3)$" - k0: a Math \[text\] that says "$frac(3, 5) = frac(60, 100) = 60%$" - k1: a Math \[text\] that says "$upright("0,65") = frac(65, 100) = 65%$" - k2: a Math \[text\] that says "$frac(2, 3) approx upright("66,7%")$" - kpk: a Math \[text\] that says "$upright("KPK")(5, 3) = 15$" - lima: a Polygon \[blue\] drawn in banding (vertices=((1.0, 1.05), (1.72, 1.05), (1.72, 1.65), (1.0, 1.65)), fill\_opacity=0.45) - lima\_2: a Polygon \[blue\] drawn in banding (vertices=((1.72, 1.05), (2.44, 1.05), (2.44, 1.65), (1.72, 1.65)), fill\_opacity=0.45) - lima\_3: a Polygon \[blue\] drawn in banding (vertices=((2.44, 1.05), (3.16, 1.05), (3.16, 1.65), (2.44, 1.65)), fill\_opacity=0.45) - lima\_4: a Polygon \[gray\] drawn in banding (vertices=((3.16, 1.05), (3.88, 1.05), (3.88, 1.65), (3.16, 1.65)), filled=False, fill\_opacity=0.45) - lima\_5: a Polygon \[gray\] drawn in banding (vertices=((3.88, 1.05), (4.6, 1.05), (4.6, 1.65), (3.88, 1.65)), filled=False, fill\_opacity=0.45) - nama\_lima: a Math \[text\] that says "$frac(3, 5)$" drawn in banding - nama\_tiga: a Math \[text\] that says "$frac(2, 3)$" drawn in banding - p1: a Point \[blue\] labelled "frac(3, 5)" drawn in garis\_persen (location=(60.0, 0.0)) - p2: a Point \[green\] labelled "upright("0,65")" drawn in garis\_persen (location=(65.0, 0.0)) - p3: a Point \[yellow\] labelled "frac(2, 3)" drawn in garis\_persen (location=(66.66666666666667, 0.0)) - p4: a Point \[red\] labelled "70%" drawn in garis\_persen (location=(70.0, 0.0)) - tepi\_lima: a Line \[blue\] drawn in banding (start=(3.16, 1.05), end=(3.16, 0.15), dashed=True) - tepi\_tiga: a Line \[green\] drawn in banding (start=(3.4, 1.65), end=(3.4, 0.15), dashed=True) - tiga: a Polygon \[green\] drawn in banding (vertices=((1.0, 0.25), (2.2, 0.25), (2.2, 0.85), (1.0, 0.85)), fill\_opacity=0.45) - tiga\_2: a Polygon \[green\] drawn in banding (vertices=((2.2, 0.25), (3.4000000000000004, 0.25), (3.4000000000000004, …, fill\_opacity=0.45) - tiga\_3: a Polygon \[gray\] drawn in banding (vertices=((3.4, 0.25), (4.6, 0.25), (4.6, 0.85), (3.4, 0.85)), filled=False, fill\_opacity=0.45) - urut: a Math \[text\] that says "$frac(3, 5) \< upright("0,65") \< frac(2, 3) \< 70%$" #### Beats ##### [07:25.318](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=445.31804166666655) Narration: Di ujian kamu sering diminta membandingkan dua pecahan. Mana yang lebih besar, tiga per lima atau dua per tiga? Board: Empty. Actions: - [07:25.318](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=445.31804166666655): head\_banding is shown on the screen, written out. - [07:25.318](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=445.31804166666655): banding is shown on the screen, written out. ##### [07:33.941](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=453.94054166666655) Narration: Dua pita ini sama panjang. Pita atas dibagi lima bagian, tiga di antaranya biru. Pita bawah dibagi tiga bagian, dua di antaranya hijau. Board: banding — a Figure (x\_range=(0.0, 4.8), y\_range=(0.0, 1.9), aspect=(4.8, 1.9)); head\_banding — a Heading that says "Mana yang Lebih Besar?" Actions: - [07:36.715](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=456.71504166666654): nama\_lima is shown on the screen, written out. - [07:37.482](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=457.48204166666653): lima is shown on the screen, written out. - [07:37.588](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=457.5876660321488): lima\_2 is shown on the screen, written out. - [07:37.693](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=457.693290397631): lima\_3 is shown on the screen, written out. - [07:37.887](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=457.8867199661589): lima\_4 is shown on the screen, written out. - [07:38.142](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=458.1422377326564): lima\_5 is shown on the screen, written out. - [07:41.162](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=461.16204166666654): nama\_tiga is shown on the screen, written out. - [07:41.858](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=461.85804166666657): tiga is shown on the screen, written out. - [07:41.979](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=461.9785777072757): tiga\_2 is shown on the screen, written out. - [07:42.099](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=462.0991137478848): tiga\_3 is shown on the screen, written out. ##### [07:45.443](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=465.44254166666656) Narration: Bagian berwarna pada pita bawah berakhir sedikit lebih ke kanan. Jadi dua per tiga tampak lebih besar. Tetapi mata bisa keliru, maka kita buktikan dengan hitungan. Board: banding — a Figure (x\_range=(0.0, 4.8), y\_range=(0.0, 1.9), aspect=(4.8, 1.9)); head\_banding — a Heading that says "Mana yang Lebih Besar?"; nama\_lima — a Math \[text\] that says "$frac(3, 5)$" drawn in banding; lima — a Polygon \[blue\] drawn in banding (vertices=((1.0, 1.05), (1.72, 1.05), (1.72, 1.65), (1.0, 1.65)), fill\_opacity=0.45); lima\_2 — a Polygon \[blue\] drawn in banding (vertices=((1.72, 1.05), (2.44, 1.05), (2.44, 1.65), (1.72, 1.65)), fill\_opacity=0.45); lima\_3 — a Polygon \[blue\] drawn in banding (vertices=((2.44, 1.05), (3.16, 1.05), (3.16, 1.65), (2.44, 1.65)), fill\_opacity=0.45); lima\_4 — a Polygon \[gray\] drawn in banding (vertices=((3.16, 1.05), (3.88, 1.05), (3.88, 1.65), (3.16, 1.65)), filled=False, fill\_opacity=0.45); lima\_5 — a Polygon \[gray\] drawn in banding (vertices=((3.88, 1.05), (4.6, 1.05), (4.6, 1.65), (3.88, 1.65)), filled=False, fill\_opacity=0.45); nama\_tiga — a Math \[text\] that says "$frac(2, 3)$" drawn in banding; tiga — a Polygon \[green\] drawn in banding (vertices=((1.0, 0.25), (2.2, 0.25), (2.2, 0.85), (1.0, 0.85)), fill\_opacity=0.45); tiga\_2 — a Polygon \[green\] drawn in banding (vertices=((2.2, 0.25), (3.4000000000000004, 0.25), (3.4000000000000004, …, fill\_opacity=0.45); tiga\_3 — a Polygon \[gray\] drawn in banding (vertices=((3.4, 0.25), (4.6, 0.25), (4.6, 0.85), (3.4, 0.85)), filled=False, fill\_opacity=0.45) Actions: - [07:47.463](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=467.4630416666665): tepi\_lima is shown on the screen, written out. - [07:48.635](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=468.63504166666655): tepi\_tiga is shown on the screen, written out. ##### [07:56.562](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=476.5615416666665) Narration: Caranya, samakan dulu penyebutnya. Kelipatan persekutuan terkecil dari lima dan tiga adalah lima belas. Board: banding — a Figure (x\_range=(0.0, 4.8), y\_range=(0.0, 1.9), aspect=(4.8, 1.9)); head\_banding — a Heading that says "Mana yang Lebih Besar?"; nama\_lima — a Math \[text\] that says "$frac(3, 5)$" drawn in banding; lima — a Polygon \[blue\] drawn in banding (vertices=((1.0, 1.05), (1.72, 1.05), (1.72, 1.65), (1.0, 1.65)), fill\_opacity=0.45); lima\_2 — a Polygon \[blue\] drawn in banding (vertices=((1.72, 1.05), (2.44, 1.05), (2.44, 1.65), (1.72, 1.65)), fill\_opacity=0.45); lima\_3 — a Polygon \[blue\] drawn in banding (vertices=((2.44, 1.05), (3.16, 1.05), (3.16, 1.65), (2.44, 1.65)), fill\_opacity=0.45); lima\_4 — a Polygon \[gray\] drawn in banding (vertices=((3.16, 1.05), (3.88, 1.05), (3.88, 1.65), (3.16, 1.65)), filled=False, fill\_opacity=0.45); lima\_5 — a Polygon \[gray\] drawn in banding (vertices=((3.88, 1.05), (4.6, 1.05), (4.6, 1.65), (3.88, 1.65)), filled=False, fill\_opacity=0.45); nama\_tiga — a Math \[text\] that says "$frac(2, 3)$" drawn in banding; tiga — a Polygon \[green\] drawn in banding (vertices=((1.0, 0.25), (2.2, 0.25), (2.2, 0.85), (1.0, 0.85)), fill\_opacity=0.45); tiga\_2 — a Polygon \[green\] drawn in banding (vertices=((2.2, 0.25), (3.4000000000000004, 0.25), (3.4000000000000004, …, fill\_opacity=0.45); tiga\_3 — a Polygon \[gray\] drawn in banding (vertices=((3.4, 0.25), (4.6, 0.25), (4.6, 0.85), (3.4, 0.85)), filled=False, fill\_opacity=0.45); tepi\_lima — a Line \[blue\] drawn in banding (start=(3.16, 1.05), end=(3.16, 0.15), dashed=True); tepi\_tiga — a Line \[green\] drawn in banding (start=(3.4, 1.65), end=(3.4, 0.15), dashed=True) Actions: - [08:3.341](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=483.34104166666657): banding moves to a new place on the board. - [08:3.341](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=483.34104166666657): kpk is shown on the screen, written out. ##### [08:5.021](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=485.0210416666665) Narration: Tiga per lima dikalikan tiga, di atas dan di bawah, menjadi sembilan per lima belas. Board: kpk — a Math \[text\] that says "$upright("KPK")(5, 3) = 15$"; banding — a Figure (x\_range=(0.0, 4.8), y\_range=(0.0, 1.9), aspect=(4.8, 1.9)); head\_banding — a Heading that says "Mana yang Lebih Besar?"; nama\_lima — a Math \[text\] that says "$frac(3, 5)$" drawn in banding; lima — a Polygon \[blue\] drawn in banding (vertices=((1.0, 1.05), (1.72, 1.05), (1.72, 1.65), (1.0, 1.65)), fill\_opacity=0.45); lima\_2 — a Polygon \[blue\] drawn in banding (vertices=((1.72, 1.05), (2.44, 1.05), (2.44, 1.65), (1.72, 1.65)), fill\_opacity=0.45); lima\_3 — a Polygon \[blue\] drawn in banding (vertices=((2.44, 1.05), (3.16, 1.05), (3.16, 1.65), (2.44, 1.65)), fill\_opacity=0.45); lima\_4 — a Polygon \[gray\] drawn in banding (vertices=((3.16, 1.05), (3.88, 1.05), (3.88, 1.65), (3.16, 1.65)), filled=False, fill\_opacity=0.45); lima\_5 — a Polygon \[gray\] drawn in banding (vertices=((3.88, 1.05), (4.6, 1.05), (4.6, 1.65), (3.88, 1.65)), filled=False, fill\_opacity=0.45); nama\_tiga — a Math \[text\] that says "$frac(2, 3)$" drawn in banding; tiga — a Polygon \[green\] drawn in banding (vertices=((1.0, 0.25), (2.2, 0.25), (2.2, 0.85), (1.0, 0.85)), fill\_opacity=0.45); tiga\_2 — a Polygon \[green\] drawn in banding (vertices=((2.2, 0.25), (3.4000000000000004, 0.25), (3.4000000000000004, …, fill\_opacity=0.45); tiga\_3 — a Polygon \[gray\] drawn in banding (vertices=((3.4, 0.25), (4.6, 0.25), (4.6, 0.85), (3.4, 0.85)), filled=False, fill\_opacity=0.45); tepi\_lima — a Line \[blue\] drawn in banding (start=(3.16, 1.05), end=(3.16, 0.15), dashed=True); tepi\_tiga — a Line \[green\] drawn in banding (start=(3.4, 1.65), end=(3.4, 0.15), dashed=True) Actions: - [08:9.073](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=489.07304166666654): hitung is shown on the screen, written out. ##### [08:11.496](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=491.49554166666655) Narration: Dua per tiga dikalikan lima, di atas dan di bawah, menjadi sepuluh per lima belas. Board: Unchanged from the preceding beat in this scene. Actions: - [08:15.478](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=495.4780416666665): hitung is shown on the screen, written out. ##### [08:17.924](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=497.92354166666655) Narration: Sekarang penyebutnya sama, jadi cukup bandingkan pembilangnya: sembilan lebih kecil daripada sepuluh. Board: Unchanged from the preceding beat in this scene. Actions: - [08:21.081](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=501.0810416666665): hitung is shown on the screen, written out. ##### [08:24.817](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=504.8165416666665) Narration: Berarti tiga per lima memang lebih kecil daripada dua per tiga. Hitungan dan gambar memberi jawaban yang sama. Board: Unchanged from the preceding beat in this scene. Actions: - [08:26.372](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=506.3720416666665): hitung is shown on the screen, written out. - [08:29.483](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=509.4830416666665): A box is drawn around hitung. - [08:32.212](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=512.2115416666666): banding is hidden from the screen — left the board. - [08:32.212](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=512.2115416666666): nama\_lima is hidden from the screen — banding left the board. - [08:32.212](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=512.2115416666666): lima is hidden from the screen — banding left the board. - [08:32.212](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=512.2115416666666): lima\_2 is hidden from the screen — banding left the board. - [08:32.212](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=512.2115416666666): lima\_3 is hidden from the screen — banding left the board. - [08:32.212](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=512.2115416666666): lima\_4 is hidden from the screen — banding left the board. - [08:32.212](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=512.2115416666666): lima\_5 is hidden from the screen — banding left the board. - [08:32.212](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=512.2115416666666): nama\_tiga is hidden from the screen — banding left the board. - [08:32.212](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=512.2115416666666): tiga is hidden from the screen — banding left the board. - [08:32.212](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=512.2115416666666): tiga\_2 is hidden from the screen — banding left the board. - [08:32.212](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=512.2115416666666): tiga\_3 is hidden from the screen — banding left the board. - [08:32.212](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=512.2115416666666): tepi\_lima is hidden from the screen — banding left the board. - [08:32.212](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=512.2115416666666): tepi\_tiga is hidden from the screen — banding left the board. - [08:32.212](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=512.2115416666666): head\_banding is hidden from the screen — left the board. - [08:32.212](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=512.2115416666666): hitung is hidden from the screen — left the board. - [08:32.212](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=512.2115416666666): kpk is hidden from the screen — left the board. ##### [08:33.412](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=513.4115416666665) Narration: Bagaimana kalau bentuknya bercampur? Misalnya tiga per lima, nol koma enam lima, dua per tiga, dan tujuh puluh persen. Cara paling aman adalah mengubah semuanya menjadi persen. Board: Empty. Actions: - [08:33.412](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=513.4115416666665): head\_urut is shown on the screen, written out. - [08:33.412](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=513.4115416666665): garis\_persen is shown on the screen, written out. ##### [08:46.667](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=526.6670416666666) Narration: Tiga per lima sama dengan enam puluh per seratus, yaitu enam puluh persen. Board: garis\_persen — a NumberLine labelled "%" (x\_range=(55.0, 75.0), include\_numbers=True, ticks\_every=5.0); head\_urut — a Heading that says "Mengurutkan Bentuk yang Bercampur" Actions: - [08:49.024](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=529.0240416666666): garis\_persen moves to a new place on the board. - [08:49.024](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=529.0240416666666): k0 is shown on the screen, written out. - [08:50.312](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=530.3120416666666): p1 is shown on the screen, written out. ##### [08:52.387](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=532.3865416666665) Narration: Nol koma enam lima berarti enam puluh lima per seratus, yaitu enam puluh lima persen. Board: k0 — a Math \[text\] that says "$frac(3, 5) = frac(60, 100) = 60%$"; garis\_persen — a NumberLine labelled "%" (x\_range=(55.0, 75.0), include\_numbers=True, ticks\_every=5.0); head\_urut — a Heading that says "Mengurutkan Bentuk yang Bercampur"; p1 — a Point \[blue\] labelled "frac(3, 5)" drawn in garis\_persen (location=(60.0, 0.0)) Actions: - [08:55.556](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=535.5560416666665): k1 is shown on the screen, written out. - [08:57.332](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=537.3320416666666): p2 is shown on the screen, written out. ##### [08:59.001](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=539.0005416666665) Narration: Dua per tiga tidak bulat, tetapi nilainya kira kira enam puluh enam koma tujuh persen, sedikit di atas enam puluh lima. Board: k0 — a Math \[text\] that says "$frac(3, 5) = frac(60, 100) = 60%$"; k1 — a Math \[text\] that says "$upright("0,65") = frac(65, 100) = 65%$"; garis\_persen — a NumberLine labelled "%" (x\_range=(55.0, 75.0), include\_numbers=True, ticks\_every=5.0); head\_urut — a Heading that says "Mengurutkan Bentuk yang Bercampur"; p1 — a Point \[blue\] labelled "frac(3, 5)" drawn in garis\_persen (location=(60.0, 0.0)); p2 — a Point \[green\] labelled "upright("0,65")" drawn in garis\_persen (location=(65.0, 0.0)) Actions: - [09:1.044](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=541.0440416666665): k2 is shown on the screen, written out. - [09:3.401](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=543.4010416666665): p3 is shown on the screen, written out. ##### [09:7.554](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=547.5535416666665) Narration: Dan tujuh puluh persen sudah berbentuk persen, letaknya paling kanan. Board: k0 — a Math \[text\] that says "$frac(3, 5) = frac(60, 100) = 60%$"; k1 — a Math \[text\] that says "$upright("0,65") = frac(65, 100) = 65%$"; k2 — a Math \[text\] that says "$frac(2, 3) approx upright("66,7%")$"; garis\_persen — a NumberLine labelled "%" (x\_range=(55.0, 75.0), include\_numbers=True, ticks\_every=5.0); head\_urut — a Heading that says "Mengurutkan Bentuk yang Bercampur"; p1 — a Point \[blue\] labelled "frac(3, 5)" drawn in garis\_persen (location=(60.0, 0.0)); p2 — a Point \[green\] labelled "upright("0,65")" drawn in garis\_persen (location=(65.0, 0.0)); p3 — a Point \[yellow\] labelled "frac(2, 3)" drawn in garis\_persen (location=(66.66666666666667, 0.0)) Actions: - [09:11.443](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=551.4430416666665): p4 is shown on the screen, written out. ##### [09:12.763](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=552.7625416666665) Narration: Sekarang urutannya terlihat jelas pada garis bilangan, dari nilai terkecil sampai terbesar, dan itulah jawaban yang diminta soal. Board: k0 — a Math \[text\] that says "$frac(3, 5) = frac(60, 100) = 60%$"; k1 — a Math \[text\] that says "$upright("0,65") = frac(65, 100) = 65%$"; k2 — a Math \[text\] that says "$frac(2, 3) approx upright("66,7%")$"; garis\_persen — a NumberLine labelled "%" (x\_range=(55.0, 75.0), include\_numbers=True, ticks\_every=5.0); head\_urut — a Heading that says "Mengurutkan Bentuk yang Bercampur"; p1 — a Point \[blue\] labelled "frac(3, 5)" drawn in garis\_persen (location=(60.0, 0.0)); p2 — a Point \[green\] labelled "upright("0,65")" drawn in garis\_persen (location=(65.0, 0.0)); p3 — a Point \[yellow\] labelled "frac(2, 3)" drawn in garis\_persen (location=(66.66666666666667, 0.0)); p4 — a Point \[red\] labelled "70%" drawn in garis\_persen (location=(70.0, 0.0)) Actions: - [09:16.675](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=556.6750416666665): urut is shown on the screen, written out. - [09:18.904](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=558.9040416666666): A box is drawn around urut. ##### [09:21.31](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=561.3095416666665) Narration: Jadi kalau bentuknya bercampur, jangan langsung dibandingkan. Ubah dulu ke bentuk yang sama, baru urutkan. Sesudah ini kita berhitung dengan pecahan. Board: k0 — a Math \[text\] that says "$frac(3, 5) = frac(60, 100) = 60%$"; k1 — a Math \[text\] that says "$upright("0,65") = frac(65, 100) = 65%$"; k2 — a Math \[text\] that says "$frac(2, 3) approx upright("66,7%")$"; urut — a Math \[text\] that says "$frac(3, 5) \< upright("0,65") \< frac(2, 3) \< 70%$"; garis\_persen — a NumberLine labelled "%" (x\_range=(55.0, 75.0), include\_numbers=True, ticks\_every=5.0); head\_urut — a Heading that says "Mengurutkan Bentuk yang Bercampur"; p1 — a Point \[blue\] labelled "frac(3, 5)" drawn in garis\_persen (location=(60.0, 0.0)); p2 — a Point \[green\] labelled "upright("0,65")" drawn in garis\_persen (location=(65.0, 0.0)); p3 — a Point \[yellow\] labelled "frac(2, 3)" drawn in garis\_persen (location=(66.66666666666667, 0.0)); p4 — a Point \[red\] labelled "70%" drawn in garis\_persen (location=(70.0, 0.0)) Actions: - [09:27.26](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=567.2600416666666): p1 is indicated — a transient flash. - [09:27.597](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=567.5971332451295): p2 is indicated — a transient flash. - [09:27.934](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=567.9342248235924): p3 is indicated — a transient flash. - [09:28.271](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=568.2713164020554): p4 is indicated — a transient flash. - [09:31.205](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=571.2047708333332): garis\_persen is hidden from the screen — left the board. - [09:31.205](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=571.2047708333332): p1 is hidden from the screen — garis\_persen left the board. - [09:31.205](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=571.2047708333332): p2 is hidden from the screen — garis\_persen left the board. - [09:31.205](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=571.2047708333332): p3 is hidden from the screen — garis\_persen left the board. - [09:31.205](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=571.2047708333332): p4 is hidden from the screen — garis\_persen left the board. - [09:31.205](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=571.2047708333332): head\_urut is hidden from the screen — left the board. - [09:31.205](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=571.2047708333332): k0 is hidden from the screen — left the board. - [09:31.205](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=571.2047708333332): k1 is hidden from the screen — left the board. - [09:31.205](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=571.2047708333332): k2 is hidden from the screen — left the board. - [09:31.205](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=571.2047708333332): urut is hidden from the screen — left the board. ### Scene 4: [Menjumlahkan dan Mengurangkan Pecahan](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=572.2464374999998) Span: 09:32.246–12:56.332 (572.2464374999998s–776.3323958333332s). #### Objects - angka: a Point \[gray\] labelled "0" drawn in garis4 - angka\_2: a Point \[gray\] labelled "1" drawn in garis4 (location=(1.0, 0.0)) - angka\_3: a Point \[gray\] labelled "2" drawn in garis4 (location=(2.0, 0.0)) - angka\_4: a Point \[gray\] labelled "3" drawn in garis4 (location=(3.0, 0.0)) - angka\_5: a Point \[gray\] labelled "4" drawn in garis4 (location=(4.0, 0.0)) - aturan\_sama: a Panel that says "Kalau penyebutnya sama, jumlahkan pembilangnya saja. Penyebutnya tidak berubah." - biru: a Polygon \[blue\] drawn in kue (vertices=((0, 0.1), (1, 0.1), (1, 1.1), (0, 1.1)), fill\_opacity=0.5) - biru6: a Polygon \[blue\] drawn in pecah (vertices=((0, 0.0), (1, 0.0), (1, 0.8), (0, 0.8)), fill\_opacity=0.45) - biru6\_2: a Polygon \[blue\] drawn in pecah (vertices=((1, 0.0), (2, 0.0), (2, 0.8), (1, 0.8)), fill\_opacity=0.45) - biru6\_3: a Polygon \[blue\] drawn in pecah (vertices=((2, 0.0), (3, 0.0), (3, 0.8), (2, 0.8)), fill\_opacity=0.45) - biru\_2: a Polygon \[blue\] drawn in kue (vertices=((1, 0.1), (2, 0.1), (2, 1.1), (1, 1.1)), fill\_opacity=0.5) - dua: a Polygon \[blue\] drawn in pecah (vertices=((0, 2.4), (3, 2.4), (3, 3.2), (0, 3.2)), fill\_opacity=0.45) - dua\_2: a Polygon \[gray\] drawn in pecah (vertices=((3, 2.4), (6, 2.4), (6, 3.2), (3, 3.2)), filled=False, fill\_opacity=0.45) - garis4: a NumberLine (x\_range=(0.0, 4.0), ticks\_every=0.25) - gula: a Figure (x\_range=(0.0, 4.0), y\_range=(-0.2, 1.4), aspect=(4.0, 1.6)) - head\_beda: a Heading that says "Penyebut Berbeda" - head\_kurang: a Heading that says "Pengurangan Pecahan Campuran" - head\_sama: a Heading that says "Penyebut Sama" - hijau: a Polygon \[green\] drawn in kue (vertices=((2, 0.1), (3, 0.1), (3, 1.1), (2, 1.1)), fill\_opacity=0.5) - hijau6: a Polygon \[green\] drawn in pecah (vertices=((3, 0.0), (4, 0.0), (4, 0.8), (3, 0.8)), fill\_opacity=0.45) - hijau6\_2: a Polygon \[green\] drawn in pecah (vertices=((4, 0.0), (5, 0.0), (5, 0.8), (4, 0.8)), fill\_opacity=0.45) - hijau\_2: a Polygon \[green\] drawn in kue (vertices=((3, 0.1), (4, 0.1), (4, 1.1), (3, 1.1)), fill\_opacity=0.5) - hijau\_3: a Polygon \[green\] drawn in kue (vertices=((4, 0.1), (5, 0.1), (5, 1.1), (4, 1.1)), fill\_opacity=0.5) - isi: a Polygon \[green\] drawn in gula (vertices=((0, 0.1), (1, 0.1), (1, 1.1), (0, 1.1)), fill\_opacity=0.5) - isi\_2: a Polygon \[green\] drawn in gula (vertices=((1, 0.1), (2, 0.1), (2, 1.1), (1, 1.1)), fill\_opacity=0.5) - isi\_3: a Polygon \[green\] drawn in gula (vertices=((2, 0.1), (3, 0.1), (3, 1.1), (2, 1.1)), fill\_opacity=0.5) - jawab: a Math \[text\] that says "$frac(1, 4) thin upright("kg")$" - jumlah: a Derivation \[text\] that says "$frac(2, 7) + frac(3, 7) &= frac(2 + 3, 7) \\ &= frac(5, 7)$" - kpk2: a Math \[text\] that says "$upright("KPK")(2, 3) = 6$" - kue: a Figure (x\_range=(0.0, 7.0), y\_range=(-0.2, 1.4), aspect=(7.0, 1.6)) - nilai: a VariableNumber (initial\_value=3.25) - pecah: a Figure (x\_range=(0.0, 6.0), y\_range=(-0.2, 3.4), aspect=(6.0, 3.6)) - rangka: a Polygon \[gray\] drawn in kue (vertices=((0, 0.1), (1, 0.1), (1, 1.1), (0, 1.1)), filled=False) - rangka4: a Polygon \[gray\] drawn in gula (vertices=((0, 0.1), (1, 0.1), (1, 1.1), (0, 1.1)), filled=False) - rangka4\_2: a Polygon \[gray\] drawn in gula (vertices=((1, 0.1), (2, 0.1), (2, 1.1), (1, 1.1)), filled=False) - rangka4\_3: a Polygon \[gray\] drawn in gula (vertices=((2, 0.1), (3, 0.1), (3, 1.1), (2, 1.1)), filled=False) - rangka4\_4: a Polygon \[gray\] drawn in gula (vertices=((3, 0.1), (4, 0.1), (4, 1.1), (3, 1.1)), filled=False) - rangka6: a Polygon \[gray\] drawn in pecah (vertices=((0, 0.0), (1, 0.0), (1, 0.8), (0, 0.8)), filled=False) - rangka6\_2: a Polygon \[gray\] drawn in pecah (vertices=((1, 0.0), (2, 0.0), (2, 0.8), (1, 0.8)), filled=False) - rangka6\_3: a Polygon \[gray\] drawn in pecah (vertices=((2, 0.0), (3, 0.0), (3, 0.8), (2, 0.8)), filled=False) - rangka6\_4: a Polygon \[gray\] drawn in pecah (vertices=((3, 0.0), (4, 0.0), (4, 0.8), (3, 0.8)), filled=False) - rangka6\_5: a Polygon \[gray\] drawn in pecah (vertices=((4, 0.0), (5, 0.0), (5, 0.8), (4, 0.8)), filled=False) - rangka6\_6: a Polygon \[gray\] drawn in pecah (vertices=((5, 0.0), (6, 0.0), (6, 0.8), (5, 0.8)), filled=False) - rangka\_2: a Polygon \[gray\] drawn in kue (vertices=((1, 0.1), (2, 0.1), (2, 1.1), (1, 1.1)), filled=False) - rangka\_3: a Polygon \[gray\] drawn in kue (vertices=((2, 0.1), (3, 0.1), (3, 1.1), (2, 1.1)), filled=False) - rangka\_4: a Polygon \[gray\] drawn in kue (vertices=((3, 0.1), (4, 0.1), (4, 1.1), (3, 1.1)), filled=False) - rangka\_5: a Polygon \[gray\] drawn in kue (vertices=((4, 0.1), (5, 0.1), (5, 1.1), (4, 1.1)), filled=False) - rangka\_6: a Polygon \[gray\] drawn in kue (vertices=((5, 0.1), (6, 0.1), (6, 1.1), (5, 1.1)), filled=False) - rangka\_7: a Polygon \[gray\] drawn in kue (vertices=((6, 0.1), (7, 0.1), (7, 1.1), (6, 1.1)), filled=False) - salah\_paham: a Math \[gray\] that says "$frac(5, 14)$" - selisih: a Derivation \[text\] that says "$3 frac(1, 4) - 1 frac(1, 2) &= frac(13, 4) - frac(3, 2) \\ &= frac(13, 4) - frac(6, 4) \\ &= frac(7, 4) \\ &= 1 frac(3, 4)$" - sisa\_kerja: a Derivation \[text\] that says "$frac(3, 4) - frac(1, 2) &= frac(3, 4) - frac(2, 4) \\ &= frac(1, 4)$" - soal\_gula: a Panel that says "Ibu punya $frac(3, 4)$ kg gula. Sebanyak $frac(1, 2)$ kg dipakai untuk membuat kue. Berapa kilogram gula yang tersisa?" - tambah: a Derivation \[text\] that says "$frac(1, 2) + frac(1, 3) &= frac(3, 6) + frac(2, 6) \\ &= frac(3 + 2, 6) \\ &= frac(5, 6)$" - tiga: a Polygon \[green\] drawn in pecah (vertices=((0, 1.2), (2, 1.2), (2, 2.0), (0, 2.0)), fill\_opacity=0.45) - tiga\_2: a Polygon \[gray\] drawn in pecah (vertices=((2, 1.2), (4, 1.2), (4, 2.0), (2, 2.0)), filled=False, fill\_opacity=0.45) - tiga\_3: a Polygon \[gray\] drawn in pecah (vertices=((4, 1.2), (6, 1.2), (6, 2.0), (4, 2.0)), filled=False, fill\_opacity=0.45) - titik4: a Point \[yellow\] labelled "3 frac(1, 4)" drawn in garis4 (location=(\, 0.0)) #### Beats ##### [09:32.246](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=572.2464374999998) Narration: Sekarang kita berhitung dengan pecahan, mulai dari penjumlahan. Keadaan paling mudah adalah kalau penyebutnya sudah sama. Board: Empty. Actions: - [09:32.246](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=572.2464374999998): head\_sama is shown on the screen, written out. - [09:32.246](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=572.2464374999998): kue is shown on the screen, written out. ##### [09:40.567](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=580.5669374999999) Narration: Sebuah kue dibagi menjadi tujuh bagian sama besar. Dua bagian diambil Ani, dan tiga bagian diambil Budi. Board: kue — a Figure (x\_range=(0.0, 7.0), y\_range=(-0.2, 1.4), aspect=(7.0, 1.6)); head\_sama — a Heading that says "Penyebut Sama" Actions: - [09:42.215](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=582.2154374999999): rangka is shown on the screen, written out. - [09:42.309](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=582.3089511468265): rangka\_2 is shown on the screen, written out. - [09:42.402](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=582.4024647936533): rangka\_3 is shown on the screen, written out. - [09:42.496](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=582.4959784404799): rangka\_4 is shown on the screen, written out. - [09:42.596](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=582.5960686363742): rangka\_5 is shown on the screen, written out. - [09:42.702](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=582.7021192776106): rangka\_6 is shown on the screen, written out. - [09:42.808](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=582.808169918847): rangka\_7 is shown on the screen, written out. - [09:45.025](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=585.0254374999998): biru is shown on the screen, written out. - [09:45.176](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=585.1756348035184): biru\_2 is shown on the screen, written out. - [09:46.987](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=586.9874374999998): hijau is shown on the screen, written out. - [09:47.127](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=587.1266289666227): hijau\_2 is shown on the screen, written out. - [09:47.266](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=587.2658204332455): hijau\_3 is shown on the screen, written out. ##### [09:48.783](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=588.7829374999999) Narration: Dua per tujuh ditambah tiga per tujuh. Karena penyebutnya sama, kita cukup menjumlahkan pembilangnya: dua ditambah tiga sama dengan lima. Board: kue — a Figure (x\_range=(0.0, 7.0), y\_range=(-0.2, 1.4), aspect=(7.0, 1.6)); head\_sama — a Heading that says "Penyebut Sama"; rangka — a Polygon \[gray\] drawn in kue (vertices=((0, 0.1), (1, 0.1), (1, 1.1), (0, 1.1)), filled=False); rangka\_2 — a Polygon \[gray\] drawn in kue (vertices=((1, 0.1), (2, 0.1), (2, 1.1), (1, 1.1)), filled=False); rangka\_3 — a Polygon \[gray\] drawn in kue (vertices=((2, 0.1), (3, 0.1), (3, 1.1), (2, 1.1)), filled=False); rangka\_4 — a Polygon \[gray\] drawn in kue (vertices=((3, 0.1), (4, 0.1), (4, 1.1), (3, 1.1)), filled=False); rangka\_5 — a Polygon \[gray\] drawn in kue (vertices=((4, 0.1), (5, 0.1), (5, 1.1), (4, 1.1)), filled=False); rangka\_6 — a Polygon \[gray\] drawn in kue (vertices=((5, 0.1), (6, 0.1), (6, 1.1), (5, 1.1)), filled=False); rangka\_7 — a Polygon \[gray\] drawn in kue (vertices=((6, 0.1), (7, 0.1), (7, 1.1), (6, 1.1)), filled=False); biru — a Polygon \[blue\] drawn in kue (vertices=((0, 0.1), (1, 0.1), (1, 1.1), (0, 1.1)), fill\_opacity=0.5); biru\_2 — a Polygon \[blue\] drawn in kue (vertices=((1, 0.1), (2, 0.1), (2, 1.1), (1, 1.1)), fill\_opacity=0.5); hijau — a Polygon \[green\] drawn in kue (vertices=((2, 0.1), (3, 0.1), (3, 1.1), (2, 1.1)), fill\_opacity=0.5); hijau\_2 — a Polygon \[green\] drawn in kue (vertices=((3, 0.1), (4, 0.1), (4, 1.1), (3, 1.1)), fill\_opacity=0.5); hijau\_3 — a Polygon \[green\] drawn in kue (vertices=((4, 0.1), (5, 0.1), (5, 1.1), (4, 1.1)), fill\_opacity=0.5) Actions: - [09:53.752](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=593.7524374999998): kue moves to a new place on the board. - [09:53.752](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=593.7524374999998): jumlah is shown on the screen, written out. ##### [09:58.718](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=598.7179374999998) Narration: Penyebutnya tetap tujuh, jadi hasilnya lima per tujuh. Pada gambar, lima bagian dari tujuh sudah berwarna. Board: Unchanged from the preceding beat in this scene. Actions: - [09:59.704](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=599.7044374999998): jumlah is shown on the screen, written out. - [10:5.183](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=605.1834374999999): biru is indicated — a transient flash. - [10:5.183](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=605.1834374999999): biru\_2 is indicated — a transient flash. - [10:5.183](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=605.1834374999999): hijau is indicated — a transient flash. - [10:5.183](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=605.1834374999999): hijau\_2 is indicated — a transient flash. - [10:5.183](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=605.1834374999999): hijau\_3 is indicated — a transient flash. ##### [10:6.614](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=606.6139374999998) Narration: Ingatlah, penyebutnya tidak ikut dijumlahkan. Hasil lima per empat belas itu keliru, karena tujuh ditambah tujuh tidak ada dalam aturan. Board: Unchanged from the preceding beat in this scene. Actions: - [10:8.454](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=608.4544374999998): aturan\_sama is shown on the screen, written out. - [10:11.263](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=611.2634374999998): salah\_paham is shown on the screen, written out. - [10:15.257](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=615.2574374999998): salah\_paham is hidden from the screen. - [10:15.257](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=615.2574374999998): aturan\_sama is hidden from the screen — left the board. - [10:15.257](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=615.2574374999998): head\_sama is hidden from the screen — left the board. - [10:15.257](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=615.2574374999998): jumlah is hidden from the screen — left the board. - [10:15.257](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=615.2574374999998): kue is hidden from the screen — left the board. - [10:15.257](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=615.2574374999998): rangka is hidden from the screen — kue left the board. - [10:15.257](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=615.2574374999998): rangka\_2 is hidden from the screen — kue left the board. - [10:15.257](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=615.2574374999998): rangka\_3 is hidden from the screen — kue left the board. - [10:15.257](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=615.2574374999998): rangka\_4 is hidden from the screen — kue left the board. - [10:15.257](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=615.2574374999998): rangka\_5 is hidden from the screen — kue left the board. - [10:15.257](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=615.2574374999998): rangka\_6 is hidden from the screen — kue left the board. - [10:15.257](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=615.2574374999998): rangka\_7 is hidden from the screen — kue left the board. - [10:15.257](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=615.2574374999998): biru is hidden from the screen — kue left the board. - [10:15.257](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=615.2574374999998): biru\_2 is hidden from the screen — kue left the board. - [10:15.257](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=615.2574374999998): hijau is hidden from the screen — kue left the board. - [10:15.257](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=615.2574374999998): hijau\_2 is hidden from the screen — kue left the board. - [10:15.257](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=615.2574374999998): hijau\_3 is hidden from the screen — kue left the board. ##### [10:16.457](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=616.4574374999999) Narration: Bagaimana kalau penyebutnya berbeda? Misalnya setengah ditambah sepertiga. Board: Empty. Actions: - [10:16.457](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=616.4574374999999): head\_beda is shown on the screen, written out. - [10:16.457](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=616.4574374999999): pecah is shown on the screen, written out. ##### [10:22.073](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=622.0729374999999) Narration: Pita pertama dibagi dua, satu bagian diwarnai, itulah setengah. Pita kedua dibagi tiga, satu bagian diwarnai, itulah sepertiga. Board: pecah — a Figure (x\_range=(0.0, 6.0), y\_range=(-0.2, 3.4), aspect=(6.0, 3.6)); head\_beda — a Heading that says "Penyebut Berbeda" Actions: - [10:22.92](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=622.9204374999998): dua is shown on the screen, written out. - [10:23.071](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=623.0705993122975): dua\_2 is shown on the screen, written out. - [10:27.773](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=627.7734374999999): tiga is shown on the screen, written out. - [10:27.907](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=627.9065859049929): tiga\_2 is shown on the screen, written out. - [10:28.04](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=628.039734309986): tiga\_3 is shown on the screen, written out. ##### [10:32.24](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=632.2399374999999) Narration: Keduanya tidak bisa langsung dijumlahkan, karena ukuran bagiannya tidak sama. Kita perlu satu ukuran yang cocok untuk keduanya. Board: pecah — a Figure (x\_range=(0.0, 6.0), y\_range=(-0.2, 3.4), aspect=(6.0, 3.6)); head\_beda — a Heading that says "Penyebut Berbeda"; dua — a Polygon \[blue\] drawn in pecah (vertices=((0, 2.4), (3, 2.4), (3, 3.2), (0, 3.2)), fill\_opacity=0.45); dua\_2 — a Polygon \[gray\] drawn in pecah (vertices=((3, 2.4), (6, 2.4), (6, 3.2), (3, 3.2)), filled=False, fill\_opacity=0.45); tiga — a Polygon \[green\] drawn in pecah (vertices=((0, 1.2), (2, 1.2), (2, 2.0), (0, 2.0)), fill\_opacity=0.45); tiga\_2 — a Polygon \[gray\] drawn in pecah (vertices=((2, 1.2), (4, 1.2), (4, 2.0), (2, 2.0)), filled=False, fill\_opacity=0.45); tiga\_3 — a Polygon \[gray\] drawn in pecah (vertices=((4, 1.2), (6, 1.2), (6, 2.0), (4, 2.0)), filled=False, fill\_opacity=0.45) Actions: - [10:35.223](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=635.2234374999998): dua is indicated — a transient flash. - [10:35.223](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=635.2234374999998): tiga is indicated — a transient flash. ##### [10:41.408](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=641.4084374999999) Narration: Kelipatan persekutuan terkecil dari dua dan tiga adalah enam. Jadi kita pakai pita yang dibagi enam. Board: Unchanged from the preceding beat in this scene. Actions: - [10:44.809](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=644.8094374999998): pecah moves to a new place on the board. - [10:44.809](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=644.8094374999998): kpk2 is shown on the screen, written out. - [10:47.456](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=647.4564374999999): rangka6 is shown on the screen, written out. - [10:47.591](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=647.5905122252746): rangka6\_2 is shown on the screen, written out. - [10:47.725](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=647.7245869505493): rangka6\_3 is shown on the screen, written out. - [10:47.859](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=647.858661675824): rangka6\_4 is shown on the screen, written out. - [10:48.029](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=648.0291860678703): rangka6\_5 is shown on the screen, written out. - [10:48.222](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=648.2219287826898): rangka6\_6 is shown on the screen, written out. ##### [10:49.148](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=649.1479374999999) Narration: Setengah sama dengan tiga per enam, yaitu tiga kotak biru. Dan sepertiga sama dengan dua per enam, yaitu dua kotak hijau. Board: kpk2 — a Math \[text\] that says "$upright("KPK")(2, 3) = 6$"; pecah — a Figure (x\_range=(0.0, 6.0), y\_range=(-0.2, 3.4), aspect=(6.0, 3.6)); head\_beda — a Heading that says "Penyebut Berbeda"; dua — a Polygon \[blue\] drawn in pecah (vertices=((0, 2.4), (3, 2.4), (3, 3.2), (0, 3.2)), fill\_opacity=0.45); dua\_2 — a Polygon \[gray\] drawn in pecah (vertices=((3, 2.4), (6, 2.4), (6, 3.2), (3, 3.2)), filled=False, fill\_opacity=0.45); tiga — a Polygon \[green\] drawn in pecah (vertices=((0, 1.2), (2, 1.2), (2, 2.0), (0, 2.0)), fill\_opacity=0.45); tiga\_2 — a Polygon \[gray\] drawn in pecah (vertices=((2, 1.2), (4, 1.2), (4, 2.0), (2, 2.0)), filled=False, fill\_opacity=0.45); tiga\_3 — a Polygon \[gray\] drawn in pecah (vertices=((4, 1.2), (6, 1.2), (6, 2.0), (4, 2.0)), filled=False, fill\_opacity=0.45); rangka6 — a Polygon \[gray\] drawn in pecah (vertices=((0, 0.0), (1, 0.0), (1, 0.8), (0, 0.8)), filled=False); rangka6\_2 — a Polygon \[gray\] drawn in pecah (vertices=((1, 0.0), (2, 0.0), (2, 0.8), (1, 0.8)), filled=False); rangka6\_3 — a Polygon \[gray\] drawn in pecah (vertices=((2, 0.0), (3, 0.0), (3, 0.8), (2, 0.8)), filled=False); rangka6\_4 — a Polygon \[gray\] drawn in pecah (vertices=((3, 0.0), (4, 0.0), (4, 0.8), (3, 0.8)), filled=False); rangka6\_5 — a Polygon \[gray\] drawn in pecah (vertices=((4, 0.0), (5, 0.0), (5, 0.8), (4, 0.8)), filled=False); rangka6\_6 — a Polygon \[gray\] drawn in pecah (vertices=((5, 0.0), (6, 0.0), (6, 0.8), (5, 0.8)), filled=False) Actions: - [10:52.015](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=652.0154374999998): biru6 is shown on the screen, written out. - [10:52.202](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=652.2018551570457): biru6\_2 is shown on the screen, written out. - [10:52.387](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=652.3871734932087): biru6\_3 is shown on the screen, written out. - [10:54.883](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=654.8834374999999): tambah is shown on the screen, written out. - [10:56.486](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=656.4864374999999): hijau6 is shown on the screen, written out. - [10:56.629](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=656.6288398769099): hijau6\_2 is shown on the screen, written out. ##### [10:58.584](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=658.5839374999998) Narration: Sekarang penyebutnya sudah sama, jadi pembilangnya tinggal dijumlahkan: tiga ditambah dua sama dengan lima. Board: kpk2 — a Math \[text\] that says "$upright("KPK")(2, 3) = 6$"; pecah — a Figure (x\_range=(0.0, 6.0), y\_range=(-0.2, 3.4), aspect=(6.0, 3.6)); head\_beda — a Heading that says "Penyebut Berbeda"; dua — a Polygon \[blue\] drawn in pecah (vertices=((0, 2.4), (3, 2.4), (3, 3.2), (0, 3.2)), fill\_opacity=0.45); dua\_2 — a Polygon \[gray\] drawn in pecah (vertices=((3, 2.4), (6, 2.4), (6, 3.2), (3, 3.2)), filled=False, fill\_opacity=0.45); tiga — a Polygon \[green\] drawn in pecah (vertices=((0, 1.2), (2, 1.2), (2, 2.0), (0, 2.0)), fill\_opacity=0.45); tiga\_2 — a Polygon \[gray\] drawn in pecah (vertices=((2, 1.2), (4, 1.2), (4, 2.0), (2, 2.0)), filled=False, fill\_opacity=0.45); tiga\_3 — a Polygon \[gray\] drawn in pecah (vertices=((4, 1.2), (6, 1.2), (6, 2.0), (4, 2.0)), filled=False, fill\_opacity=0.45); rangka6 — a Polygon \[gray\] drawn in pecah (vertices=((0, 0.0), (1, 0.0), (1, 0.8), (0, 0.8)), filled=False); rangka6\_2 — a Polygon \[gray\] drawn in pecah (vertices=((1, 0.0), (2, 0.0), (2, 0.8), (1, 0.8)), filled=False); rangka6\_3 — a Polygon \[gray\] drawn in pecah (vertices=((2, 0.0), (3, 0.0), (3, 0.8), (2, 0.8)), filled=False); rangka6\_4 — a Polygon \[gray\] drawn in pecah (vertices=((3, 0.0), (4, 0.0), (4, 0.8), (3, 0.8)), filled=False); rangka6\_5 — a Polygon \[gray\] drawn in pecah (vertices=((4, 0.0), (5, 0.0), (5, 0.8), (4, 0.8)), filled=False); rangka6\_6 — a Polygon \[gray\] drawn in pecah (vertices=((5, 0.0), (6, 0.0), (6, 0.8), (5, 0.8)), filled=False); biru6 — a Polygon \[blue\] drawn in pecah (vertices=((0, 0.0), (1, 0.0), (1, 0.8), (0, 0.8)), fill\_opacity=0.45); biru6\_2 — a Polygon \[blue\] drawn in pecah (vertices=((1, 0.0), (2, 0.0), (2, 0.8), (1, 0.8)), fill\_opacity=0.45); biru6\_3 — a Polygon \[blue\] drawn in pecah (vertices=((2, 0.0), (3, 0.0), (3, 0.8), (2, 0.8)), fill\_opacity=0.45); hijau6 — a Polygon \[green\] drawn in pecah (vertices=((3, 0.0), (4, 0.0), (4, 0.8), (3, 0.8)), fill\_opacity=0.45); hijau6\_2 — a Polygon \[green\] drawn in pecah (vertices=((4, 0.0), (5, 0.0), (5, 0.8), (4, 0.8)), fill\_opacity=0.45) Actions: - [11:2.229](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=662.2294374999999): tambah is shown on the screen, written out. ##### [11:6.974](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=666.9739374999998) Narration: Hasilnya lima per enam, dan pada gambar memang ada lima kotak yang berwarna dari enam kotak. Board: Unchanged from the preceding beat in this scene. Actions: - [11:7.903](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=667.9034374999999): tambah is shown on the screen, written out. - [11:11.269](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=671.2694374999999): biru6 is indicated — a transient flash. - [11:11.269](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=671.2694374999999): biru6\_2 is indicated — a transient flash. - [11:11.269](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=671.2694374999999): biru6\_3 is indicated — a transient flash. - [11:11.269](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=671.2694374999999): hijau6 is indicated — a transient flash. - [11:11.269](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=671.2694374999999): hijau6\_2 is indicated — a transient flash. - [11:13.017](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=673.0169374999998): head\_beda is hidden from the screen — left the board. - [11:13.017](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=673.0169374999998): kpk2 is hidden from the screen — left the board. - [11:13.017](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=673.0169374999998): pecah is hidden from the screen — left the board. - [11:13.017](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=673.0169374999998): dua is hidden from the screen — pecah left the board. - [11:13.017](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=673.0169374999998): dua\_2 is hidden from the screen — pecah left the board. - [11:13.017](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=673.0169374999998): tiga is hidden from the screen — pecah left the board. - [11:13.017](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=673.0169374999998): tiga\_2 is hidden from the screen — pecah left the board. - [11:13.017](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=673.0169374999998): tiga\_3 is hidden from the screen — pecah left the board. - [11:13.017](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=673.0169374999998): rangka6 is hidden from the screen — pecah left the board. - [11:13.017](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=673.0169374999998): rangka6\_2 is hidden from the screen — pecah left the board. - [11:13.017](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=673.0169374999998): rangka6\_3 is hidden from the screen — pecah left the board. - [11:13.017](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=673.0169374999998): rangka6\_4 is hidden from the screen — pecah left the board. - [11:13.017](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=673.0169374999998): rangka6\_5 is hidden from the screen — pecah left the board. - [11:13.017](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=673.0169374999998): rangka6\_6 is hidden from the screen — pecah left the board. - [11:13.017](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=673.0169374999998): biru6 is hidden from the screen — pecah left the board. - [11:13.017](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=673.0169374999998): biru6\_2 is hidden from the screen — pecah left the board. - [11:13.017](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=673.0169374999998): biru6\_3 is hidden from the screen — pecah left the board. - [11:13.017](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=673.0169374999998): hijau6 is hidden from the screen — pecah left the board. - [11:13.017](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=673.0169374999998): hijau6\_2 is hidden from the screen — pecah left the board. - [11:13.017](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=673.0169374999998): tambah is hidden from the screen — left the board. ##### [11:14.217](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=674.2169374999999) Narration: Sekarang pengurangan, dan kali ini dengan pecahan campuran. Tiga satu per empat dikurangi satu setengah. Board: Empty. Actions: - [11:14.217](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=674.2169374999999): head\_kurang is shown on the screen, written out. - [11:14.217](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=674.2169374999999): garis4 is shown on the screen, written out. - [11:17.125](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=677.1254374999999): angka is shown on the screen, written out. - [11:17.324](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=677.3238015249916): angka\_2 is shown on the screen, written out. - [11:17.522](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=677.5221655499834): angka\_3 is shown on the screen, written out. - [11:17.721](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=677.7205295749751): angka\_4 is shown on the screen, written out. - [11:17.919](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=677.918893599967): angka\_5 is shown on the screen, written out. - [11:19.4](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=679.4004374999998): titik4 is shown on the screen, written out. ##### [11:21.603](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=681.6029374999998) Narration: Langkah pertama, ubah keduanya menjadi pecahan biasa. Tiga satu per empat menjadi tiga belas per empat, dan satu setengah menjadi tiga per dua. Board: garis4 — a NumberLine (x\_range=(0.0, 4.0), ticks\_every=0.25); head\_kurang — a Heading that says "Pengurangan Pecahan Campuran"; angka — a Point \[gray\] labelled "0" drawn in garis4; angka\_2 — a Point \[gray\] labelled "1" drawn in garis4 (location=(1.0, 0.0)); angka\_3 — a Point \[gray\] labelled "2" drawn in garis4 (location=(2.0, 0.0)); angka\_4 — a Point \[gray\] labelled "3" drawn in garis4 (location=(3.0, 0.0)); angka\_5 — a Point \[gray\] labelled "4" drawn in garis4 (location=(4.0, 0.0)); titik4 — a Point \[yellow\] labelled "3 frac(1, 4)" drawn in garis4 (location=(\, 0.0)) Actions: - [11:26.931](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=686.9314374999999): garis4 moves to a new place on the board. - [11:26.931](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=686.9314374999999): selisih is shown on the screen, written out. ##### [11:31.839](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=691.8394374999998) Narration: Penyebutnya belum sama, jadi ubah tiga per dua menjadi enam per empat. Board: Unchanged from the preceding beat in this scene. Actions: - [11:35.566](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=695.5664374999999): selisih is shown on the screen, written out. ##### [11:37.524](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=697.5244374999999) Narration: Sekarang kurangkan pembilangnya: tiga belas dikurangi enam sama dengan tujuh, jadi hasilnya tujuh per empat. Board: Unchanged from the preceding beat in this scene. Actions: - [11:43.538](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=703.5384374999999): selisih is shown on the screen, written out. ##### [11:45.218](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=705.2179374999998) Narration: Tujuh per empat sama dengan satu tiga per empat. Perhatikan titiknya bergeser ke kiri, lalu berhenti tepat di satu tiga per empat. Board: Unchanged from the preceding beat in this scene. Actions: - [11:46.692](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=706.6924374999999): selisih is shown on the screen, written out. - [11:49.281](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=709.2814374999998): titik4 is redrawn as the numbers it depends on change. - [11:49.281](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=709.2814374999998): nilai ticks to 1.75. - [11:50.849](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=710.8494374999998): titik4: one name gives way to another over the same drawing (label\_becomes). ##### [11:53.696](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=713.6959374999999) Narration: Kalau ada pecahan campuran, ubahlah dahulu ke pecahan biasa. Itu cara yang paling jarang membuat keliru. Board: Unchanged from the preceding beat in this scene. Actions: - [11:56.755](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=716.7554374999999): selisih (the "frac(13, 4)" part) is indicated — a transient flash. - [12:0.807](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=720.8069374999998): garis4 is hidden from the screen — left the board. - [12:0.807](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=720.8069374999998): angka is hidden from the screen — garis4 left the board. - [12:0.807](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=720.8069374999998): angka\_2 is hidden from the screen — garis4 left the board. - [12:0.807](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=720.8069374999998): angka\_3 is hidden from the screen — garis4 left the board. - [12:0.807](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=720.8069374999998): angka\_4 is hidden from the screen — garis4 left the board. - [12:0.807](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=720.8069374999998): angka\_5 is hidden from the screen — garis4 left the board. - [12:0.807](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=720.8069374999998): titik4 is hidden from the screen — garis4 left the board. - [12:0.807](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=720.8069374999998): head\_kurang is hidden from the screen — left the board. - [12:0.807](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=720.8069374999998): selisih is hidden from the screen — left the board. ##### [12:2.007](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=722.0069374999998) Narration: Sekarang satu soal cerita seperti di ujian. Ibu punya tiga per empat kilogram gula. Setengah kilogram dipakai untuk membuat kue. Berapa kilogram gula yang tersisa? Board: Empty. Actions: - [12:2.007](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=722.0069374999998): soal\_gula is shown on the screen, written out. - [12:5.571](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=725.5714374999998): gula is shown on the screen, written out. - [12:5.731](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=725.731342101571): rangka4 is shown on the screen, written out. - [12:5.811](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=725.8112944023567): rangka4\_2 is shown on the screen, written out. - [12:5.849](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=725.8494374999998): isi is shown on the screen, written out. - [12:5.906](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=725.9061055134679): rangka4\_3 is shown on the screen, written out. - [12:6.012](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=726.0119880050504): isi\_2 is shown on the screen, written out. - [12:6.014](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=726.0144725168349): rangka4\_4 is shown on the screen, written out. - [12:6.171](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=726.1711268939392): isi\_3 is shown on the screen, written out. ##### [12:14.054](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=734.0539374999998) Narration: Gula ibu digambarkan sebagai tiga dari empat bagian. Setengah kilogram sama dengan dua dari empat bagian, jadi dua bagian itu diambil. Board: gula — a Figure (x\_range=(0.0, 4.0), y\_range=(-0.2, 1.4), aspect=(4.0, 1.6)); soal\_gula — a Panel that says "Ibu punya $frac(3, 4)$ kg gula. Sebanyak $frac(1, 2)$ kg dipakai untuk membuat kue. Berapa kilogram gula yang tersisa?"; rangka4 — a Polygon \[gray\] drawn in gula (vertices=((0, 0.1), (1, 0.1), (1, 1.1), (0, 1.1)), filled=False); rangka4\_2 — a Polygon \[gray\] drawn in gula (vertices=((1, 0.1), (2, 0.1), (2, 1.1), (1, 1.1)), filled=False); rangka4\_3 — a Polygon \[gray\] drawn in gula (vertices=((2, 0.1), (3, 0.1), (3, 1.1), (2, 1.1)), filled=False); rangka4\_4 — a Polygon \[gray\] drawn in gula (vertices=((3, 0.1), (4, 0.1), (4, 1.1), (3, 1.1)), filled=False); isi — a Polygon \[green\] drawn in gula (vertices=((0, 0.1), (1, 0.1), (1, 1.1), (0, 1.1)), fill\_opacity=0.5); isi\_2 — a Polygon \[green\] drawn in gula (vertices=((1, 0.1), (2, 0.1), (2, 1.1), (1, 1.1)), fill\_opacity=0.5); isi\_3 — a Polygon \[green\] drawn in gula (vertices=((2, 0.1), (3, 0.1), (3, 1.1), (2, 1.1)), fill\_opacity=0.5) Actions: - [12:21.844](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=741.8444374999999): isi\_2 is hidden from the screen. - [12:22.198](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=742.1980889232383): isi\_3 is hidden from the screen. ##### [12:23.455](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=743.4549374999999) Narration: Tinggal satu bagian dari empat. Mari kita periksa dengan hitungan: tiga per empat dikurangi setengah, dan setengah sama dengan dua per empat. Board: gula — a Figure (x\_range=(0.0, 4.0), y\_range=(-0.2, 1.4), aspect=(4.0, 1.6)); soal\_gula — a Panel that says "Ibu punya $frac(3, 4)$ kg gula. Sebanyak $frac(1, 2)$ kg dipakai untuk membuat kue. Berapa kilogram gula yang tersisa?"; rangka4 — a Polygon \[gray\] drawn in gula (vertices=((0, 0.1), (1, 0.1), (1, 1.1), (0, 1.1)), filled=False); rangka4\_2 — a Polygon \[gray\] drawn in gula (vertices=((1, 0.1), (2, 0.1), (2, 1.1), (1, 1.1)), filled=False); rangka4\_3 — a Polygon \[gray\] drawn in gula (vertices=((2, 0.1), (3, 0.1), (3, 1.1), (2, 1.1)), filled=False); rangka4\_4 — a Polygon \[gray\] drawn in gula (vertices=((3, 0.1), (4, 0.1), (4, 1.1), (3, 1.1)), filled=False); isi — a Polygon \[green\] drawn in gula (vertices=((0, 0.1), (1, 0.1), (1, 1.1), (0, 1.1)), fill\_opacity=0.5) Actions: - [12:27.274](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=747.2744374999999): gula moves to a new place on the board. - [12:27.274](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=747.2744374999999): sisa\_kerja is shown on the screen, written out. ##### [12:33.784](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=753.7839374999999) Narration: Tiga per empat dikurangi dua per empat sama dengan satu per empat. Jadi sisa gula ibu satu per empat kilogram, sesuai gambar. Board: Unchanged from the preceding beat in this scene. Actions: - [12:36.895](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=756.8954374999998): sisa\_kerja is shown on the screen, written out. - [12:38.532](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=758.5324374999999): jawab is shown on the screen, written out. - [12:41.573](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=761.5734374999998): A box is drawn around jawab. ##### [12:43.114](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=763.1139374999999) Narration: Untuk penjumlahan dan pengurangan, kuncinya satu: penyebut harus sama dahulu. Sesudah itu pekerjaannya mudah. Berikutnya kita belajar perkalian dan pembagian pecahan. Board: jawab — a Math \[text\] that says "$frac(1, 4) thin upright("kg")$"; gula — a Figure (x\_range=(0.0, 4.0), y\_range=(-0.2, 1.4), aspect=(4.0, 1.6)); soal\_gula — a Panel that says "Ibu punya $frac(3, 4)$ kg gula. Sebanyak $frac(1, 2)$ kg dipakai untuk membuat kue. Berapa kilogram gula yang tersisa?"; rangka4 — a Polygon \[gray\] drawn in gula (vertices=((0, 0.1), (1, 0.1), (1, 1.1), (0, 1.1)), filled=False); rangka4\_2 — a Polygon \[gray\] drawn in gula (vertices=((1, 0.1), (2, 0.1), (2, 1.1), (1, 1.1)), filled=False); rangka4\_3 — a Polygon \[gray\] drawn in gula (vertices=((2, 0.1), (3, 0.1), (3, 1.1), (2, 1.1)), filled=False); rangka4\_4 — a Polygon \[gray\] drawn in gula (vertices=((3, 0.1), (4, 0.1), (4, 1.1), (3, 1.1)), filled=False); isi — a Polygon \[green\] drawn in gula (vertices=((0, 0.1), (1, 0.1), (1, 1.1), (0, 1.1)), fill\_opacity=0.5) Actions: - [12:50.405](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=770.4054374999998): isi is indicated — a transient flash. - [12:55.291](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=775.2907291666666): gula is hidden from the screen — left the board. - [12:55.291](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=775.2907291666666): rangka4 is hidden from the screen — gula left the board. - [12:55.291](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=775.2907291666666): rangka4\_2 is hidden from the screen — gula left the board. - [12:55.291](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=775.2907291666666): rangka4\_3 is hidden from the screen — gula left the board. - [12:55.291](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=775.2907291666666): rangka4\_4 is hidden from the screen — gula left the board. - [12:55.291](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=775.2907291666666): isi is hidden from the screen — gula left the board. - [12:55.291](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=775.2907291666666): jawab is hidden from the screen — left the board. - [12:55.291](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=775.2907291666666): sisa\_kerja is hidden from the screen — left the board. - [12:55.291](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=775.2907291666666): soal\_gula is hidden from the screen — left the board. ### Scene 5: [Perkalian dan Pembagian Pecahan](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=776.3323958333332) Span: 12:56.332–16:48.966 (776.3323958333332s–1008.9660624999998s). #### Objects - aturan\_bagi: a Panel that says "Membagi dengan sebuah pecahan sama dengan mengalikan dengan kebalikannya." - aturan\_kali: a Panel that says "Kalikan pembilang dengan pembilang, dan penyebut dengan penyebut. Sederhanakan bila masih bisa." - bagi: a Derivation \[text\] that says "$frac(3, 4) : frac(1, 2) &= frac(3, 4) times frac(2, 1) \\ &= frac(6, 4) \\ &= 1 frac(1, 2)$" - bagi\_asli: a Derivation \[text\] that says "$frac(2, 3) : 4 &= frac(2, 3) times frac(1, 4) \\ &= frac(2, 12) = frac(1, 6)$" - garis20: a NumberLine (x\_range=(0.0, 20.0), include\_numbers=True, ticks\_every=5.0) - gunting: a Figure (x\_range=(0.0, 8.0), y\_range=(-0.2, 1.2), aspect=(8.0, 1.4)) - head\_bagi: a Heading that says "Pembagian Pecahan" - head\_ingat: a Heading that says "Yang Perlu Diingat" - head\_kali: a Heading that says "Perkalian Pecahan" - ingat: a Block \[text\] that says "Bilangan cacah: kurung dahulu, lalu kali dan bagi, baru tambah dan kurang. Satu nilai bisa ditulis sebagai pecahan, desimal, atau persen. Membandingkan pecahan: samakan penyebutnya, atau ubah ke persen. Tambah dan kurang pecahan: samakan p…" - isi\_pita: a Polygon \[blue\] drawn in pita (vertices=((0, 1.2), (1, 1.2), (1, 2.1), (0, 2.1)), fill\_opacity=0.45) - isi\_pita\_2: a Polygon \[blue\] drawn in pita (vertices=((1, 1.2), (2, 1.2), (2, 2.1), (1, 2.1)), fill\_opacity=0.45) - isi\_pita\_3: a Polygon \[blue\] drawn in pita (vertices=((2, 1.2), (3, 1.2), (3, 2.1), (2, 2.1)), fill\_opacity=0.45) - jawab\_potong: a Math \[text\] that says "$8 thin upright("potong")$" - kali: a Derivation \[text\] that says "$frac(3, 4) times frac(2, 3) &= frac(3 times 2, 4 times 3) \\ &= frac(6, 12) \\ &= frac(1, 2)$" - kali\_asli: a Derivation \[text\] that says "$frac(3, 4) times 20 &= frac(3, 4) times frac(20, 1) \\ &= frac(60, 4) \\ &= 15$" - kisi: a Polygon \[gray\] drawn in luas (vertices=((0, 0), (1, 0), (1, 1), (0, 1)), filled=False) - kisi\_10: a Polygon \[gray\] drawn in luas (vertices=((1, 2), (2, 2), (2, 3), (1, 3)), filled=False) - kisi\_11: a Polygon \[gray\] drawn in luas (vertices=((2, 2), (3, 2), (3, 3), (2, 3)), filled=False) - kisi\_12: a Polygon \[gray\] drawn in luas (vertices=((3, 2), (4, 2), (4, 3), (3, 3)), filled=False) - kisi\_2: a Polygon \[gray\] drawn in luas (vertices=((1, 0), (2, 0), (2, 1), (1, 1)), filled=False) - kisi\_3: a Polygon \[gray\] drawn in luas (vertices=((2, 0), (3, 0), (3, 1), (2, 1)), filled=False) - kisi\_4: a Polygon \[gray\] drawn in luas (vertices=((3, 0), (4, 0), (4, 1), (3, 1)), filled=False) - kisi\_5: a Polygon \[gray\] drawn in luas (vertices=((0, 1), (1, 1), (1, 2), (0, 2)), filled=False) - kisi\_6: a Polygon \[gray\] drawn in luas (vertices=((1, 1), (2, 1), (2, 2), (1, 2)), filled=False) - kisi\_7: a Polygon \[gray\] drawn in luas (vertices=((2, 1), (3, 1), (3, 2), (2, 2)), filled=False) - kisi\_8: a Polygon \[gray\] drawn in luas (vertices=((3, 1), (4, 1), (4, 2), (3, 2)), filled=False) - kisi\_9: a Polygon \[gray\] drawn in luas (vertices=((0, 2), (1, 2), (1, 3), (0, 3)), filled=False) - luas: a Figure (x\_range=(-0.9, 4.2), y\_range=(-0.8, 3.2), aspect=(5.1, 4.0)) - nama\_datar: a Math \[text\] that says "$frac(3, 4)$" drawn in luas - nama\_tegak: a Math \[text\] that says "$frac(2, 3)$" drawn in luas - penutup: a Text \[text\] that says "Kerjakan langkah demi langkah, dan tulis setiap baris dengan rapi." - pita: a Figure (x\_range=(0.0, 4.0), y\_range=(-0.2, 2.4), aspect=(4.0, 2.6)) - potong: a Derivation \[text\] that says "$frac(4, 5) : frac(1, 10) &= frac(4, 5) times frac(10, 1) \\ &= frac(40, 5) \\ &= 8$" - potongan: a Polygon \[blue\] drawn in gunting (vertices=((0, 0.1), (1, 0.1), (1, 0.9), (0, 0.9)), fill\_opacity=0.4) - potongan\_2: a Polygon \[blue\] drawn in gunting (vertices=((1, 0.1), (2, 0.1), (2, 0.9), (1, 0.9)), fill\_opacity=0.4) - potongan\_3: a Polygon \[blue\] drawn in gunting (vertices=((2, 0.1), (3, 0.1), (3, 0.9), (2, 0.9)), fill\_opacity=0.4) - potongan\_4: a Polygon \[blue\] drawn in gunting (vertices=((3, 0.1), (4, 0.1), (4, 0.9), (3, 0.9)), fill\_opacity=0.4) - potongan\_5: a Polygon \[blue\] drawn in gunting (vertices=((4, 0.1), (5, 0.1), (5, 0.9), (4, 0.9)), fill\_opacity=0.4) - potongan\_6: a Polygon \[blue\] drawn in gunting (vertices=((5, 0.1), (6, 0.1), (6, 0.9), (5, 0.9)), fill\_opacity=0.4) - potongan\_7: a Polygon \[blue\] drawn in gunting (vertices=((6, 0.1), (7, 0.1), (7, 0.9), (6, 0.9)), fill\_opacity=0.4) - potongan\_8: a Polygon \[blue\] drawn in gunting (vertices=((7, 0.1), (8, 0.1), (8, 0.9), (7, 0.9)), fill\_opacity=0.4) - rangka\_pita: a Polygon \[gray\] drawn in pita (vertices=((0, 1.2), (1, 1.2), (1, 2.1), (0, 2.1)), filled=False) - rangka\_pita\_2: a Polygon \[gray\] drawn in pita (vertices=((1, 1.2), (2, 1.2), (2, 2.1), (1, 2.1)), filled=False) - rangka\_pita\_3: a Polygon \[gray\] drawn in pita (vertices=((2, 1.2), (3, 1.2), (3, 2.1), (2, 2.1)), filled=False) - rangka\_pita\_4: a Polygon \[gray\] drawn in pita (vertices=((3, 1.2), (4, 1.2), (4, 2.1), (3, 2.1)), filled=False) - sisa\_ukur: a Polygon \[green\] drawn in pita (vertices=((2.0, 0.1), (3.0, 0.1), (3.0, 1.0), (2.0, 1.0)), fill\_opacity=0.35) - soal\_asli: a Panel that says "Dari 20 soal, $frac(3, 4)$ bagian sudah dikerjakan. Berapa soal yang sudah dikerjakan?" - soal\_pita: a Panel that says "Pita sepanjang $frac(4, 5)$ meter dipotong menjadi bagian sepanjang $frac(1, 10)$ meter. Berapa potong pita yang didapat?" - titik15: a Point \[red\] labelled "15" drawn in garis20 (location=(15.0, 0.0)) - tumpang: a Polygon \[red\] drawn in luas (vertices=((0, 0), (1, 0), (1, 1), (0, 1)), fill\_opacity=0.4) - tumpang\_2: a Polygon \[red\] drawn in luas (vertices=((1, 0), (2, 0), (2, 1), (1, 1)), fill\_opacity=0.4) - tumpang\_3: a Polygon \[red\] drawn in luas (vertices=((2, 0), (3, 0), (3, 1), (2, 1)), fill\_opacity=0.4) - tumpang\_4: a Polygon \[red\] drawn in luas (vertices=((0, 1), (1, 1), (1, 2), (0, 2)), fill\_opacity=0.4) - tumpang\_5: a Polygon \[red\] drawn in luas (vertices=((1, 1), (2, 1), (2, 2), (1, 2)), fill\_opacity=0.4) - tumpang\_6: a Polygon \[red\] drawn in luas (vertices=((2, 1), (3, 1), (3, 2), (2, 2)), fill\_opacity=0.4) - ukur: a Polygon \[green\] drawn in pita (vertices=((0, 0.1), (2, 0.1), (2, 1.0), (0, 1.0)), filled=False) - ukur\_2: a Polygon \[green\] drawn in pita (vertices=((2, 0.1), (4, 0.1), (4, 1.0), (2, 1.0)), filled=False) #### Beats ##### [12:56.332](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=776.3323958333332) Narration: Sekarang perkalian pecahan, dan ini justru lebih mudah daripada penjumlahan, karena penyebutnya tidak perlu disamakan. Board: Empty. Actions: - [12:56.332](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=776.3323958333332): head\_kali is shown on the screen, written out. - [12:56.332](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=776.3323958333332): luas is shown on the screen, written out. ##### [13:4.189](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=784.1888958333332) Narration: Bayangkan sebuah persegi. Sisi datarnya dibagi empat dan sisi tegaknya dibagi tiga, sehingga ada dua belas kotak kecil. Board: luas — a Figure (x\_range=(-0.9, 4.2), y\_range=(-0.8, 3.2), aspect=(5.1, 4.0)); head\_kali — a Heading that says "Perkalian Pecahan" Actions: - [13:11.027](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=791.0273958333332): kisi is shown on the screen, written out. - [13:11.102](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=791.1024821394321): kisi\_2 is shown on the screen, written out. - [13:11.178](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=791.1775684455312): kisi\_3 is shown on the screen, written out. - [13:11.253](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=791.2526547516301): kisi\_4 is shown on the screen, written out. - [13:11.323](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=791.3234602752204): kisi\_5 is shown on the screen, written out. - [13:11.367](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=791.3674763856923): kisi\_6 is shown on the screen, written out. - [13:11.411](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=791.411492496164): kisi\_7 is shown on the screen, written out. - [13:11.456](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=791.4555086066358): kisi\_8 is shown on the screen, written out. - [13:11.5](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=791.4995247171076): kisi\_9 is shown on the screen, written out. - [13:11.544](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=791.5435408275795): kisi\_10 is shown on the screen, written out. - [13:11.587](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=791.5869029296124): kisi\_11 is shown on the screen, written out. - [13:11.629](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=791.629020305907): kisi\_12 is shown on the screen, written out. ##### [13:13.072](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=793.0718958333332) Narration: Tiga per empat diambil ke arah datar, dan dua per tiga ke arah tegak. Daerah yang bertumpang berisi enam kotak. Board: luas — a Figure (x\_range=(-0.9, 4.2), y\_range=(-0.8, 3.2), aspect=(5.1, 4.0)); head\_kali — a Heading that says "Perkalian Pecahan"; kisi — a Polygon \[gray\] drawn in luas (vertices=((0, 0), (1, 0), (1, 1), (0, 1)), filled=False); kisi\_2 — a Polygon \[gray\] drawn in luas (vertices=((1, 0), (2, 0), (2, 1), (1, 1)), filled=False); kisi\_3 — a Polygon \[gray\] drawn in luas (vertices=((2, 0), (3, 0), (3, 1), (2, 1)), filled=False); kisi\_4 — a Polygon \[gray\] drawn in luas (vertices=((3, 0), (4, 0), (4, 1), (3, 1)), filled=False); kisi\_5 — a Polygon \[gray\] drawn in luas (vertices=((0, 1), (1, 1), (1, 2), (0, 2)), filled=False); kisi\_6 — a Polygon \[gray\] drawn in luas (vertices=((1, 1), (2, 1), (2, 2), (1, 2)), filled=False); kisi\_7 — a Polygon \[gray\] drawn in luas (vertices=((2, 1), (3, 1), (3, 2), (2, 2)), filled=False); kisi\_8 — a Polygon \[gray\] drawn in luas (vertices=((3, 1), (4, 1), (4, 2), (3, 2)), filled=False); kisi\_9 — a Polygon \[gray\] drawn in luas (vertices=((0, 2), (1, 2), (1, 3), (0, 3)), filled=False); kisi\_10 — a Polygon \[gray\] drawn in luas (vertices=((1, 2), (2, 2), (2, 3), (1, 3)), filled=False); kisi\_11 — a Polygon \[gray\] drawn in luas (vertices=((2, 2), (3, 2), (3, 3), (2, 3)), filled=False); kisi\_12 — a Polygon \[gray\] drawn in luas (vertices=((3, 2), (4, 2), (4, 3), (3, 3)), filled=False) Actions: - [13:14.9](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=794.9003958333332): nama\_datar is shown on the screen, written out. - [13:16.979](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=796.9793958333332): nama\_tegak is shown on the screen, written out. - [13:19.324](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=799.3243958333331): tumpang is shown on the screen, written out. - [13:19.412](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=799.4124352907932): tumpang\_2 is shown on the screen, written out. - [13:19.5](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=799.500474748253): tumpang\_3 is shown on the screen, written out. - [13:19.595](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=799.5953692534367): tumpang\_4 is shown on the screen, written out. - [13:19.75](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=799.7495953785739): tumpang\_5 is shown on the screen, written out. - [13:19.904](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=799.9038215037111): tumpang\_6 is shown on the screen, written out. ##### [13:20.882](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=800.8818958333331) Narration: Enam dari dua belas kotak. Aturannya memang begitu: pembilang dikali pembilang, dan penyebut dikali penyebut. Board: luas — a Figure (x\_range=(-0.9, 4.2), y\_range=(-0.8, 3.2), aspect=(5.1, 4.0)); head\_kali — a Heading that says "Perkalian Pecahan"; kisi — a Polygon \[gray\] drawn in luas (vertices=((0, 0), (1, 0), (1, 1), (0, 1)), filled=False); kisi\_2 — a Polygon \[gray\] drawn in luas (vertices=((1, 0), (2, 0), (2, 1), (1, 1)), filled=False); kisi\_3 — a Polygon \[gray\] drawn in luas (vertices=((2, 0), (3, 0), (3, 1), (2, 1)), filled=False); kisi\_4 — a Polygon \[gray\] drawn in luas (vertices=((3, 0), (4, 0), (4, 1), (3, 1)), filled=False); kisi\_5 — a Polygon \[gray\] drawn in luas (vertices=((0, 1), (1, 1), (1, 2), (0, 2)), filled=False); kisi\_6 — a Polygon \[gray\] drawn in luas (vertices=((1, 1), (2, 1), (2, 2), (1, 2)), filled=False); kisi\_7 — a Polygon \[gray\] drawn in luas (vertices=((2, 1), (3, 1), (3, 2), (2, 2)), filled=False); kisi\_8 — a Polygon \[gray\] drawn in luas (vertices=((3, 1), (4, 1), (4, 2), (3, 2)), filled=False); kisi\_9 — a Polygon \[gray\] drawn in luas (vertices=((0, 2), (1, 2), (1, 3), (0, 3)), filled=False); kisi\_10 — a Polygon \[gray\] drawn in luas (vertices=((1, 2), (2, 2), (2, 3), (1, 3)), filled=False); kisi\_11 — a Polygon \[gray\] drawn in luas (vertices=((2, 2), (3, 2), (3, 3), (2, 3)), filled=False); kisi\_12 — a Polygon \[gray\] drawn in luas (vertices=((3, 2), (4, 2), (4, 3), (3, 3)), filled=False); nama\_datar — a Math \[text\] that says "$frac(3, 4)$" drawn in luas; nama\_tegak — a Math \[text\] that says "$frac(2, 3)$" drawn in luas; tumpang — a Polygon \[red\] drawn in luas (vertices=((0, 0), (1, 0), (1, 1), (0, 1)), fill\_opacity=0.4); tumpang\_2 — a Polygon \[red\] drawn in luas (vertices=((1, 0), (2, 0), (2, 1), (1, 1)), fill\_opacity=0.4); tumpang\_3 — a Polygon \[red\] drawn in luas (vertices=((2, 0), (3, 0), (3, 1), (2, 1)), fill\_opacity=0.4); tumpang\_4 — a Polygon \[red\] drawn in luas (vertices=((0, 1), (1, 1), (1, 2), (0, 2)), fill\_opacity=0.4); tumpang\_5 — a Polygon \[red\] drawn in luas (vertices=((1, 1), (2, 1), (2, 2), (1, 2)), fill\_opacity=0.4); tumpang\_6 — a Polygon \[red\] drawn in luas (vertices=((2, 1), (3, 1), (3, 2), (2, 2)), fill\_opacity=0.4) Actions: - [13:24.545](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=804.5453958333331): luas moves to a new place on the board. - [13:24.545](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=804.5453958333331): kali is shown on the screen, written out. ##### [13:28.454](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=808.4538958333331) Narration: Tiga kali dua sama dengan enam, empat kali tiga sama dengan dua belas. Jadi hasilnya enam per dua belas. Board: Unchanged from the preceding beat in this scene. Actions: - [13:33.353](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=813.3533958333331): kali is shown on the screen, written out. ##### [13:35.753](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=815.7528958333331) Narration: Enam per dua belas masih bisa disederhanakan: bagi keduanya dengan enam, hasilnya setengah. Aturan ini singkat, dan berlaku untuk semua perkalian pecahan. Board: Unchanged from the preceding beat in this scene. Actions: - [13:40.072](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=820.0723958333332): kali is shown on the screen, written out. - [13:42.196](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=822.1963958333332): aturan\_kali is shown on the screen, written out. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): aturan\_kali is hidden from the screen — left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): head\_kali is hidden from the screen — left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): kali is hidden from the screen — left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): luas is hidden from the screen — left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): kisi is hidden from the screen — luas left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): kisi\_2 is hidden from the screen — luas left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): kisi\_3 is hidden from the screen — luas left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): kisi\_4 is hidden from the screen — luas left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): kisi\_5 is hidden from the screen — luas left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): kisi\_6 is hidden from the screen — luas left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): kisi\_7 is hidden from the screen — luas left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): kisi\_8 is hidden from the screen — luas left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): kisi\_9 is hidden from the screen — luas left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): kisi\_10 is hidden from the screen — luas left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): kisi\_11 is hidden from the screen — luas left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): kisi\_12 is hidden from the screen — luas left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): nama\_datar is hidden from the screen — luas left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): nama\_tegak is hidden from the screen — luas left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): tumpang is hidden from the screen — luas left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): tumpang\_2 is hidden from the screen — luas left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): tumpang\_3 is hidden from the screen — luas left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): tumpang\_4 is hidden from the screen — luas left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): tumpang\_5 is hidden from the screen — luas left the board. - [13:45.54](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=825.5403958333332): tumpang\_6 is hidden from the screen — luas left the board. ##### [13:46.74](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=826.7403958333332) Narration: Perkalian pecahan dengan bilangan asli caranya sama. Dari dua puluh soal, tiga per empat bagian sudah dikerjakan. Berapa soal itu? Board: Empty. Actions: - [13:46.74](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=826.7403958333332): soal\_asli is shown on the screen, written out. - [13:51.001](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=831.0013958333332): garis20 is shown on the screen, written out. ##### [13:56.675](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=836.6748958333332) Narration: Tulis dua puluh sebagai dua puluh per satu, lalu kalikan seperti biasa. Board: garis20 — a NumberLine (x\_range=(0.0, 20.0), include\_numbers=True, ticks\_every=5.0); soal\_asli — a Panel that says "Dari 20 soal, $frac(3, 4)$ bagian sudah dikerjakan. Berapa soal yang sudah dikerjakan?" Actions: - [13:59.891](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=839.8913958333331): garis20 moves to a new place on the board. - [13:59.891](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=839.8913958333331): kali\_asli is shown on the screen, written out. ##### [14:2.082](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=842.0818958333332) Narration: Tiga kali dua puluh sama dengan enam puluh, dan empat kali satu sama dengan empat. Enam puluh per empat sama dengan lima belas. Board: Unchanged from the preceding beat in this scene. Actions: - [14:5.82](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=845.8203958333331): kali\_asli is shown on the screen, written out. - [14:9.013](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=849.0133958333331): kali\_asli is shown on the screen, written out. ##### [14:10.855](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=850.8553958333332) Narration: Jadi lima belas soal sudah dikerjakan, dan pada garis bilangan letaknya di sini, tiga per empat dari dua puluh. Board: Unchanged from the preceding beat in this scene. Actions: - [14:12.562](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=852.5623958333332): A box is drawn around kali\_asli. - [14:15.209](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=855.2093958333331): titik15 is shown on the screen, written out. - [14:15.859](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=855.8593958333331): The segment (0.0, 0.0) to (15.0, 0.0) in garis20 is lit up. - [14:16.66](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=856.6603958333332): garis20: retire a lit segment (unemphasize\_line). - [14:17.961](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=857.9608958333332): garis20 is hidden from the screen — left the board. - [14:17.961](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=857.9608958333332): titik15 is hidden from the screen — garis20 left the board. - [14:17.961](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=857.9608958333332): kali\_asli is hidden from the screen — left the board. - [14:17.961](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=857.9608958333332): soal\_asli is hidden from the screen — left the board. ##### [14:19.161](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=859.1608958333331) Narration: Sekarang pembagian, bagian yang paling sering ditanyakan. Pertanyaannya begini: ada berapa bagian setengah di dalam tiga per empat? Board: Empty. Actions: - [14:19.161](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=859.1608958333331): head\_bagi is shown on the screen, written out. - [14:19.161](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=859.1608958333331): pita is shown on the screen, written out. - [14:23.816](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=863.8163958333332): rangka\_pita is shown on the screen, written out. - [14:24.057](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=864.0569489191072): rangka\_pita\_2 is shown on the screen, written out. - [14:24.298](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=864.2975020048813): rangka\_pita\_3 is shown on the screen, written out. - [14:24.538](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=864.5380550906552): rangka\_pita\_4 is shown on the screen, written out. - [14:26.73](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=866.7303958333332): isi\_pita is shown on the screen, written out. - [14:26.875](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=866.8748571304043): isi\_pita\_2 is shown on the screen, written out. - [14:27.015](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=867.0150417538352): isi\_pita\_3 is shown on the screen, written out. ##### [14:28.515](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=868.5148958333332) Narration: Pita atas menunjukkan tiga per empat. Kotak hijau di bawahnya panjangnya setengah pita utuh. Board: pita — a Figure (x\_range=(0.0, 4.0), y\_range=(-0.2, 2.4), aspect=(4.0, 2.6)); head\_bagi — a Heading that says "Pembagian Pecahan"; rangka\_pita — a Polygon \[gray\] drawn in pita (vertices=((0, 1.2), (1, 1.2), (1, 2.1), (0, 2.1)), filled=False); rangka\_pita\_2 — a Polygon \[gray\] drawn in pita (vertices=((1, 1.2), (2, 1.2), (2, 2.1), (1, 2.1)), filled=False); rangka\_pita\_3 — a Polygon \[gray\] drawn in pita (vertices=((2, 1.2), (3, 1.2), (3, 2.1), (2, 2.1)), filled=False); rangka\_pita\_4 — a Polygon \[gray\] drawn in pita (vertices=((3, 1.2), (4, 1.2), (4, 2.1), (3, 2.1)), filled=False); isi\_pita — a Polygon \[blue\] drawn in pita (vertices=((0, 1.2), (1, 1.2), (1, 2.1), (0, 2.1)), fill\_opacity=0.45); isi\_pita\_2 — a Polygon \[blue\] drawn in pita (vertices=((1, 1.2), (2, 1.2), (2, 2.1), (1, 2.1)), fill\_opacity=0.45); isi\_pita\_3 — a Polygon \[blue\] drawn in pita (vertices=((2, 1.2), (3, 1.2), (3, 2.1), (2, 2.1)), fill\_opacity=0.45) Actions: - [14:32.241](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=872.2413958333332): ukur is shown on the screen, written out. - [14:32.397](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=872.3967987297312): ukur\_2 is shown on the screen, written out. ##### [14:35.755](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=875.7553958333332) Narration: Kotak hijau pertama masuk seluruhnya. Kotak kedua hanya terisi separuh. Jadi jawabannya satu setengah. Board: pita — a Figure (x\_range=(0.0, 4.0), y\_range=(-0.2, 2.4), aspect=(4.0, 2.6)); head\_bagi — a Heading that says "Pembagian Pecahan"; rangka\_pita — a Polygon \[gray\] drawn in pita (vertices=((0, 1.2), (1, 1.2), (1, 2.1), (0, 2.1)), filled=False); rangka\_pita\_2 — a Polygon \[gray\] drawn in pita (vertices=((1, 1.2), (2, 1.2), (2, 2.1), (1, 2.1)), filled=False); rangka\_pita\_3 — a Polygon \[gray\] drawn in pita (vertices=((2, 1.2), (3, 1.2), (3, 2.1), (2, 2.1)), filled=False); rangka\_pita\_4 — a Polygon \[gray\] drawn in pita (vertices=((3, 1.2), (4, 1.2), (4, 2.1), (3, 2.1)), filled=False); isi\_pita — a Polygon \[blue\] drawn in pita (vertices=((0, 1.2), (1, 1.2), (1, 2.1), (0, 2.1)), fill\_opacity=0.45); isi\_pita\_2 — a Polygon \[blue\] drawn in pita (vertices=((1, 1.2), (2, 1.2), (2, 2.1), (1, 2.1)), fill\_opacity=0.45); isi\_pita\_3 — a Polygon \[blue\] drawn in pita (vertices=((2, 1.2), (3, 1.2), (3, 2.1), (2, 2.1)), fill\_opacity=0.45); ukur — a Polygon \[green\] drawn in pita (vertices=((0, 0.1), (2, 0.1), (2, 1.0), (0, 1.0)), filled=False); ukur\_2 — a Polygon \[green\] drawn in pita (vertices=((2, 0.1), (4, 0.1), (4, 1.0), (2, 1.0)), filled=False) Actions: - [14:36.742](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=876.7423958333331): ukur is indicated — a transient flash. - [14:39.946](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=879.9463958333331): sisa\_ukur is shown on the screen, written out. ##### [14:43.507](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=883.5068958333331) Narration: Dengan hitungan, membagi dengan setengah sama dengan mengalikan dengan dua per satu, yaitu kebalikannya. Board: pita — a Figure (x\_range=(0.0, 4.0), y\_range=(-0.2, 2.4), aspect=(4.0, 2.6)); head\_bagi — a Heading that says "Pembagian Pecahan"; rangka\_pita — a Polygon \[gray\] drawn in pita (vertices=((0, 1.2), (1, 1.2), (1, 2.1), (0, 2.1)), filled=False); rangka\_pita\_2 — a Polygon \[gray\] drawn in pita (vertices=((1, 1.2), (2, 1.2), (2, 2.1), (1, 2.1)), filled=False); rangka\_pita\_3 — a Polygon \[gray\] drawn in pita (vertices=((2, 1.2), (3, 1.2), (3, 2.1), (2, 2.1)), filled=False); rangka\_pita\_4 — a Polygon \[gray\] drawn in pita (vertices=((3, 1.2), (4, 1.2), (4, 2.1), (3, 2.1)), filled=False); isi\_pita — a Polygon \[blue\] drawn in pita (vertices=((0, 1.2), (1, 1.2), (1, 2.1), (0, 2.1)), fill\_opacity=0.45); isi\_pita\_2 — a Polygon \[blue\] drawn in pita (vertices=((1, 1.2), (2, 1.2), (2, 2.1), (1, 2.1)), fill\_opacity=0.45); isi\_pita\_3 — a Polygon \[blue\] drawn in pita (vertices=((2, 1.2), (3, 1.2), (3, 2.1), (2, 2.1)), fill\_opacity=0.45); ukur — a Polygon \[green\] drawn in pita (vertices=((0, 0.1), (2, 0.1), (2, 1.0), (0, 1.0)), filled=False); ukur\_2 — a Polygon \[green\] drawn in pita (vertices=((2, 0.1), (4, 0.1), (4, 1.0), (2, 1.0)), filled=False); sisa\_ukur — a Polygon \[green\] drawn in pita (vertices=((2.0, 0.1), (3.0, 0.1), (3.0, 1.0), (2.0, 1.0)), fill\_opacity=0.35) Actions: - [14:48.928](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=888.9283958333332): pita moves to a new place on the board. - [14:48.928](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=888.9283958333332): bagi is shown on the screen, written out. ##### [14:50.631](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=890.6313958333332) Narration: Tiga per empat kali dua per satu sama dengan enam per empat, dan enam per empat sama dengan satu setengah, tepat seperti gambar. Board: Unchanged from the preceding beat in this scene. Actions: - [14:53.394](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=893.3943958333332): bagi is shown on the screen, written out. - [14:55.647](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=895.6473958333331): bagi is shown on the screen, written out. - [14:58.306](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=898.3058958333331): bagi is hidden from the screen — left the board. ##### [14:58.906](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=898.9058958333331) Narration: Kalau pembaginya bilangan asli, caranya juga sama. Dua per tiga dibagi empat berarti dua per tiga kali seperempat, hasilnya dua per dua belas, atau seperenam. Board: Unchanged from the preceding beat in this scene. Actions: - [15:5.639](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=905.6393958333332): bagi\_asli is shown on the screen, written out. - [15:8.576](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=908.5763958333332): bagi\_asli is shown on the screen, written out. ##### [15:10.291](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=910.2913958333331) Narration: Ingat kalimatnya: bagi berubah menjadi kali, dan pecahan pembaginya dibalik. Board: Unchanged from the preceding beat in this scene. Actions: - [15:11.069](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=911.0693958333331): aturan\_bagi is shown on the screen, written out. - [15:15.481](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=915.4808958333332): aturan\_bagi is hidden from the screen — left the board. - [15:15.481](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=915.4808958333332): bagi\_asli is hidden from the screen — left the board. - [15:15.481](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=915.4808958333332): head\_bagi is hidden from the screen — left the board. - [15:15.481](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=915.4808958333332): pita is hidden from the screen — left the board. - [15:15.481](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=915.4808958333332): rangka\_pita is hidden from the screen — pita left the board. - [15:15.481](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=915.4808958333332): rangka\_pita\_2 is hidden from the screen — pita left the board. - [15:15.481](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=915.4808958333332): rangka\_pita\_3 is hidden from the screen — pita left the board. - [15:15.481](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=915.4808958333332): rangka\_pita\_4 is hidden from the screen — pita left the board. - [15:15.481](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=915.4808958333332): isi\_pita is hidden from the screen — pita left the board. - [15:15.481](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=915.4808958333332): isi\_pita\_2 is hidden from the screen — pita left the board. - [15:15.481](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=915.4808958333332): isi\_pita\_3 is hidden from the screen — pita left the board. - [15:15.481](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=915.4808958333332): ukur is hidden from the screen — pita left the board. - [15:15.481](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=915.4808958333332): ukur\_2 is hidden from the screen — pita left the board. - [15:15.481](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=915.4808958333332): sisa\_ukur is hidden from the screen — pita left the board. ##### [15:16.681](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=916.6808958333331) Narration: Satu soal cerita lagi. Pita sepanjang empat per lima meter dipotong menjadi bagian sepanjang satu per sepuluh meter. Berapa potong yang didapat? Board: Empty. Actions: - [15:16.681](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=916.6808958333331): soal\_pita is shown on the screen, written out. - [15:21.22](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=921.2203958333332): gunting is shown on the screen, written out. ##### [15:26.94](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=926.9403958333332) Narration: Ini pembagian: empat per lima dibagi satu per sepuluh. Ubahlah menjadi perkalian dengan kebalikannya, yaitu sepuluh per satu. Board: gunting — a Figure (x\_range=(0.0, 8.0), y\_range=(-0.2, 1.2), aspect=(8.0, 1.4)); soal\_pita — a Panel that says "Pita sepanjang $frac(4, 5)$ meter dipotong menjadi bagian sepanjang $frac(1, 10)$ meter. Berapa potong pita yang didapat?" Actions: - [15:32.664](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=932.6643958333332): gunting moves to a new place on the board. - [15:32.664](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=932.6643958333332): potong is shown on the screen, written out. ##### [15:35.888](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=935.8878958333332) Narration: Empat kali sepuluh sama dengan empat puluh, dan lima kali satu sama dengan lima. Empat puluh per lima sama dengan delapan. Board: Unchanged from the preceding beat in this scene. Actions: - [15:39.557](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=939.5573958333332): potong is shown on the screen, written out. - [15:42.564](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=942.5643958333332): potong is shown on the screen, written out. ##### [15:43.988](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=943.9878958333331) Narration: Jadi didapat delapan potong pita. Hitung kotaknya: satu, dua, tiga, empat, lima, enam, tujuh, delapan. Board: Unchanged from the preceding beat in this scene. Actions: - [15:44.893](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=944.8933958333332): jawab\_potong is shown on the screen, written out. - [15:47.622](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=947.6223958333331): potongan is shown on the screen, written out. - [15:48.156](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=948.1563958333331): potongan\_2 is shown on the screen, written out. - [15:48.551](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=948.5513958333331): potongan\_3 is shown on the screen, written out. - [15:49.212](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=949.2123958333332): potongan\_4 is shown on the screen, written out. - [15:49.874](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=949.8743958333332): potongan\_5 is shown on the screen, written out. - [15:50.362](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=950.3623958333332): potongan\_6 is shown on the screen, written out. - [15:51](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=951.0003958333332): potongan\_7 is shown on the screen, written out. - [15:51.662](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=951.6623958333332): potongan\_8 is shown on the screen, written out. ##### [15:53.075](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=953.0748958333331) Narration: Delapan potong. Kalau soalnya menanyakan berapa banyak potongan, itu tandanya pembagian, bukan perkalian. Board: jawab\_potong — a Math \[text\] that says "$8 thin upright("potong")$"; gunting — a Figure (x\_range=(0.0, 8.0), y\_range=(-0.2, 1.2), aspect=(8.0, 1.4)); soal\_pita — a Panel that says "Pita sepanjang $frac(4, 5)$ meter dipotong menjadi bagian sepanjang $frac(1, 10)$ meter. Berapa potong pita yang didapat?"; potongan — a Polygon \[blue\] drawn in gunting (vertices=((0, 0.1), (1, 0.1), (1, 0.9), (0, 0.9)), fill\_opacity=0.4); potongan\_2 — a Polygon \[blue\] drawn in gunting (vertices=((1, 0.1), (2, 0.1), (2, 0.9), (1, 0.9)), fill\_opacity=0.4); potongan\_3 — a Polygon \[blue\] drawn in gunting (vertices=((2, 0.1), (3, 0.1), (3, 0.9), (2, 0.9)), fill\_opacity=0.4); potongan\_4 — a Polygon \[blue\] drawn in gunting (vertices=((3, 0.1), (4, 0.1), (4, 0.9), (3, 0.9)), fill\_opacity=0.4); potongan\_5 — a Polygon \[blue\] drawn in gunting (vertices=((4, 0.1), (5, 0.1), (5, 0.9), (4, 0.9)), fill\_opacity=0.4); potongan\_6 — a Polygon \[blue\] drawn in gunting (vertices=((5, 0.1), (6, 0.1), (6, 0.9), (5, 0.9)), fill\_opacity=0.4); potongan\_7 — a Polygon \[blue\] drawn in gunting (vertices=((6, 0.1), (7, 0.1), (7, 0.9), (6, 0.9)), fill\_opacity=0.4); potongan\_8 — a Polygon \[blue\] drawn in gunting (vertices=((7, 0.1), (8, 0.1), (8, 0.9), (7, 0.9)), fill\_opacity=0.4) Actions: - [15:57.684](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=957.6843958333332): A box is drawn around jawab\_potong. - [16:0.111](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=960.1108958333332): gunting is hidden from the screen — left the board. - [16:0.111](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=960.1108958333332): potongan is hidden from the screen — gunting left the board. - [16:0.111](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=960.1108958333332): potongan\_2 is hidden from the screen — gunting left the board. - [16:0.111](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=960.1108958333332): potongan\_3 is hidden from the screen — gunting left the board. - [16:0.111](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=960.1108958333332): potongan\_4 is hidden from the screen — gunting left the board. - [16:0.111](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=960.1108958333332): potongan\_5 is hidden from the screen — gunting left the board. - [16:0.111](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=960.1108958333332): potongan\_6 is hidden from the screen — gunting left the board. - [16:0.111](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=960.1108958333332): potongan\_7 is hidden from the screen — gunting left the board. - [16:0.111](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=960.1108958333332): potongan\_8 is hidden from the screen — gunting left the board. - [16:0.111](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=960.1108958333332): jawab\_potong is hidden from the screen — left the board. - [16:0.111](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=960.1108958333332): potong is hidden from the screen — left the board. - [16:0.111](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=960.1108958333332): soal\_pita is hidden from the screen — left the board. ##### [16:1.311](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=961.3108958333331) Narration: Mari kita ingat kembali semuanya. Ada lima hal penting. Board: Empty. Actions: - [16:1.311](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=961.3108958333331): head\_ingat is shown on the screen, written out. - [16:4.469](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=964.4693958333331): ingat is shown on the screen, written out. ##### [16:6.276](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=966.2763958333331) Narration: Satu, pada bilangan cacah: kurung dahulu, lalu kali dan bagi, baru tambah dan kurang. Board: ingat — a Block \[text\] that says "Bilangan cacah: kurung dahulu, lalu kali dan bagi, baru tambah dan kurang. Satu nilai bisa ditulis sebagai pecahan, desimal, atau persen. Membandingkan pecahan: samakan penyebutnya, atau ubah ke persen. Tambah dan kurang pecahan: samakan p…"; head\_ingat — a Heading that says "Yang Perlu Diingat" Actions: - [16:9.028](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=969.0283958333332): ingat (the "kurung dahulu" part) is emphasized. ##### [16:13.459](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=973.4593958333331) Narration: Dua, satu nilai bisa ditulis sebagai pecahan, desimal, atau persen. Tiga, untuk membandingkan pecahan, samakan penyebutnya atau ubah ke persen. Board: Unchanged from the preceding beat in this scene. Actions: - [16:15.258](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=975.2583958333331): ingat (the "Satu nilai" part) is emphasized. - [16:15.258](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=975.2583958333331): ingat (the "kurung dahulu" part) is no longer emphasized. - [16:20.204](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=980.2043958333331): ingat (the "Membandingkan pecahan" part) is emphasized. - [16:20.204](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=980.2043958333331): ingat (the "Satu nilai" part) is no longer emphasized. ##### [16:24.961](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=984.9608958333331) Narration: Empat, untuk tambah dan kurang pecahan, samakan penyebutnya lebih dahulu. Lima, untuk kali, pembilang dikali pembilang, dan untuk bagi, kalikan dengan kebalikannya. Board: Unchanged from the preceding beat in this scene. Actions: - [16:28.084](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=988.0843958333331): ingat (the "Membandingkan pecahan" part) is no longer emphasized. - [16:28.084](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=988.0843958333331): ingat (the "lebih dahulu" part) is emphasized. - [16:35.862](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=995.8623958333332): ingat (the "lebih dahulu" part) is no longer emphasized. - [16:35.862](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=995.8623958333332): ingat (the "pembilang kali pembilang" part) is emphasized. ##### [16:37.415](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=997.4148958333332) Narration: Kerjakan setiap soal langkah demi langkah, dan tulis barisnya dengan rapi. Kalau kamu sudah terbiasa, soal ujian akan terasa jauh lebih ringan. Semangat berlatih! Board: Unchanged from the preceding beat in this scene. Actions: - [16:41.431](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=1001.4313958333331): penutup is shown on the screen, written out. - [16:41.431](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=1001.4313958333331): ingat (the "pembilang kali pembilang" part) is no longer emphasized. - [16:47.924](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=1007.9243958333332): head\_ingat is hidden from the screen — left the board. - [16:47.924](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=1007.9243958333332): ingat is hidden from the screen — left the board. - [16:47.924](https://academa.ai/@panca12345/lectures/operasi-hitung-bilangan-cacah-dan-pecahan-untuk-persiapan-ujian-sd?t=1007.9243958333332): penutup is hidden from the screen — left the board.