[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"public-settings":3,"content:materi:penjumlahan-pecahan":11,"public-catalog":202},{"features.tutoring.enabled":4,"sections.subjects.enabled":5,"sections.pricing.enabled":5,"sections.teachers.enabled":5,"sections.testimonials.enabled":4,"sections.faqs.enabled":5,"bankSoal.enabled":5,"site.maintenance":4,"whatsapp.number":6,"brand.name":7,"brand.tagline":8,"contact.email":9,"contact.address":10},false,true,"6285156084435","MyFismat","Platform belajar Matematika, Fisika, dan Pemrograman untuk SD, SMP, SMA, dan Kuliah","support@myfismat.com","Indonesia",{"id":12,"type":13,"slug":14,"title":15,"excerpt":16,"coverUrl":17,"status":18,"publishedAt":19,"featured":5,"subjectId":20,"blocks":21,"seoTitle":17,"seoDescription":17,"readingMinutes":100,"order":101,"createdAt":102,"updatedAt":102,"subject":103,"levels":108,"topics":113,"tags":117,"author":17,"resolved":118,"related":127},"demo-v2-m-matematika-sd-1","MATERIAL","penjumlahan-pecahan","Penjumlahan Pecahan Beda Penyebut + Contoh Soal","Cara penjumlahan pecahan berpenyebut sama dan beda penyebut memakai KPK, pecahan senilai, dan pecahan campuran, lengkap dengan contoh soal SD.",null,"PUBLISHED","2026-10-08T23:58:22.560Z","cmuzbyhdg000471r9l54yc9ia",[22,27,34,38,42,46,50,56,60,64,68,72,78,82,86,90,94],{"id":23,"data":24,"type":26},"s1-1",{"markdown":25},"**Penjumlahan pecahan** dilakukan dengan menjumlahkan pembilang ketika penyebutnya sudah sama. Jika penyebutnya berbeda, ubah dulu kedua pecahan menjadi pecahan senilai dengan penyebut yang sama, biasanya memakai KPK dari kedua penyebut. Contohnya, $\\frac12+\\frac13=\\frac36+\\frac26=\\frac56$. Penyebut tidak ikut dijumlahkan karena penyebut menunjukkan ukuran setiap bagian.","text",{"id":28,"data":29,"type":33},"s1-2",{"title":30,"variant":31,"markdown":32},"Rumus penjumlahan pecahan","info","Penyebut sama:\n$$\\frac{a}{c}+\\frac{b}{c}=\\frac{a+b}{c}$$\nPenyebut berbeda: samakan penyebut dengan KPK, lalu jumlahkan pembilangnya.\n$$\\frac{a}{b}+\\frac{c}{d}=\\frac{a\\times d}{b\\times d}+\\frac{c\\times b}{d\\times b}=\\frac{ad+bc}{bd}$$","callout",{"id":35,"data":36,"type":26},"s2-1",{"markdown":37},"## Apa Itu Pecahan?\n\nPecahan menyatakan bagian dari satu keseluruhan yang dibagi **sama besar**. Bayangkan satu pizza dipotong menjadi empat potong yang sama. Satu potong ditulis $\\frac14$ dan tiga potong ditulis $\\frac34$.\n\n- **Pembilang** adalah angka atas, yaitu banyak bagian yang diambil.\n- **Penyebut** adalah angka bawah, yaitu banyak bagian sama besar dalam satu keseluruhan.\n- Garis pecahan juga berarti pembagian: $\\frac34$ sama dengan $3:4$.\n\nIngat, bagian-bagiannya harus sama besar. Empat potong yang ukurannya berbeda-beda belum bisa disebut seperempat.",{"id":39,"data":40,"type":26},"s3-1",{"markdown":41},"## Pecahan Senilai: Kunci Menyamakan Penyebut\n\n**Pecahan senilai** adalah pecahan yang bentuknya berbeda tetapi nilainya sama. Caranya: kalikan atau bagi pembilang dan penyebut dengan bilangan yang sama (bukan nol).\n\n$$\\frac12=\\frac24=\\frac36=\\frac48$$\n\nCoba lipat kertas menjadi dua, lalu lipat lagi. Daerah setengah kertas sekarang terdiri dari dua bagian seperempat. Luasnya tidak berubah; hanya ukuran potongannya yang lebih kecil. Inilah alasan kita boleh mengubah $\\frac12$ menjadi $\\frac24$ sebelum menjumlahkan.",{"id":43,"data":44,"type":26},"s4-1",{"markdown":45},"## Penjumlahan Pecahan Penyebut Sama\n\nJika penyebutnya sudah sama, setiap bagian punya ukuran yang sama. Jadi kita cukup menghitung banyak bagian.\n\n$$\\frac27+\\frac37=\\frac{2+3}{7}=\\frac57$$\n\nDua potong sepertujuh ditambah tiga potong sepertujuh menjadi lima potong sepertujuh. Penyebut tetap 7 karena ukuran potongannya tetap sepertujuh.",{"id":47,"data":48,"type":26},"s5-1",{"markdown":49},"## Cara Penjumlahan Pecahan Beda Penyebut\n\nIkuti langkah berikut setiap kali penyebutnya berbeda:\n\n1. Cari **KPK** (kelipatan persekutuan terkecil) dari kedua penyebut.\n2. Ubah setiap pecahan menjadi pecahan senilai dengan penyebut KPK tersebut.\n3. Jumlahkan pembilangnya, penyebut tetap.\n4. Sederhanakan hasilnya jika pembilang dan penyebut masih bisa dibagi bilangan yang sama.\n\nMisalnya $\\frac13+\\frac14$. KPK dari 3 dan 4 adalah 12. Maka $\\frac13=\\frac4{12}$ dan $\\frac14=\\frac3{12}$. Hasilnya $\\frac4{12}+\\frac3{12}=\\frac7{12}$.",{"id":51,"data":52,"type":33},"s5-2",{"title":53,"variant":54,"markdown":55},"Cek hasil dengan perkiraan","tip","Hasil penjumlahan dua pecahan positif harus lebih besar daripada masing-masing pecahan. Karena $\\frac7{12}$ lebih besar dari $\\frac13$ dan $\\frac14$ tetapi kurang dari 1, jawabannya masuk akal.",{"id":57,"data":58,"type":26},"s6-1",{"markdown":59},"## Penjumlahan Pecahan Campuran\n\n**Pecahan campuran** terdiri dari bilangan bulat dan pecahan, misalnya $2\\frac13$. Ada dua cara menjumlahkannya:\n\n- **Cara 1:** jumlahkan bilangan bulat dengan bilangan bulat, pecahan dengan pecahan.\n- **Cara 2:** ubah dulu menjadi pecahan biasa, misalnya $2\\frac13=\\frac{2\\times3+1}{3}=\\frac73$.\n\nContoh dengan cara 1: $1\\frac12+2\\frac13=(1+2)+(\\frac36+\\frac26)=3\\frac56$. Jika bagian pecahannya lebih dari 1, misalnya $\\frac76$, ubah menjadi $1\\frac16$ lalu tambahkan ke bilangan bulat.",{"id":61,"data":62,"type":26},"s7-1",{"markdown":63},"## Pengurangan Pecahan Memakai Langkah yang Sama\n\nPengurangan pecahan mengikuti langkah yang sama dengan penjumlahan: samakan penyebut, lalu kurangkan pembilangnya. Misalnya $\\frac34-\\frac16$. KPK dari 4 dan 6 adalah 12, sehingga $\\frac9{12}-\\frac2{12}=\\frac7{12}$.\n\nPada pecahan campuran, kadang bagian pecahan yang dikurangi lebih besar. Pinjam satu dari bilangan bulat. Contohnya $3\\frac14-1\\frac12$: ubah menjadi $2\\frac54-1\\frac24=1\\frac34$. Cek dengan desimal: $3{,}25-1{,}5=1{,}75$.",{"id":65,"data":66,"type":26},"s8-1",{"markdown":67},"## Contoh Soal Penjumlahan Pecahan dan Pembahasan\n\n### Contoh 1: Pita dengan penyebut sama\n\nRani memakai $\\frac27$ meter pita, lalu $\\frac37$ meter lagi. Berapa pita yang dipakai?\n\n1. Penyebut sama-sama 7, jadi langsung jumlahkan pembilang: $2+3=5$.\n2. Hasilnya $\\frac57$ meter.\n3. Cek: sisa pita $\\frac27$ meter, dan $\\frac57+\\frac27=1$ meter.\n\n### Contoh 2: Air dengan penyebut berbeda\n\nAda $\\frac12$ liter air dan $\\frac14$ liter air. Berapa jumlahnya?\n\n1. KPK dari 2 dan 4 adalah 4.\n2. Ubah $\\frac12=\\frac24$.\n3. Jumlahkan: $\\frac24+\\frac14=\\frac34$ liter.\n\n### Contoh 3: Hasil yang perlu disederhanakan\n\nHitung $\\frac56+\\frac14$.\n\n1. KPK dari 6 dan 4 adalah 12.\n2. $\\frac56=\\frac{10}{12}$ dan $\\frac14=\\frac3{12}$.\n3. $\\frac{10}{12}+\\frac3{12}=\\frac{13}{12}=1\\frac1{12}$.\n\nHasilnya lebih dari 1 karena $\\frac56$ sudah hampir satu utuh.",{"id":69,"data":70,"type":26},"s9-1",{"markdown":71},"## Kesalahan yang Sering Terjadi",{"id":73,"data":74,"type":33},"s9-2",{"title":75,"variant":76,"markdown":77},"Jangan menjumlahkan penyebut","warning","$\\frac12+\\frac14$ **bukan** $\\frac26$. Menjumlahkan penyebut mengubah ukuran setiap bagian. Bahkan $\\frac26$ lebih kecil dari $\\frac12$, padahal kita menambah air.",{"id":79,"data":80,"type":26},"s9-3",{"markdown":81},"- Mengubah penyebut tanpa mengubah pembilang. $\\frac12$ tidak sama dengan $\\frac14$.\n- Lupa menyederhanakan. $\\frac6{8}$ lebih rapi ditulis $\\frac34$.\n- Lupa satuan. Jika soal tentang liter atau meter, tulis satuannya di jawaban.",{"id":83,"data":84,"type":26},"s10-1",{"markdown":85},"## Ringkasan\n\n- Pecahan menghitung bagian sama besar dari satu keseluruhan.\n- Penyebut sama: jumlahkan pembilang, penyebut tetap.\n- Penyebut berbeda: samakan dengan KPK memakai pecahan senilai, lalu jumlahkan.\n- Pecahan campuran: jumlahkan bagian bulat dan bagian pecahan, atau ubah ke pecahan biasa.",{"id":87,"data":88,"type":26},"s11-1",{"markdown":89},"## Materi Terkait\n\nSetelah lancar menjumlahkan pecahan, lanjutkan ke [rumus keliling dan luas bangun datar](\u002Fmateri\u002Frumus-keliling-dan-luas-bangun-datar), karena ukuran sisi sering berbentuk pecahan. Pecahan juga muncul saat menghitung [volume kubus](\u002Fmateri\u002Frumus-volume-kubus) dan [peluang suatu kejadian](\u002Fmateri\u002Frumus-peluang). Lihat semua materi di [halaman Matematika](\u002Fmapel\u002Fmatematika).",{"id":91,"data":92,"type":26},"sources",{"markdown":93},"## Sumber belajar\n\n- [OpenStax Prealgebra 2e — Add and Subtract Fractions with Common Denominators](https:\u002F\u002Fopenstax.org\u002Fbooks\u002Fprealgebra-2e\u002Fpages\u002F4-4-add-and-subtract-fractions-with-common-denominators)\n- [OpenStax Prealgebra 2e — Add and Subtract Fractions with Different Denominators](https:\u002F\u002Fopenstax.org\u002Fbooks\u002Fprealgebra-2e\u002Fpages\u002F4-5-add-and-subtract-fractions-with-different-denominators)\n\nPenjelasan dan contoh disusun ulang untuk materi ini; sumber dapat dibuka untuk belajar lebih lanjut.",{"id":95,"data":96,"type":99},"practice",{"title":97,"questionSetId":98},"Latihan soal Penjumlahan Pecahan","demo-v2-p-matematika-sd-1","quiz",4,0,"2026-10-08T23:58:22.573Z",{"id":20,"slug":104,"name":105,"color":106,"icon":107},"matematika","Matematika","#8B5CF6","sigma",[109],{"id":110,"slug":111,"name":112},"cmv0762210004113f6m6v04vs","sd","SD",[114],{"id":115,"slug":14,"name":116,"subjectId":20},"demo-v2-topic-matematika-sd-1","Penjumlahan Pecahan",[],{"assets":119,"videos":120,"questionSets":121},{},{},{"demo-v2-p-matematika-sd-1":122},{"id":98,"slug":123,"title":124,"mode":125,"description":126,"questionCount":100,"durationMinutes":17},"latihan-soal-penjumlahan-pecahan","Latihan Soal Penjumlahan Pecahan","PRACTICE","4 soal Penjumlahan Pecahan (Matematika SD) lengkap dengan pembahasan langkah demi langkah dan alasan pilihan yang keliru.",[128,154,171,187],{"id":129,"type":130,"slug":131,"title":132,"excerpt":133,"coverUrl":17,"status":18,"publishedAt":134,"featured":5,"readingMinutes":135,"order":101,"updatedAt":136,"subject":137,"levels":138,"topics":152,"tags":153,"author":17},"demo-v2-a-matematika","ARTICLE","cara-belajar-matematika-dari-nol","Cara Belajar Matematika dari Nol: Urutan Materi SD–Kuliah","Cara belajar matematika dari nol: urutan materi dari pecahan, bangun ruang, aljabar, hingga kalkulus, kebiasaan belajar efektif, dan rencana 4 minggu.","2026-10-08T23:58:23.084Z",7,"2026-10-08T23:58:23.086Z",{"id":20,"slug":104,"name":105,"color":106,"icon":107},[139,140,144,148],{"id":110,"slug":111,"name":112},{"id":141,"slug":142,"name":143},"cmuzbyhdb000171r9dcbyf0qg","smp","SMP",{"id":145,"slug":146,"name":147},"cmuzbyhdb000271r9up0bfli4","sma","SMA",{"id":149,"slug":150,"name":151},"cmuzbyhdb000371r9qk125qjd","kuliah","Kuliah",[],[],{"id":155,"type":13,"slug":156,"title":157,"excerpt":158,"coverUrl":17,"status":18,"publishedAt":159,"featured":4,"readingMinutes":160,"order":161,"updatedAt":162,"subject":163,"levels":164,"topics":166,"tags":170,"author":17},"demo-v2-m-matematika-kuliah-3","vektor-3-dimensi-dot-product","Vektor 3 Dimensi dan Dot Product (Perkalian Titik)","Vektor 3 dimensi: komponen, panjang vektor, vektor satuan, dot product atau perkalian titik, sudut antara dua vektor, proyeksi, dan contoh soal.","2026-10-08T23:58:23.070Z",5,2,"2026-10-08T23:58:23.072Z",{"id":20,"slug":104,"name":105,"color":106,"icon":107},[165],{"id":149,"slug":150,"name":151},[167],{"id":168,"slug":156,"name":169,"subjectId":20},"demo-v2-topic-matematika-kuliah-3","Vektor 3D dan Dot Product",[],{"id":172,"type":13,"slug":173,"title":174,"excerpt":175,"coverUrl":17,"status":18,"publishedAt":176,"featured":4,"readingMinutes":100,"order":177,"updatedAt":178,"subject":179,"levels":180,"topics":182,"tags":186,"author":17},"demo-v2-m-matematika-kuliah-2","integral-tentu","Integral Tentu: Rumus, Luas, dan Volume Benda Putar","Integral tentu dan teorema dasar kalkulus, sifat-sifatnya, luas daerah antara kurva, volume benda putar metode cakram dan kulit tabung, plus contoh soal.","2026-10-08T23:58:23.034Z",1,"2026-10-08T23:58:23.037Z",{"id":20,"slug":104,"name":105,"color":106,"icon":107},[181],{"id":149,"slug":150,"name":151},[183],{"id":184,"slug":173,"name":185,"subjectId":20},"cmuzbyhvn00gc71r9tl4peyfx","Integral Tentu",[],{"id":188,"type":13,"slug":189,"title":190,"excerpt":191,"coverUrl":17,"status":18,"publishedAt":192,"featured":5,"readingMinutes":100,"order":101,"updatedAt":193,"subject":194,"levels":195,"topics":197,"tags":201,"author":17},"demo-v2-m-matematika-kuliah-1","definisi-turunan-limit","Definisi Turunan dengan Limit dan Garis Singgung","Definisi turunan dengan limit f′(x) = lim [f(x+h) − f(x)]\u002Fh, langkah menghitungnya, gradien garis singgung, syarat diferensiabel, dan contoh soal.","2026-10-08T23:58:23.002Z","2026-10-08T23:58:23.004Z",{"id":20,"slug":104,"name":105,"color":106,"icon":107},[196],{"id":149,"slug":150,"name":151},[198],{"id":199,"slug":189,"name":200,"subjectId":20},"demo-v2-topic-matematika-kuliah-1","Definisi Turunan",[],{"subjects":203,"levels":223,"topics":235,"tags":2022},[204,207,215],{"id":20,"slug":104,"name":105,"description":205,"icon":107,"color":106,"order":101,"published":5,"createdAt":206,"updatedAt":206},"Aljabar, geometri, kalkulus, statistika, dan cara berpikir matematis.","2026-10-08T09:24:40.948Z",{"id":208,"slug":209,"name":210,"description":211,"icon":212,"color":213,"order":177,"published":5,"createdAt":214,"updatedAt":214},"cmuzbyhdq000571r9nsdk6scx","fisika","Fisika","Gerak, gaya, energi, listrik, gelombang, hingga fisika modern.","atom","#0EA5E9","2026-10-08T09:24:40.958Z",{"id":216,"slug":217,"name":218,"description":219,"icon":220,"color":221,"order":161,"published":5,"createdAt":222,"updatedAt":222},"cmuzbyhdt000671r91cdnnt22","pemrograman","Pemrograman","Logika, algoritma, dan coding dari dasar sampai proyek nyata.","code","#3B82F6","2026-10-08T09:24:40.962Z",[224,227,230,232],{"id":110,"slug":111,"name":112,"description":225,"order":101,"createdAt":226,"updatedAt":226},"Jenjang SD","2026-10-08T23:58:22.441Z",{"id":141,"slug":142,"name":143,"description":228,"order":177,"createdAt":229,"updatedAt":229},"Sekolah Menengah Pertama","2026-10-08T09:24:40.943Z",{"id":145,"slug":146,"name":147,"description":231,"order":161,"createdAt":229,"updatedAt":229},"Sekolah Menengah Atas",{"id":149,"slug":150,"name":151,"description":233,"order":234,"createdAt":229,"updatedAt":229},"Perguruan tinggi \u002F universitas",3,[236,243,249,255,261,267,272,278,284,290,295,301,307,313,319,325,331,337,343,349,355,361,367,373,379,385,391,397,403,409,415,421,427,433,439,445,451,457,463,469,474,480,486,492,498,504,510,516,522,528,534,540,546,552,558,564,570,576,581,586,591,596,601,606,611,616,621,626,632,637,642,647,652,657,662,667,672,677,682,687,692,697,699,704,709,714,719,724,729,734,739,744,749,754,759,764,769,774,780,785,790,795,800,805,810,815,820,825,830,835,840,845,850,855,860,865,870,875,880,885,890,895,901,906,911,916,921,926,931,936,941,946,951,956,961,966,971,976,981,986,991,997,1002,1007,1012,1017,1022,1027,1032,1037,1042,1047,1052,1057,1062,1067,1072,1077,1082,1087,1092,1097,1102,1107,1113,1118,1123,1128,1133,1138,1143,1148,1153,1158,1163,1168,1173,1178,1183,1188,1193,1198,1203,1208,1213,1218,1223,1228,1233,1238,1241,1247,1252,1257,1262,1267,1272,1277,1282,1287,1291,1296,1301,1306,1311,1316,1321,1326,1331,1336,1341,1346,1351,1356,1361,1366,1371,1376,1381,1386,1391,1396,1401,1406,1411,1416,1421,1426,1431,1436,1441,1446,1451,1456,1460,1465,1470,1475,1480,1485,1490,1496,1501,1506,1511,1516,1521,1526,1531,1536,1541,1546,1551,1556,1561,1567,1572,1578,1583,1589,1594,1600,1605,1611,1616,1622,1628,1634,1639,1645,1650,1656,1659,1665,1670,1676,1681,1686,1691,1697,1702,1708,1713,1719,1724,1730,1734,1740,1745,1751,1756,1762,1767,1773,1778,1784,1789,1795,1800,1806,1811,1818,1825,1832,1835,1841,1847,1853,1859,1865,1871,1877,1883,1885,1891,1897,1904,1910,1916,1922,1928,1934,1940,1946,1952,1958,1965,1971,1977,1983,1989,1995,1997,2003,2010,2016],{"id":237,"subjectId":208,"levelId":145,"parentId":238,"slug":239,"name":240,"description":241,"order":101,"createdAt":242,"updatedAt":242},"cmuzbyhm9007o71r91e76ir5n","cmuzbyhm6007m71r9multkwzz","arus-dan-tegangan-listrik-bolak-balik","Arus dan Tegangan Listrik Bolak Balik","","2026-10-08T09:24:41.265Z",{"id":244,"subjectId":20,"levelId":145,"parentId":245,"slug":246,"name":247,"description":241,"order":101,"createdAt":248,"updatedAt":248},"cmuzbyht500e271r9p86b0fxe","cmuzbyht300e071r93gyvjn0r","barisan","Barisan","2026-10-08T09:24:41.514Z",{"id":250,"subjectId":20,"levelId":145,"parentId":251,"slug":252,"name":253,"description":241,"order":101,"createdAt":254,"updatedAt":254},"cmuzbyhok009w71r9688mekrn","cmuzbyhoi009u71r9i6j09wcn","barisan-dan-deret-barisan-dan-deret-kelas-10","Barisan dan Deret","2026-10-08T09:24:41.348Z",{"id":256,"subjectId":20,"levelId":145,"parentId":257,"slug":258,"name":259,"description":241,"order":101,"createdAt":260,"updatedAt":260},"cmuzbyhpm00aw71r94xosa04y","cmuzbyhpk00au71r9d9ugx39r","bentuk-umum-dan-akar-persamaan-kuadrat","Bentuk Umum dan Akar Persamaan 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Wajib.","2026-10-08T09:24:41.547Z",{"id":417,"subjectId":20,"levelId":145,"parentId":17,"slug":1735,"name":1736,"description":1737,"order":1738,"createdAt":1739,"updatedAt":1739},"geometri-analitik","Geometri Analitik","Geometri Analitik — Kelas 12 Lanjut.",24,"2026-10-08T09:24:41.553Z",{"id":411,"subjectId":208,"levelId":145,"parentId":17,"slug":1741,"name":1742,"description":1743,"order":1738,"createdAt":1744,"updatedAt":1744},"kemagnetan","Kemagnetan","Kemagnetan — Kelas 12.","2026-10-08T09:24:41.245Z",{"id":286,"subjectId":20,"levelId":145,"parentId":17,"slug":1746,"name":1747,"description":1748,"order":1749,"createdAt":1750,"updatedAt":1750},"limit","Limit","Limit — Kelas 12 Lanjut.",25,"2026-10-08T09:24:41.562Z",{"id":238,"subjectId":208,"levelId":145,"parentId":17,"slug":1752,"name":1753,"description":1754,"order":1749,"createdAt":1755,"updatedAt":1755},"listrik-ac-arus-bolak-balik","Listrik AC \u002F Arus Bolak Balik","Listrik AC \u002F Arus Bolak Balik — Kelas 12.","2026-10-08T09:24:41.263Z",{"id":476,"subjectId":208,"levelId":145,"parentId":17,"slug":1757,"name":1758,"description":1759,"order":1760,"createdAt":1761,"updatedAt":1761},"gelombang-elektromagnetik","Gelombang Elektromagnetik","Gelombang Elektromagnetik — Kelas 12.",26,"2026-10-08T09:24:41.273Z",{"id":292,"subjectId":20,"levelId":145,"parentId":17,"slug":1763,"name":1764,"description":1765,"order":1760,"createdAt":1766,"updatedAt":1766},"turunan-fungsi","Turunan Fungsi","Turunan Fungsi — Kelas 12 Lanjut.","2026-10-08T09:24:41.575Z",{"id":500,"subjectId":20,"levelId":145,"parentId":17,"slug":1768,"name":1769,"description":1770,"order":1771,"createdAt":1772,"updatedAt":1772},"aplikasi-turunan","Aplikasi Turunan","Aplikasi Turunan — Kelas 12 Lanjut.",27,"2026-10-08T09:24:41.587Z",{"id":530,"subjectId":208,"levelId":145,"parentId":17,"slug":1774,"name":1775,"description":1776,"order":1771,"createdAt":1777,"updatedAt":1777},"pengantar-instrumental-digital","Pengantar Instrumental Digital","Pengantar Instrumental Digital — Kelas 12.","2026-10-08T09:24:41.283Z",{"id":375,"subjectId":20,"levelId":145,"parentId":17,"slug":1779,"name":1780,"description":1781,"order":1782,"createdAt":1783,"updatedAt":1783},"integral","Integral","Integral — Kelas 12 Lanjut.",28,"2026-10-08T09:24:41.599Z",{"id":518,"subjectId":208,"levelId":145,"parentId":17,"slug":1785,"name":1786,"description":1787,"order":1782,"createdAt":1788,"updatedAt":1788},"relativitas-khusus","Relativitas Khusus","Relativitas Khusus — Kelas 12.","2026-10-08T09:24:41.291Z",{"id":524,"subjectId":208,"levelId":145,"parentId":17,"slug":1790,"name":1791,"description":1792,"order":1793,"createdAt":1794,"updatedAt":1794},"gejala-kuantum","Gejala Kuantum","Gejala Kuantum — Kelas 12.",29,"2026-10-08T09:24:41.303Z",{"id":423,"subjectId":20,"levelId":145,"parentId":17,"slug":1796,"name":1797,"description":1798,"order":1793,"createdAt":1799,"updatedAt":1799},"penerapan-integral","Penerapan Integral","Penerapan Integral — Kelas 12 Lanjut.","2026-10-08T09:24:41.607Z",{"id":315,"subjectId":20,"levelId":145,"parentId":17,"slug":1801,"name":1802,"description":1803,"order":1804,"createdAt":1805,"updatedAt":1805},"analisis-data-peluang","Analisis Data & Peluang","Analisis Data & Peluang — Kelas 12 Lanjut.",30,"2026-10-08T09:24:41.611Z",{"id":459,"subjectId":208,"levelId":145,"parentId":17,"slug":1807,"name":1808,"description":1809,"order":1804,"createdAt":1810,"updatedAt":1810},"fisika-inti-dan-radioaktivitas","Fisika Inti dan Radioaktivitas","Fisika Inti dan Radioaktivitas — Kelas 12.","2026-10-08T09:24:41.318Z",{"id":1812,"subjectId":20,"levelId":145,"parentId":17,"slug":1813,"name":1814,"description":1815,"order":1816,"createdAt":1817,"updatedAt":1817},"cmuzbyhw700gw71r9o87lq7vd","logaritma","Logaritma","Logaritma — Kelas 12 Lanjut.",31,"2026-10-08T09:24:41.623Z",{"id":1819,"subjectId":20,"levelId":145,"parentId":17,"slug":1820,"name":1821,"description":1822,"order":1823,"createdAt":1824,"updatedAt":1824},"cmuzbyhw900gy71r9d9sjh9ie","program-linier","Program Linier","Program Linier — Kelas 12 Lanjut.",32,"2026-10-08T09:24:41.625Z",{"id":1826,"subjectId":20,"levelId":145,"parentId":17,"slug":1827,"name":1828,"description":1829,"order":1830,"createdAt":1831,"updatedAt":1831},"cmuzbyhwb00h071r97764r7hr","bangun-ruang","Bangun Ruang","Bangun Ruang — Kelas 12 Lanjut.",33,"2026-10-08T09:24:41.627Z",{"id":199,"subjectId":20,"levelId":149,"parentId":17,"slug":189,"name":200,"description":191,"order":1833,"createdAt":1834,"updatedAt":1834},100,"2026-10-08T23:58:22.977Z",{"id":1836,"subjectId":20,"levelId":145,"parentId":17,"slug":1837,"name":1838,"description":1839,"order":1833,"createdAt":1840,"updatedAt":1840},"demo-v2-topic-matematika-sma-1","fungsi-kuadrat","Fungsi Kuadrat","Fungsi kuadrat f(x) = ax² + bx + c: pengaruh a, b, c pada grafik, rumus titik puncak, sumbu simetri, diskriminan, dan contoh soal nilai maksimum.","2026-10-08T23:58:22.868Z",{"id":1842,"subjectId":216,"levelId":145,"parentId":17,"slug":1843,"name":1844,"description":1845,"order":1833,"createdAt":1846,"updatedAt":1846},"demo-v2-topic-pemrograman-sma-1","fungsi-python-def-return","Fungsi Python","Pelajari cara membuat fungsi Python dengan def, parameter, nilai default, dan return, plus perbedaan return dan print lewat contoh program yang jelas.","2026-10-08T23:58:23.661Z",{"id":1848,"subjectId":208,"levelId":141,"parentId":17,"slug":1849,"name":1850,"description":1851,"order":1833,"createdAt":1852,"updatedAt":1852},"demo-v2-topic-fisika-smp-1","glb-dan-glbb","GLB dan GLBB","Rumus GLB dan GLBB lengkap: jarak, kecepatan, percepatan, grafik posisi–waktu, perbedaan GLB dan GLBB, plus contoh soal gerak lurus dan pembahasannya.","2026-10-08T23:58:23.189Z",{"id":1854,"subjectId":208,"levelId":149,"parentId":17,"slug":1855,"name":1856,"description":1857,"order":1833,"createdAt":1858,"updatedAt":1858},"demo-v2-topic-fisika-kuliah-1","gerak-harmonik-sederhana","Gerak Harmonik Sederhana","Gerak harmonik sederhana untuk fisika dasar: persamaan x = A cos(ωt + φ), kecepatan, percepatan, periode pegas dan bandul, energi, serta contoh soal.","2026-10-08T23:58:23.364Z",{"id":1860,"subjectId":208,"levelId":145,"parentId":17,"slug":1861,"name":1862,"description":1863,"order":1833,"createdAt":1864,"updatedAt":1864},"demo-v2-topic-fisika-sma-1","hukum-newton-2","Hukum Newton 2","Hukum Newton 2: bunyi, rumus ΣF = m·a, diagram gaya, gaya gesek statis dan kinetis, serta contoh soal mencari percepatan dan massa beserta pembahasan.","2026-10-08T23:58:23.280Z",{"id":1866,"subjectId":216,"levelId":149,"parentId":17,"slug":1867,"name":1868,"description":1869,"order":1833,"createdAt":1870,"updatedAt":1870},"demo-v2-topic-pemrograman-kuliah-1","notasi-big-o-kompleksitas-waktu","Notasi Big O","Pahami notasi Big O dan kompleksitas waktu algoritma: O(1), O(log n), O(n), O(n²), cara menghitungnya dari kode Python, dan contoh soalnya.","2026-10-08T23:58:23.797Z",{"id":1872,"subjectId":216,"levelId":110,"parentId":17,"slug":1873,"name":1874,"description":1875,"order":1833,"createdAt":1876,"updatedAt":1876},"demo-v2-topic-pemrograman-sd-1","pengertian-algoritma","Pengertian Algoritma","Algoritma adalah langkah-langkah urut untuk menyelesaikan masalah. Pelajari pengertian, ciri, dan contoh algoritma sehari-hari untuk siswa SD.","2026-10-08T23:58:23.477Z",{"id":1878,"subjectId":208,"levelId":110,"parentId":17,"slug":1879,"name":1880,"description":1881,"order":1833,"createdAt":1882,"updatedAt":1882},"demo-v2-topic-fisika-sd-1","pengukuran-panjang","Pengukuran Panjang","Belajar pengukuran panjang untuk SD: satuan baku, alat ukur panjang, cara memakai penggaris, dan tangga satuan panjang km sampai mm + contoh soal.","2026-10-08T23:58:23.095Z",{"id":115,"subjectId":20,"levelId":110,"parentId":17,"slug":14,"name":116,"description":16,"order":1833,"createdAt":1884,"updatedAt":1884},"2026-10-08T23:58:22.508Z",{"id":1886,"subjectId":20,"levelId":141,"parentId":17,"slug":1887,"name":1888,"description":1889,"order":1833,"createdAt":1890,"updatedAt":1890},"demo-v2-topic-matematika-smp-1","teorema-pythagoras","Teorema Pythagoras","Teorema Pythagoras a² + b² = c² untuk mencari sisi miring dan sisi siku-siku, tripel Pythagoras, diagonal ruang balok, dan contoh soal kelas 8.","2026-10-08T23:58:22.690Z",{"id":1892,"subjectId":216,"levelId":141,"parentId":17,"slug":1893,"name":1894,"description":1895,"order":1833,"createdAt":1896,"updatedAt":1896},"demo-v2-topic-pemrograman-smp-1","variabel-dan-tipe-data-python","Variabel dan Tipe Data Python","Belajar variabel dan tipe data Python dari nol: int, float, string, boolean, operator, print, dan input, lengkap dengan contoh program dan latihan.","2026-10-08T23:58:23.562Z",{"id":1898,"subjectId":216,"levelId":149,"parentId":17,"slug":1899,"name":1900,"description":1901,"order":1902,"createdAt":1903,"updatedAt":1903},"demo-v2-topic-pemrograman-kuliah-2","class-dan-object-python","Class dan Object Python","Pelajari class dan object Python untuk OOP: __init__, self, atribut, method, inheritance, dan invarian objek lewat contoh program dompet digital.",101,"2026-10-08T23:58:23.830Z",{"id":1905,"subjectId":20,"levelId":145,"parentId":17,"slug":1906,"name":1907,"description":1908,"order":1902,"createdAt":1909,"updatedAt":1909},"demo-v2-topic-matematika-sma-2","eksponen-dan-logaritma","Eksponen dan Logaritma","Materi eksponen dan logaritma kelas 10: sifat-sifat eksponen, definisi dan sifat logaritma, persamaan eksponen dan logaritma, serta contoh soal.","2026-10-08T23:58:22.902Z",{"id":1911,"subjectId":208,"levelId":110,"parentId":17,"slug":1912,"name":1913,"description":1914,"order":1902,"createdAt":1915,"updatedAt":1915},"demo-v2-topic-fisika-sd-2","macam-macam-gaya","Gaya dan Macam-Macamnya","Gaya adalah tarikan atau dorongan. Pelajari macam-macam gaya (otot, gravitasi, magnet, gesek, pegas), pengaruhnya pada benda, dan contoh soalnya.","2026-10-08T23:58:23.126Z",{"id":1917,"subjectId":20,"levelId":110,"parentId":17,"slug":1918,"name":1919,"description":1920,"order":1902,"createdAt":1921,"updatedAt":1921},"demo-v2-topic-matematika-sd-2","rumus-keliling-dan-luas-bangun-datar","Keliling dan Luas Bangun Datar","Rumus keliling dan luas bangun datar: persegi, persegi panjang, segitiga, jajargenjang, trapesium, dan lingkaran, dengan cara mudah dan contoh soal.","2026-10-08T23:58:22.588Z",{"id":1923,"subjectId":216,"levelId":145,"parentId":17,"slug":1924,"name":1925,"description":1926,"order":1902,"createdAt":1927,"updatedAt":1927},"demo-v2-topic-pemrograman-sma-2","list-dan-dictionary-python","List dan Dictionary Python","Pahami list dan dictionary Python: indeks, append, key-value, get, dan perulangan, plus perbedaan keduanya lewat contoh pengolahan data nilai siswa.","2026-10-08T23:58:23.694Z",{"id":1929,"subjectId":208,"levelId":141,"parentId":17,"slug":1930,"name":1931,"description":1932,"order":1902,"createdAt":1933,"updatedAt":1933},"demo-v2-topic-fisika-smp-2","rumus-massa-jenis","Massa Jenis","Rumus massa jenis ρ = m\u002FV lengkap dengan satuan kg\u002Fm³ dan g\u002Fcm³, tabel massa jenis air, besi, dan minyak, cara menghitung, serta contoh soal pembahasan.","2026-10-08T23:58:23.217Z",{"id":1935,"subjectId":216,"levelId":141,"parentId":17,"slug":1936,"name":1937,"description":1938,"order":1902,"createdAt":1939,"updatedAt":1939},"demo-v2-topic-pemrograman-smp-2","percabangan-python-if-else","Percabangan Python","Pelajari percabangan Python dengan if, elif, dan else: operator perbandingan, operator logika, dan contoh program nilai rapor lengkap dengan outputnya.","2026-10-08T23:58:23.592Z",{"id":1941,"subjectId":216,"levelId":110,"parentId":17,"slug":1942,"name":1943,"description":1944,"order":1902,"createdAt":1945,"updatedAt":1945},"demo-v2-topic-pemrograman-sd-2","percabangan-dalam-algoritma","Percabangan dalam Algoritma","Percabangan dalam algoritma memilih tindakan berdasarkan syarat jika-maka. Pelajari pengertian, contoh sehari-hari, dan simbol flowchart-nya.","2026-10-08T23:58:23.503Z",{"id":1947,"subjectId":20,"levelId":141,"parentId":17,"slug":1948,"name":1949,"description":1950,"order":1902,"createdAt":1951,"updatedAt":1951},"demo-v2-topic-matematika-smp-2","persamaan-garis-lurus","Persamaan Garis Lurus","Persamaan garis lurus y = mx + c, rumus gradien dari dua titik, garis sejajar dan tegak lurus, cara menggambar grafik, serta contoh soal kelas 8.","2026-10-08T23:58:22.730Z",{"id":1953,"subjectId":208,"levelId":149,"parentId":17,"slug":1954,"name":1955,"description":1956,"order":1902,"createdAt":1957,"updatedAt":1957},"demo-v2-topic-fisika-kuliah-2","usaha-oleh-gaya-berubah","Usaha Gaya Berubah","Usaha oleh gaya berubah dengan integral W = ∫F dx, rumus usaha W = F·s sebagai dot product, usaha pegas, dan teorema usaha–energi, plus contoh soal.","2026-10-08T23:58:23.394Z",{"id":1959,"subjectId":20,"levelId":145,"parentId":17,"slug":1960,"name":1961,"description":1962,"order":1963,"createdAt":1964,"updatedAt":1964},"demo-v2-topic-matematika-sma-3","rumus-peluang","Peluang Kejadian","Rumus peluang P(A) = n(A)\u002Fn(S), ruang sampel, peluang komplemen, frekuensi harapan, kejadian saling lepas dan saling bebas, plus contoh soal dadu dan koin.",102,"2026-10-08T23:58:22.934Z",{"id":1966,"subjectId":216,"levelId":145,"parentId":17,"slug":1967,"name":1968,"description":1969,"order":1963,"createdAt":1970,"updatedAt":1970},"demo-v2-topic-pemrograman-sma-3","pencarian-linear-dan-biner","Pencarian Linear dan Biner","Pelajari pencarian linear dan pencarian biner (binary search): cara kerja, syarat data terurut, kode Python, dan perbandingan jumlah langkahnya.","2026-10-08T23:58:23.724Z",{"id":1972,"subjectId":216,"levelId":141,"parentId":17,"slug":1973,"name":1974,"description":1975,"order":1963,"createdAt":1976,"updatedAt":1976},"demo-v2-topic-pemrograman-smp-3","perulangan-python-for-while","Perulangan Python","Pelajari perulangan Python dengan for, range(), dan while, lengkap dengan contoh program menghitung total, break, continue, dan latihan soal.","2026-10-08T23:58:23.624Z",{"id":1978,"subjectId":216,"levelId":110,"parentId":17,"slug":1979,"name":1980,"description":1981,"order":1963,"createdAt":1982,"updatedAt":1982},"demo-v2-topic-pemrograman-sd-3","perulangan-dalam-algoritma","Perulangan dalam Algoritma","Perulangan dalam algoritma mengulang langkah yang sama beberapa kali. Pelajari pengertian, contoh perulangan sehari-hari, dan cara menghitung hasilnya.","2026-10-08T23:58:23.529Z",{"id":1984,"subjectId":20,"levelId":141,"parentId":17,"slug":1985,"name":1986,"description":1987,"order":1963,"createdAt":1988,"updatedAt":1988},"demo-v2-topic-matematika-smp-3","rumus-prisma-dan-limas","Prisma dan Limas","Rumus volume prisma dan limas, luas permukaan, sifat sisi-rusuk-titik sudut, jaring-jaring, limas 3D interaktif, dan contoh soal bangun ruang sisi datar.","2026-10-08T23:58:22.780Z",{"id":1990,"subjectId":216,"levelId":149,"parentId":17,"slug":1991,"name":1992,"description":1993,"order":1963,"createdAt":1994,"updatedAt":1994},"demo-v2-topic-pemrograman-kuliah-3","unit-test-python","Unit Test Python","Pelajari unit test Python dengan modul unittest: assertEqual, assertRaises, nilai batas, dan cara menjalankan tes, lengkap dengan contoh dan versi pytest.","2026-10-08T23:58:23.864Z",{"id":168,"subjectId":20,"levelId":149,"parentId":17,"slug":156,"name":169,"description":158,"order":1963,"createdAt":1996,"updatedAt":1996},"2026-10-08T23:58:23.045Z",{"id":1998,"subjectId":20,"levelId":110,"parentId":17,"slug":1999,"name":2000,"description":2001,"order":1963,"createdAt":2002,"updatedAt":2002},"demo-v2-topic-matematika-sd-3","rumus-volume-kubus","Volume dan Luas Permukaan Kubus","Rumus volume kubus V = s³ dan luas permukaan kubus L = 6s², sifat kubus, jaring-jaring, kubus 3D interaktif, dan contoh soal bertingkat.","2026-10-08T23:58:22.619Z",{"id":2004,"subjectId":20,"levelId":141,"parentId":17,"slug":2005,"name":2006,"description":2007,"order":2008,"createdAt":2009,"updatedAt":2009},"demo-v2-topic-matematika-smp-4","rumus-tabung-dan-kerucut","Tabung dan Kerucut","Rumus volume tabung dan kerucut, luas permukaan, garis pelukis, jaring-jaring berupa persegi panjang dan juring, kerucut 3D interaktif, dan contoh soal.",103,"2026-10-08T23:58:22.828Z",{"id":2011,"subjectId":216,"levelId":145,"parentId":17,"slug":2012,"name":2013,"description":2014,"order":2008,"createdAt":2015,"updatedAt":2015},"demo-v2-topic-pemrograman-sma-4","try-except-python","Try Except dan Membaca File","Pelajari try except Python untuk menangani error seperti ValueError dan FileNotFoundError, serta cara membaca dan menulis file txt dengan with open.","2026-10-08T23:58:23.755Z",{"id":2017,"subjectId":20,"levelId":110,"parentId":17,"slug":2018,"name":2019,"description":2020,"order":2008,"createdAt":2021,"updatedAt":2021},"demo-v2-topic-matematika-sd-4","rumus-volume-balok","Volume dan Luas Permukaan Balok","Rumus volume balok V = p × l × t dan luas permukaan balok L = 2(pl + pt + lt), sifat balok, jaring-jaring, balok 3D interaktif, dan contoh soal.","2026-10-08T23:58:22.651Z",[]]