G COUNTING 6 : Fraction

Gasing Counting Introduction

Matematika selama ini telah menjadi mata pelajaran yang ditakuti banyak siswa. Siswa kesulitan ketika mengerjakan soal-soal matematika karena lemahnya kemampuan konsep matematika mereka. Untuk itu diperlukan suatu cara agar siswa tertarik dengan matematika dan dapat belajar matematika dengan mudah.

Oleh karena itu Prof.Yohanes Surya, Ph.D di Surya Institute mengembangkan metode pembelajaran matematika yang dinamakan metode Gasing (GAmpang, aSyIk, MenyenaNGkan). Pembelajaran Matematika Gasing dibuat secara bertahap, bertingkat dan berlanjut, dari konsep yang termudah hingga tersulit. Dengan cara ini siswa lebih mudah memahami matematika dan menemukan sendiri “AHA”-nya. Lewat metode Gasing ini diharapkan jutaan anak-anak Indonesia menjadi pandai berhitung dan tidak lagi takut dengan matematika.

Modul pertama ini disusun untuk memberi bimbingan pada orangtua atau pendidik bagaimana mengajar berhitung GASING yang meliputi BAKAL KUBAGI (penjumlahan atau penamBAhan, perKALian, pengurangan atau KUrang dan pemBAGIan). Pada Modul kedua nanti kita akan belajar GASING untuk materi PEDE (PEcahan dan DEsimal). Seorang yang mampu menguasai BAKAL KUBAGI PEDE akan mampu belajar matematika dengan sangat mudah.

Ucapan terima kasih tak lupa kami sampaikan kepada semua pihak yang telah membantu terselesaikannya modul ini. Akhirnya, saran dan masukan berkaitan dengan modul ini dapat disampaikan kepada penyusun melalui situs Kandel.

Tim Penyusun

Meaning GASING

Arti Metode GASING

Metode adalah cara (langkah demi langkah) untuk mencapai suatu hasil. GASING adalah GAmpang, aSIk, dan menyenaNGkan. Jadi Metode GASING berhitung adalah langkah demi langkah pembelajaran berhitung secara gampang, asik dan menyenangkan.

Pembelajaran Berhitung Gasing dibuat berurutan dari konsep yang termudah hingga tersulit sehingga siswa dapat dengan mudah memahami matematika dan menemukan sendiri “AHA”-nya.

Beberapa hal penting dalam metode Gasing

• Konkret - Abstrak

Setiap materi pembelajaran Gasing selalu dimulai dengan sesuatu yang kongkret, sesuatu yang mudah divisualisasikan. Hal yang konkret ini membuat siswa lebih mudah mengerti. Tanpa bisa membayangkan lebih sulit bagi siswa untuk belajar suatu mata pelajaran.

Misalnya seorang berkata cinq + vier = enea. Sulit bagi kita mengingat atau mengerti maksudnya. Tetapi kalau ia menunjukan jari 5 sambil berkata cinq (bahasa perancis), lalu menunjukan jari 4 sambil berkata vier (bahasa Jerman) dan menunjukan hasilnya adalah sembilan jari sambil berkata enea (bahasa yunani), maka siswa bisa mengerti lebih mudah.

Setelah belajar kongkretnya, kita mengajarkan abstraknya, misalnya 5 + 4 = 9.

• Mencongak

Perhitungan dengan metode Gasing sebagian besar dilakukan dengan mencongak. Mencongak bukan berarti menghafal, tetapi mengerti sehingga mampu melakukan perhitungan secara mencogak.

Misalnya 19 x 3 sama dengan 1 puluhan x 3 satuan hasilnya adalah 3 puluhan, kemudian 9 satuan dikali 3 satuan hasilnya adalah 27 satuan yang merupakan 2 puluhan dan 7 satuan. Puluhannya digabung menjadi 3 + 2 = 5. Satuannya tetap 7. Sehingga hasilnya adalah 57.

Agar lebih mudah menghitung secara mencongak maka perhitungan BAKAL KUBAGI selalu dimulai dari kiri ke kanan bukan dari kanan ke kiri seperti yang selama ini kita ajarkan.

• Bertahap

Belajar Gasing adalah belajar setahap demi setahap. Misalnya untuk menguasai penjumlahan 5 digit dengan 5 digit tahapan yang perlu dilakukan adalah

• • menguasai arti bilangan 1-5
  • menguasai penjumlahan yang hasilnya 2 sampai 5
  • menguasai arti bilangan 6 - 10
  • menguasai penjumlahan yang hasilnya 6 sampai 10
  • dst

• Bertingkat

Disamping bertahap, pembelajaran Gasing dibuat bertingkat. Tingkat pertama adalah Penjumlahan. Setelah menguasai penjumlahan, siswa baru bisa masuk ke perkalian. Kita tidak bisa mengajarkan perkalian tanpa lewat penjumlahan. Demikian juga pengurangan dapat dipelajari kalau sudah menguasai penjumlahan. Pembagian hanya dapat dikuasai setelah menguasai penjumlahan, perkalian dan pengurangan. Tingkatan-tingkatan yang akan kita pelajari dalam berhitung ini adalah

• • Penjumlahan
  • Perkalian
  • Pengurangan
  • Pembagian
  • Bilangan bulat
  • Pecahan
  • Desimal

• Berlanjut

Setelah menguasai Gasing berhitung, kita bisa lanjut ke soal cerita, soal teka-teki berhitung atau berbagai aplikasi seperti menghitung luas, kecepatan, perbandingan dsb.

• Titik Kritis

Dalam setiap tingkatan ada titik kritisnya. Titik kritis adalah keadaan dimana siswa sudah memahami dengan baik konsep-konsep dasar dari suatu tingkatan. Siswa yang telah mencapai titik kritis akan mampu menguasai konsep lanjutan dari tingkatan itu secara mudah.

Sebagai contoh : ‘’’titik kritis penjumlahan’’’ adalah penjumlahan yang hasilnya dibawah 20. Jadi untuk semua siswa yang sudah mampu menjumlahkan bilangan yang hasilnya kurang dari 20 sudah siap untuk melanjutkan pada konsep lanjutan penjumlahan seperti penjumlahan 2 digit, penjumlahan 3 digit dsb.

• Banyak Latihan

Siswa diberikan soal Latihan setelah siswa mampu mencongak. Jadi Latihan yang banyak adalah untuk meningkatkan kemampuan motorik siswa, bagaimana menuliskan apa yang ada diotak dalam bentuk tulisan tangan. Soal Latihan yang banyak juga untuk melatih ‘’’endurance’’’ anak. Mereka harus mengerjakan soal secara cepat misalnya 120 soal dalam waktu 3 menit, ini bermanfaat untuk melatih ‘’’konsentrasi’’’ mereka dan membiasakan bekerja secara cepat dan meningkatkan kerja otak. Latihan yang banyak dengan waktu yang cepat dapat meningkatkan kecerdasan (IQ) juga dan membuat siswa semakin mahir berhitung.

Perhatikan disini langkah demi langkah Gasing:

Kongkret → mencongak → berlatih dengan tulisan.

• Banyak memuji

Selama proses belajar pengajar harus banyak memuji anak untuk progress sekecil apapun juga. Pujian ini akan mendorong anak untuk belajar dan belajar lebih banyak. Pujian ini akan meningkatkan percaya diri siswa sehingga otak siswa akan bekerja lebih baik. Pujian akan membuat anak merasa dihargai dan ini membuat anak lebih mencintai matematika (ia merasa bahwa di ‘matematika’ lah ia dipuji dan dihargai).

Pujian bisa dilakukan secara dengan kata-kata seperti “kamu hebat sekali ya…”, “kamu makin lama makin hebat ya…” , “kamu ini luar biasa sekali”, “kamu akan jadi professor matematika yang sangat hebat…” dsb. Atau pujian ini juga bisa diberikan secara tertulis pada hasil kerja mereka. Seperti begitu mereka selesai menjawab 120 soal dalam 3 menit, kita tulis “wah luar biasa sekali Emon, kamu hebat sekali…” dsb..

• Mengajar dengan hati

Mengajar yang berhasil adalah ketika kita bisa menyamakan frekuensi irama berpikir otak kita dengan irama berpikir anak, kemudian sedikit demi sedikit kita bawa anak itu berfikir dengan frekuensi kita. Teknik ini sangat powerful. Untuk melakukan Teknik ini kita perlu mengajar dengan hati. Kita harus anggap siswa kita adalah makhluk Tuhan yang perlu kita latih sehingga pandai. Kita harus mengajar dengan hati yang tulus dan semangat ingin agar anak ini bisa pandai.

• Mengajar dengan musik/lagu

Indonesia adalah negara yang mencintai musik. Hampir tiap daerah punya lagu-lagu daerahnya masing-masing. Ketika kita mengajar matematika dengan lagu, siswa akan lebih senang dan lebih menangkap apa yang kita ajarkan. Lagu yang dikombinasikan dengan Gerakan dan matematika akan melatih otak kanan dan otak kiri secara bersama-sama dan ini akan menghasilkan efek yang luar biasa pada sang anak. Anak lebih cekatan, lebih cerdas dan lebih kreatif.

• Kecerdasan 6C

Dari penjelasan diatas dapat disimpulkan bahwa GASING itu mengembangkan kecerdasan 6C: Communication, Collaboration, Creativity, Compassion, Critical Thinking, Computational Logic

Gasing Fraction

Pada pelajaran pecahan ini titik gasinya adalah siswa mampu mengerjakan 4 jenis operasi ini secara cepat.

Langkah-langkah untuk menuju ini adalah sebagai berikut

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1. Arti pecahan
2. Pecahan senilai dan penyederhanaan pecahan
3. Penjumlahan dan pengurangan pecahan dengan penyebut yang sama atau berbeda
4. Konsep ‘SATU’ dan pecahan adalah bagi
5. Pecahancampuran
6. Titik kritis GASING

Fraction concept

Ada 1 jeruk dipotong menjadi 2 bagian yang sama besar.

1 bagian jeruk kita sebut ${\frac {1}{2}}$ jeruk.

${\frac {1}{2}}$ dinamakan bilangan pecahan.

${\frac {1}{2}}$ diartikan sebagai nilai satu bagian dari satu kelompok yang terdiri dari dua bagian yang sama besar.

${\frac {1}{2}}$ dibaca “1 garis 2” atau “1 per 2”.

Angka yang diatas dinamakan pembilang

Angka yang dibawah dinamakan penyebut

Ini 1 batang biru

Batang biru dibagi dua bagian sama besar.

satu bagian batang ini bernilai ${\frac {1}{2}}$

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Potongan kuning atau potongan merah tidak bernilai ${\frac {1}{2}}$ karena bendanya tidak dipotong sama besar.

Batang kuning dibagi menjadi 3 bagian sama besar

Tiap bagian bernilai ${\frac {1}{3}}$

${\frac {1}{3}}$ artinya nilai 1 bagian dari satu kelompok yang terdiri dari 3 bagian yang sama besar.

Batang ungu dibagi menjadi 4 bagian sama besar

Tiap bagian bernilai ${\frac {1}{4}}$

${\frac {1}{4}}$ artinya nilai 1 bagian dari satu kelompok yang terdiri dari 4 bagian yang sama besar.

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1 Lingkaran dibagi menjadi 8 bagian sama besar

Bagian yang berwarna kuning bernilai ${\frac {3}{8}}$

${\frac {3}{8}}$ artinya nilai 3 bagian dari satu kelompok yang terdiri dari 8 bagian yang sama besar.

Lihat video berikut ini mengenai konsep pecahan.

{{#ev:youtube| watch?v=C4gB6iA70l4 }}

• Aktivitas 1

Tujuan: siswa mengerjakan secara cepat soal-soal mengenai konsep pecahan

Mengerjakan Latihan 1a dari buku Pecahan dan Desimal (buku 5)

Fraction equal value

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Batang kuning atas bernilai ${\frac {1}{2}}$

Batang kuning bawah bernilai ${\frac {2}{4}}$

Kedua batang tersebut sama besar sehingga kita katakan keduanya senilai.

${\frac {1}{2}}$ senilai ${\frac {2}{4}}$

${\frac {1}{2}}$ = ${\frac {2}{4}}$

Perhatikan:${\frac {1}{2}}$ dan ${\frac {2}{4}}$ nilainya sama walaupun artinya berbeda

${\frac {1}{2}}$ artinya nilai 1 bagian dari kelompok yang terdiri dari 2 bagian yang sama besar

${\frac {2}{4}}$ artinya nilai 2 bagian dari kelompok yang terdiri dari 4 bagian yang sama besar

Pada batang merah jambu

${\frac {1}{2}}$ = ${\frac {2}{4}}$ = ${\frac {3}{6}}$ = ${\frac {4}{8}}$ = ${\frac {5}{10}}$ = ${\frac {6}{12}}$

Pecahan ini semua bernilai sama

Pada batang hijau

${\frac {1}{3}}$ = ${\frac {2}{6}}$ = ${\frac {3}{9}}$ = ${\frac {4}{12}}$

Pecahan ini semua bernilai sama

bagaimana mendapatkan pecahan senilai?

Dengan mengalikan pembilang dan penyebut dengan bilangan yang sama.

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Perhatikan beberapa contoh pecahan senilai dalam video dibawah ini.

{{#ev:youtube| watch?v=PoTTD3yRsEg }}

• Aktivitas 1

Tujuan: siswa mengerjakan secara cepat soal-soal mengenai pecahan senilai

Mengerjakan Latihan 2 dari buku Pecahan dan Desimal (buku 5)

Simplify Fraction

Dalam bagian ini kita akan melakukan penyederhanaan pecahan.

Penyederhanaan pecahan adalah proses mendapatkan pecahan senilai yang terkecil (paling sederhana)

Misal

${\frac {6}{9}}$ dapat disederhanakan menjadi ${\frac {2}{3}}$

Cara menyederhanakan pecahan adalah membagi pembilang dan penyebut dengan suatu bilangan yang sama.

Untuk menyerdehanakan ::${\frac {6}{9}}$ menjadi ${\frac {2}{3}}$ kita dapat membagi pembilang dan penyebutnya dengan 3.

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Untuk bilangan yang agak besar, kita dapat membagi pembilang dan penyebutnya berulang-ulang sampai kita dapat pecahan yang paling sederhana.

Beberapa contoh menyederhanakan pecahan bisa dilihat dalam video ini

{{#ev:youtube| watch?v=PS1leZn06us }}

• Aktivitas 1

Tujuan: siswa mengerjakan secara cepat soal-soal mengenai pecahan senilai

Mengerjakan Latihan 2 dari buku Pecahan dan Desimal (buku 5)

Operation (+ and -) Fraction with same denominator

Addition

Pada penjumlahan pecahan ini pembahasan dibatasi jumlah pembilang tidak melebihi nilai penyebut.

Gambar ini adalah pecahan ${\frac {2}{8}}$

${\frac {2}{8}}$ = Nilai 2 bagian dari suatu kelompok yang terdiri dari 8 bagian yang sama besar

Kemudian kita tambahkan ${\frac {2}{8}}$ dengan ${\frac {1}{8}}$

Hasilnya adalah ${\frac {3}{8}}$

${\frac {3}{8}}$ = Nilai 3 bagian dari suatu kelompok yang terdiri dari 8 bagian yang sama besar

Contoh lain:

Apa yang kita bisa simpulkan?

Dalam menjumlahkan pecahan dengan penyebut sama, kita hanya menambahkan pembilangnya saja sedangkan penyebut (atau kelompoknya) tetap sama.

Lihat video beberapa contoh penjumlahan pecahan dengan penyebut sama

{{#ev:youtube| watch?v=rJm6Rb-47eI }}

• Aktivitas 1

Tujuan: siswa mengerjakan secara cepat soal-soal mengenai pecahan senilai

Mengerjakan Latihan 2 dari buku Pecahan dan Desimal (buku 5)

Subtraction

3 kotak biru dalam gambar ini menunjukan pecahan ${\frac {3}{5}}$

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${\frac {3}{5}}$ = Nilai 3 bagian dari suatu kelompok yang terdiri dari 5 bagian yang sama besar

Kemudian kita ambil dua kotak biru

${\frac {3}{5}}$ - ${\frac {2}{5}}$

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Hasilnya adalah ${\frac {1}{5}}$

${\frac {1}{5}}$ = Nilai 1 bagian dari suatu kelompok yang terdiri dari 5 bagian yang sama besar

Contoh lain:

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Apa yang kita bisa simpulkan?

Dalam melakukan pengurangan pecahan dengan penyebut sama, kita hanya mengurangkan pembilangnya saja sedangkan penyebut (atau kelompoknya) tetap sama.

Lihat video untuk beberapa contoh pengurangan dengan penyebut sama.

{{#ev:youtube| watch?v=k-N2vsimlQY }}

Concept ONE

Berapa separuh jeruk ditambah separuh jeruk?

Jawabnya 1 jeruk

Separuh jeruk + separuh jeruk = 1 jeruk

Karena separuh itu kita bisa tulis ${\frac {1}{2}}$

Maka kita bisa tulis

${\frac {1}{2}}$ (jeruk) + ${\frac {1}{2}}$ (jeruk) = 1 (jeruk)

Kita bisa juga tulis

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2} } + ${\frac {1}{2}}$ = 1

Namun kita tahu bahwa

${\frac {1}{2}}$ + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{2} }

Sehingga kita bisa simpulkan bahwa

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{2} } = 1

Contoh lain

Berapa seperempat batang kuning ditambah seperempat batang kuning ditambah seperempat batang kuning ditambah seperempat batang kuning ?

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Jawabnya 1 batang kuning

${\frac {1}{4}}$ (batang kuning) + ${\frac {1}{4}}$ (batang kuning) + ${\frac {1}{4}}$ (batang kuning) + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{4} } (batang kuning)= 1 (batang kuning)

Namun kita tahu bahwa

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{4} } + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{4}} +${\frac {1}{4}}$ + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{4}} = ${\frac {4}{4}}$

Sehingga boleh dikatakan bahwa

${\frac {4}{4}}$ = 1

karena Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{2} } = 1 dan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{4}{4} } = 1 maka kita boleh tuliskan,

${\frac {2}{2}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{4}{4} } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{10}{10} } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{178}{178} } = 1

Jadi bisa disimpulkan bahwa dalam konteks pecahan arti bilangan 1 adalah sebagai berikut

1 adalah nilai 2 bagian dari satu kelompok yang terdiri dari 2 bagian yang sama besar.

1 adalah nilai 3 bagian dari satu kelompok yang terdiri dari 3 bagian yang sama besar.

1 adalah nilai 5 bagian dari satu kelompok yang terdiri dari 5 bagian yang sama besar.

Video berikut ini menjelaskan konsep "satu'

{{#ev:youtube| watch?v=U8rmQGhGgew }}

Fraction and division

Kita sering mendengar bahwa pecahan itu sama dengan bagi.

Apakah itu benar?

Apakah ${\frac {1}{2}}$ = 1 ÷ 2 ?

Untuk menjawab ini, mari kita lihat gambar ini

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Disini kita punya 1 kue berwarna hijau. Kue ini hendak dimasukan dalam 2 kotak secara adil, berapa isi masing-masing kotak?

Untuk itu kita menuliskannya dalam bentuk 1 ÷ 2 = ?

Jawabnya: isi masing-masing kotak adalah separuh kue

Sekarang kita perhatikan gambar separuh kue.

Menurut definisi pecahan,

separuh atau setengah kue adalah nilai 1 bagian dari satu kue yang terdiri dari dua bagian yang sama besar.

Ini ditulis ${\frac {1}{2}}$ kue

Jadi kita bisa katakan bahwa

Separuh kue adalah hasil pembagian dari 1 kue dibagi 2

Separuh kue sama dengan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2} } kue

Dengan demikian kita bisa katakan bahwa

:: 1 kue ÷ 2 nilainya sama  dengan  Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2} }
 kue

ditulis

1 ÷ 2 = ${\frac {1}{2}}$

Ini juga berlaku untuk pecahan-pecahan lain seperti:

${\frac {1}{5}}$ nilainya sama dengan 1 dibagi 5

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{7} } nilainya sama dengan 1 dibagi 7

${\frac {1}{12}}$ nilainya sama dengan 1 dibagi 12

Sekarang kalau pembilangnya bukan 1, apakah "pecahan itu nilainya sama dengan pembagian" masih berlaku?

Apakah Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{4}{2} } nilainya sama dengan 4 dibagi 2 ?

Untuk hal ini kita lihat pelajaran sebelumnya tentang 1.

pada pelajaran sebelumnya 1 boleh didefinisikan sebagai nilai 2 bagian dari suatu kelompok yang terdiri dari 2 bagian yang sama besar.

Atau

1 = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{2} }

Dengan hasil itu kita bisa menulis,

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{4}{2}} = ${\frac {2}{2}}$ + ${\frac {2}{2}}$

${\frac {4}{2}}$ = 1 + 1 = 2

Ternyata ${\frac {4}{2}}$ = 2!

pembagian 4 ÷ 2 hasilnya adalah 2 juga

Dengan demikian maka bisa dikatakan

${\frac {4}{2}}$ nilainya sama dengan 4 dibagi 2 = 2

Jadi pecahan itu mempunyai kaitan yang erat dengan pembagian. Keduanya mempunyai nilai yang sama walaupun secara konsep berbeda.

Untuk jelasnya lihat video berikut ini

{{#ev:youtube| watch?v=raii20Dvoxg }}

Compound Fraction

Berapa ${\frac {2}{3}}$ + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{3}} ?

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{3}} + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{3}} = ${\frac {4}{3}}$

Kita bisa sederhanakan pecahan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{3}} dengan menggunakan konsep satu atau konsep pecahan dan bagi.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{4}{3}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{3}} + ${\frac {1}{3}}$

Karena ${\frac {3}{3}}$ = 1, maka

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{4}{3}} = 1 + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3}} = 1Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3}}

Dimana kita definisikan bilangan bulat + pecahan sebagai bilangan bulat pecahan

bentuk bilangan bulat pecahan seperti 1Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3}} dinamakan pecahan campuran atau pecahan majemuk.

Perhatikan beberapa contoh berikut:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{5}{3}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{3}} + ${\frac {2}{3}}$ = 1${\frac {2}{3}}$

${\frac {7}{5}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{5}{5}} + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{5}} = 1Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{5}}

${\frac {12}{7}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{7}{7}} + ${\frac {5}{7}}$ = 1${\frac {5}{12}}$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{25}{23}} = ${\frac {23}{23}}$ + ${\frac {2}{23}}$ = 1Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{23}}

Perhatikan contoh dalam video berikut

{{#ev:youtube| watch?v=RFgSVEUixCc }}

Operation (+ and -) Fraction with Different denominator

Pada bagian ini kita akan melakukan operasi penjumlahan dan pengurangan dengan penyebut berbeda.

Addition

Bagaimana menghitung Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3}}  ?

Disini penyebutnya berbeda.

Kita harus ubah penyebutnya sehingga sama.

Caranya

${\frac {1}{2}}$ dijadikan ${\frac {3}{6}}$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3}} dijadikan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{6}}

Sehingga kita peroleh

${\frac {1}{2}}$ + ${\frac {1}{3}}$ = ${\frac {3}{6}}$ + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{6}} = ${\frac {5}{6}}$

Bagaimana kita tahu penyebutnya harus dijadikan 6?

6 adalah bilangan yang bisa dibagi 2 dan bisa dibagi 3

Karena itu kita pasti bisa mengubah pecahan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} dan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3}} menjadi pecahan dengan penyebut 6.

Bagaimana mendapatkan angka 6?

Cara termudah adalah

Mengalikan penyebut pecahan yang dijumlahkan yaitu 3 x 2

Cara lain:

Dengan mencari bilangan terkecil yang bisa dibagi 2 dan bisa dibagi 3.

Apakah penyebutnya boleh 12? Bukankah 12 juga bisa dibagi 2 atau dibagi 3?

Boleh namun hasilnya nanti kamu harus sederhanakan lagi

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} + ${\frac {1}{3}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{6}{12}} + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{4}{12}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{10}{12}} = ${\frac {5}{6}}$

Kita boleh mengubah pecahan menjadi 6, 12, 18, 24 dsb. Tetapi sebaiknya ambil yang terkecil yaitu 6.

Bagaimana menghitung ${\frac {1}{4}}$ + ${\frac {1}{6}}$ = ?

Kita ubah penyebutnya menjadi 4 x 6 = 24

${\frac {1}{4}}$ + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{6}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{6}{24}} + ${\frac {4}{24}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{10}{24}} = ${\frac {5}{12}}$

Atau

cari bilangan yang bisa dibagi 4 dan 6. Dalam hal ini bilangannya adalah 12, 24, 36 dsb.

Kita pilih bilangan yang terkecil yaitu 12.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{4}} + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{6}} = ${\frac {3}{12}}$ + ${\frac {2}{12}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{5}{12}}

Bagaimana dengan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{5}} + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{10}} = ?

kita ubah penyebutnya menjadi 5 x 10 = 50

${\frac {2}{5}}$ + ${\frac {3}{10}}$ = ${\frac {20}{50}}$ + ${\frac {15}{50}}$ = ${\frac {35}{50}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{7}{10}}

Atau

Cari bilangan yang bisa dibagi 5 dan bisa dibagi 10. Dalam hal ini bilangannya adalah 10, 20, 30, 40 dst..

Kita pilih bilangan yang terkecil yaitu 10

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{5}} + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{10}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{4}{10}} + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{10}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{7}{10}}

Cara lain adalah menggunakan batang pecahan.

Misal kita akan menghitung Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} + ${\frac {1}{3}}$ =

Ini adalah batang pecahan.

Error creating thumbnail: Unable to save thumbnail to destination

Pertama kita lihat batang mana yang besarnya sama dengan batang Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} .

Ternyata Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{4}} = ${\frac {3}{6}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{4}{8}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{5}{10}} dst (bagian yang berwarna biru)

Kemudian kita lihat batang mana yang besarnya sama dengan batang Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3}}

Ternyata ${\frac {1}{3}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{6}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{9}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{4}{12}} dst (bagian yang berwarna merah)

Kita lihat mana penyebut yang sama dari kedua kelompok ini?

Jawabnya adalah 6.

Kita gabungkan kedua nilai pecahan diatas seperti pada gambar

Jadi ${\frac {1}{2}}$ + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{5}{6}}

Berikut ini adalah beberapa contoh penjumlahan pecahan

{{#ev:youtube| watch?v=1iqMwdBkLf8 }}

Addition (Quick way)

Perhatikan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{5}} + ${\frac {3}{10}}$ =

Penyebutnya dijadikan 5 x 10

${\begin{array}{lcl}{\frac {2}{5}}+{\frac {3}{10}}&=&{\frac {2\times 10}{5\times 10}}+{\frac {5\times 3}{5\times 10}}\\&=&{\frac {2\times 10+5\times 3}{5\times 10}}\end{array}}$

Lihat beberapa contoh berikut dan perhatikan polanya.

a) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{4}{5}} + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{3}} =

Penyebutnya dijadikan 5 x 3

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{lcl} \frac{4}{5} + \frac{2}{3} & = & \frac{4 \times 3}{5 \times 3} + \frac{5 \times 2}{5 \times 3} \\ & = & \frac{4 \times 3 + 5 \times 2}{5 \times 3} \end{array} }

b) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{4}} =

Penyebutnya dijadikan 2 x 4

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{lcl} \frac{1}{2} + \frac{3}{4} & = & \frac{1 \times 4}{2 \times 4} + \frac{2 \times 3}{2 \times 4} \\ & = & \frac{1 \times 4 + 2 \times 3}{2 \times 4} \end{array} }

c) ${\frac {1}{3}}$ + ${\frac {3}{5}}$ =

Penyebutnya dijadikan 3 x 5

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{lcl} \frac{1}{3} + \frac{3}{5} & = & \frac{1 \times 5}{3 \times 5} + \frac{3 \times 3}{3 \times 5} \\ & = & \frac{1 \times 5 + 3 \times 3}{3 \times 5} \end{array} }

d) ${\frac {2}{5}}$ + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{7}} =

Penyebutnya dijadikan 5 x 7

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{lcl} \frac{2}{5} + \frac{3}{7} & = & \frac{2 \times 7}{5 \times 7} + \frac{5 \times 3}{5 \times 7} \\ & = & \frac{2 \times 7 + 5 \times 3}{5 \times 7} \end{array} }

Kita perhatikan bahwa ada pola yang menarik, yaitu pola perkalian silang.

Error creating thumbnail: Unable to save thumbnail to destination

Gunakan ini untuk mempercepat perhitungan mencongak.

Video berikut ini menunjukan beberapa contoh menyelesaikan penjumlahan pecahan dengan cara cepat.

{{#ev:youtube| watch?v=buzx2IqTY6o }}

Subtraction

Pengurangan pecahan dengan penyebut berbeda sama konsepnya dengan penjumlahan pecahan dengan penyebut berbeda.

Misalnya bagaimana menghitung Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{4}} - Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{6}} = ?

Kita ubah penyebutnya menjadi 4 x 6 = 24

${\frac {1}{4}}$ - ${\frac {1}{6}}$ = ${\frac {6}{24}}$ - Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{4}{24}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{24}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{12}}

Atau

cari bilangan yang bisa dibagi 4 dan 6. Dalam hal ini bilangannya adalah 12, 24, 36 dsb.

Kita pilih bilangan yang terkecil yaitu 12.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{4}} - Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{6}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{12}} - Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{12}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{12}}

Bagaimana dengan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{5}} - ${\frac {3}{10}}$ = ?

kita ubah penyebutnya menjadi 5 x 10 = 50

${\frac {2}{5}}$ - Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{10}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{20}{50}} - ${\frac {15}{50}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{5}{50}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{10}}

Atau

Cari bilangan yang bisa dibagi 5 dan bisa dibagi 10. Dalam hal ini bilangannya adalah 10, 20, 30, 40 dst..

Kita pilih bilangan yang terkecil yaitu 10

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{5}} - ${\frac {3}{10}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{4}{10}} - Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{10}} = ${\frac {1}{10}}$

Lihat video cara mengerjakan pengurangan pecahan dengan penyebut berbeda

{{#ev:youtube| watch?v=11fENTTJJ4o }}

Substraction (Quick way)

Pola pengurangan pecahan cara cepat sama dengan pola penjumlahan pecahan cara cepat.

Perhatikan ${\frac {2}{5}}$ - Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{10}} =

Penyebutnya dijadikan 5 x 10

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{lcl} \frac{2}{5} - \frac{3}{10} & = & \frac{2 \times 10}{5 \times 10} - \frac{5 \times 3}{5 \times 10} \\ & = & \frac{2 \times 10 - 5 \times 3}{5 \times 10} \end{array} }

Bagaimana dengan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{4}{5}} - ${\frac {3}{7}}$ = ?

Penyebutnya dijadikan 5 x 7

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{lcl} \frac{4}{5} - \frac{3}{7} & = & \frac{4 \times 7}{5 \times 7} - \frac{5 \times 3}{5 \times 7} \\ & = & \frac{4 \times 7 - 5 \times 3}{5 \times 7} \end{array} }

Pola perkalian silangnya adalah

Error creating thumbnail: Unable to save thumbnail to destination

Lihat video berikut ini untuk beberapa contoh pengurangan cara cepat

{{#ev:youtube| watch?v=c3tZ95x8crc }}

Negative fraction (Quick way)

Konsep pecahan negatif, mirip dengan konsep bilangan bulat negatif.

Misalnya kita punya suatu garis bilangan. Tiap titik yang berdekatan berbeda Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{5}}

Dari titik 0 ke kanan, nilai tiap titik berturut-turut adalah Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{5}, \frac{2}{5}, \frac{3}{5} } dst.

Dari titik 0 ke kiri, nilai tiap titik berturut-turut adalah $-{\frac {1}{5}},-{\frac {2}{5}},-{\frac {3}{5}}$ dst.

Disini,

$-{\frac {1}{5}}$ nilainya sama dengan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0 -\frac{1}{5}}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\frac{2}{5}} nilainya sama dengan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0 -\frac{2}{5}}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\frac{3}{5}} nilainya sama dengan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0 -\frac{3}{5}}

Operasi penjumlahan dan pengurangan bilangan pecahan negatif, adalah seperti operasi bilangan bulat negatif.

Berikut ini adalah beberapa contoh operasi bilangan pecahan negatif.

a) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\frac{4}{5}} + ${\frac {3}{7}}$ =

Penyebutnya dijadikan 5 x 7

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{lcl} -\frac{4}{5} + \frac{3}{7} & = & \frac{-4 \times 7}{5 \times 7} + \frac{5 \times 3}{5 \times 7} \\ & = & \frac{-4 \times 7 + 5 \times 3}{5 \times 7} \end{array} }

Pola perkalian silangnya adalah

b) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\frac{4}{5}} - Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{7}} =

${\begin{array}{lcl}-{\frac {4}{5}}-{\frac {3}{7}}&=&{\frac {-4\times 7}{5\times 7}}-{\frac {5\times 3}{5\times 7}}\\&=&{\frac {-4\times 7-5\times 3}{5\times 7}}\end{array}}$

Pola perkalian silangnya adalah

Beberapa contoh penjumlahan dan pengurangan bilangan pecahan negatif dapat dilihat dalam video ini

{{#ev:youtube| watch?v=VpMnTBKeF6c }}

Pure to compound fraction and vice versa

Pure to Compound Fraction

Bagaimana menyederhanakan pecahan yang pembilangnya besar tetapi penyebutnya kecil seperti Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{44}{7}}

kita gunakan konsep pecahan dan bagi.

44 ÷ 7 = 6 sisa 2

Hasil bilangan bulatnya kita ambil, dan sisanya kita jadikan pecahan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{7}}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{44}{7}} = 6${\frac {2}{7}}$

Mari kita buktikan

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{44}{7}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{42}{7}} + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{7}}

${\frac {44}{7}}$ = 6 + ${\frac {2}{7}}$

${\frac {44}{7}}$ = 6 ${\frac {2}{7}}$

Perhatikan beberapa contoh ini

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{43}{8} = ?}

43 ÷ 8 = 5 sisa 3

${\frac {43}{8}}$ = 5Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{8}}

${\frac {25}{4}}=?$

25 ÷ 4 = 6 sisa 1

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{25}{4}} = 6${\frac {1}{4}}$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{101}{9} = ?}

101 ÷ 9 = 11 sisa 2

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{101}{9}} = 11Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{9}}

Lihat beberapa contoh mengubah pecahan atau pecahan biasa menjadi pecahan majemuk dalam video berikut.

{{#ev:youtube| watch?v=kXpA84IhSJk }}

Compound to Pure Fraction

Bagaimana mengubah pecahan majemuk menjadi pecahan biasa atau pecahan murni?

Bagaimana mengubah 2${\frac {1}{2}}$ menjadi pecahan biasa?

Perhatikan langkah-langkahnya pada contoh berikut ini lalu lihat polanya dan buat kesimpulan

${\begin{array}{lcl}2{\frac {1}{2}}&=&2+{\frac {1}{2}}\\&=&{\frac {4}{2}}+{\frac {1}{2}}\\&=&{\frac {5}{2}}\end{array}}$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{lcl} 3\frac{1}{3}& = & 3 + \frac{1}{3} \\ & = & \frac{9}{3} + \frac{1}{3} \\ & = & \frac{10}{3} \end{array} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{lcl} 5\frac{2}{7}& = & 5 + \frac{2}{7} \\ & = & \frac{35}{7} + \frac{2}{7} \\ & = & \frac{37}{7} \end{array} }

${\begin{array}{lcl}4{\frac {3}{5}}&=&4+{\frac {3}{5}}\\&=&{\frac {20}{5}}+{\frac {3}{5}}\\&=&{\frac {23}{5}}\end{array}}$

Cara cepatnya

Kalikan bilangan bulat dengan penyebut.

Tambahkan hasilnya dengan pembilang.

${\begin{array}{lcl}3{\frac {1}{2}}&=&{\frac {3\times 2+1}{2}}\\&=&{\frac {7}{2}}\end{array}}$

${\begin{array}{lcl}5{\frac {2}{7}}&=&{\frac {5\times 7+2}{7}}\\&=&{\frac {37}{7}}\end{array}}$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{lcl} 8\frac{3}{5}& = & \frac{8 \times 5 + 3}{5} \\ & = & \frac{43}{5} \end{array} }

Video ini menunjukan contoh-contoh mengubah pecahan majemuk menjadi pecahan biasa.

{{#ev:youtube| watch?v=49bF9cjeOY8 }}

Critical point

Titik Kritis untuk pecahan dicapai kalau siswa sudah mampu menguasai penjumlahan dan pengurangan seperti berikut ini

Model 1 : $2+{\frac {5}{7}}$

Penjumlahan bilangan bulat dengan pecahan dapat dilakukan sebagai berikut:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2 + \frac{5}{7} } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2 \frac{5}{7} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3 + \frac{3}{10} } = $3{\frac {3}{10}}$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 7 + \frac{2}{9} } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 7 \frac{2}{9} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 25 + \frac{5}{12} } = $25{\frac {5}{12}}$

Dapatkah Anda menemukan polanya?

Mudah kan?

Model 2 : $-2-{\frac {5}{7}}$

Penjumlahan bilangan bulat dengan pecahan untuk model 2 ini mirip dengan model 1.

Perhatikan contoh berikut

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -2 - \frac{5}{7} } = $-2{\frac {5}{7}}$

$-3-{\frac {3}{10}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -3 \frac{3}{10} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -7 - \frac{2}{9} } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -7 \frac{2}{9} }

$-25-{\frac {5}{12}}$ = $-25{\frac {5}{12}}$

Dapatkah Anda menemukan polanya?

Mudah kan?

Model 3 : $2-{\frac {5}{7}}$

Model 3 ini berbeda dengan model 1 dan 2.

• Langkah pertama adalah menghitung bentuk $1-{\frac {5}{7}}$

Cara mengerjakannya adalah mengubah 1 menjadi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{7}{7} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1 - \frac{5}{7} } = ${\frac {7}{7}}-{\frac {5}{7}}$ = ${\frac {2}{7}}$

Lihat beberapa contoh berikut

$1-{\frac {3}{11}}$ = ${\frac {11}{11}}-{\frac {3}{11}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{8}{11} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1 - \frac{4}{5} } = ${\frac {5}{5}}-{\frac {4}{5}}$ = ${\frac {1}{5}}$

$1-{\frac {5}{8}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{8}{8} - \frac{5}{8} } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{8} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1 - \frac{4}{27} } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{27}{27} - \frac{4}{27} } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{23}{27} }

• Langkah kedua adalah memecah bilangan bulatnya menjadi 1 dan sisanya

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2 - \frac{5}{7} } = 1 + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (1 - \frac{5}{7}) } = $1+{\frac {2}{7}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1 \frac{2}{7} }

Perhatikan contoh berikutnya

$5-{\frac {5}{7}}$ = 4 + $(1-{\frac {5}{7}})$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4 + \frac{2}{7} } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4 \frac{2}{7} }

$7-{\frac {5}{7}}$ = 6 + $(1-{\frac {5}{7}})$ = $6+{\frac {2}{7}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6 \frac{2}{7} }

$6-{\frac {5}{7}}$ = 5 + $(1-{\frac {5}{7}})$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 5 + \frac{2}{7} } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 5 \frac{2}{7} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 23 - \frac{5}{7} } = 22 + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (1 - \frac{5}{7}) } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 22 + \frac{2}{7} } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 22 \frac{2}{7} }

$5-{\frac {2}{9}}$ = 4 + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (1 - \frac{2}{9}) } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4 + \frac{7}{9} } = $4{\frac {7}{9}}$

$7-{\frac {3}{11}}$ = 6 + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (1 - \frac{3}{11}) } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6 + \frac{8}{11} } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6 \frac{8}{11} }

$6-{\frac {4}{5}}$ = 5 + $(1-{\frac {4}{5}})$ = $5+{\frac {1}{5}}$ = $5{\frac {1}{5}}$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 23 - \frac{7}{12} } = 22 + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (1 - \frac{7}{12}) } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 22 + \frac{5}{12} } = $22{\frac {5}{12}}$

Bisakah Anda melihat polanya?

Video

Model 4 : $-2+{\frac {5}{7}}$

Model 4 ini berbeda dengan model sebelumnya.

• Langkah pertama adalah menghitung bentuk Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -1 + \frac{5}{7} }

Cara mengerjakannya adalah mengubah -1 menjadi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\frac{7}{7} }

$-1+{\frac {5}{7}}$ = $-{\frac {7}{7}}+{\frac {5}{7}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\frac{2}{7} }

Lihat beberapa contoh berikut

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -1 + \frac{3}{11} } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\frac{11}{11} + \frac{3}{11} } = $-{\frac {8}{11}}$

$-1+{\frac {4}{5}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\frac{5}{5} + \frac{4}{5} } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\frac{1}{5} }

$-1+{\frac {5}{8}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\frac{8}{8} + \frac{5}{8} } = $-{\frac {3}{8}}$

$-1+{\frac {4}{27}}$ = $-{\frac {27}{27}}+{\frac {4}{27}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\frac{23}{27} }

• Langkah kedua adalah memecah bilangan bulatnya menjadi -1 dan sisanya

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -2 + \frac{5}{7} } = -1 + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (-1 + \frac{5}{7}) } = $-1-{\frac {2}{7}}$ = $-1{\frac {2}{7}}$

Perhatikan contoh berikutnya

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -5 + \frac{5}{7} } = -4 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (-1 + \frac{5}{7}) } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -4 - \frac{2}{7} } = $-4{\frac {2}{7}}$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -7 + \frac{5}{7} } = -6 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (-1 + \frac{5}{7}) } = $-6-{\frac {2}{7}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -6 \frac{2}{7} }

$-6+{\frac {5}{7}}$ = -5 $(-1+{\frac {5}{7}})$ = $-5-{\frac {2}{7}}$ = $-5{\frac {2}{7}}$

$-23+{\frac {5}{7}}$ = -22 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (-1 + \frac{5}{7}) } = $-22-{\frac {2}{7}}$ = $-22{\frac {2}{7}}$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -5 + \frac{2}{9} } = -4 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (-1 + \frac{2}{9}) } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -4 -\frac{7}{9} } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -4 \frac{7}{9} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -7 + \frac{3}{11} } = -6 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (-1 + \frac{3}{11}) } = $-6-{\frac {8}{11}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -6 \frac{8}{11} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -6 + \frac{4}{5} } = -5 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (-1 + \frac{4}{5}) } = $-5-{\frac {1}{5}}$ = $-5{\frac {1}{5}}$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -23 + \frac{7}{12} } = -22 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (-1 + \frac{7}{12}) } = $-22-{\frac {5}{12}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -22 \frac{5}{12} }

Bisakah Anda melihat polanya?

Video

Operation (+ and -) compound Fraction

Pada bagian ini kita belajar bagaiman melakukan penjumlahan dan pengurangan pecahan majemuk.

Ada 4 macam jenis bentuk soal-soal penjumlahan dan pengurangan pecahan majemuk ini.

model 1 : Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2\frac{2}{5} + 3\frac{3}{7} }

Pada model ini pecahan campuran positif ditambah pecahan campuran positif.

Contoh : Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2 \frac{5}{7} + 3 \frac{3}{8} }

• Langkah pertama: jumlahkan bilangan bulatnya

2 + 3 = 5

• Langkah kedua : jumlahkan pecahannya

${\begin{array}{lcl}{\frac {5}{7}}+{\frac {3}{8}}&=&{\frac {5\times 8}{7\times 8}}+{\frac {7\times 3}{7\times 8}}\\&=&{\frac {5\times 8+7\times 3}{7\times 8}}\\&=&{\frac {40+21}{56}}\\&=&{\frac {61}{56}}\\&=&1{\frac {5}{56}}\end{array}}$

• Langkah ketiga : Jumlahkan bilangan bulat dan hasil pecahan

$5+1{\frac {5}{56}}$ = $6{\frac {5}{56}}$

Jadi

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2 \frac{5}{7} + 3 \frac{3}{8} } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6\frac{5}{56} }

Dalam video ini terdapat beberapa contoh lain penjumlahan model 1 ini.

{{#ev:youtube| watch?v=bul1s5UjLsA }}

model 2 : Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -2\frac{2}{5} - 3\frac{3}{7} }

Pada model ini pecahan campuran negatif ditambah pecahan campuran negatif.

Contoh : $-2{\frac {5}{7}}-3{\frac {3}{8}}$

• Langkah pertama: jumlahkan bilangan bulatnya

-2 - 3 = -5

• Langkah kedua : jumlahkan pecahannya (ingat Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -2 \frac{5}{7} = - 2 - \frac{5}{7} }

${\begin{array}{lcl}-{\frac {5}{7}}-{\frac {3}{8}}&=&{\frac {-5\times 8}{7\times 8}}-{\frac {7\times 3}{7\times 8}}\\&=&{\frac {-5\times 8-7\times 3}{7\times 8}}\\&=&{\frac {-40-21}{56}}\\&=&{\frac {-61}{56}}\\&=&-1{\frac {5}{56}}\end{array}}$

• Langkah ketiga : Jumlahkan bilangan bulat dan hasil pecahan

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -5 - 1\frac{5}{56} } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle - 6\frac{5}{56} }

Jadi

$-2{\frac {5}{7}}-3{\frac {3}{8}}$ = $-6{\frac {5}{56}}$

Dalam video ini terdapat beberapa contoh lain penjumlahan model 2 ini.

{{#ev:youtube| watch?v=0Kw7CmMXKoI }}

model 3 : Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2\frac{2}{5} - 3\frac{3}{7} }

Pada model ini pecahan campuran positif dikurangi pecahan campuran positif.

Contoh : Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2 \frac{5}{7} - 3 \frac{3}{8} }

• Langkah pertama: kurangkan bilangan bulatnya

2 - 3 = -1

• Langkah kedua : kurangkan pecahannya

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{lcl} \frac{5}{7} - \frac{3}{8} & = & \frac{5 \times 8}{7 \times 8} - \frac{7 \times 3}{7 \times 8} \\ & = & \frac{5 \times 8 - 7 \times 3}{7 \times 8} \\ & = & \frac{40 - 21}{56} \\ & = & \frac{19}{56} \end{array} }

• Langkah ketiga : Jumlahkan bilangan bulat dan hasil pecahan

$-1+{\frac {19}{56}}$ = $-{\frac {37}{56}}$

Jadi

$2{\frac {5}{7}}-3{\frac {3}{8}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -\frac{37}{56} }

Dalam video ini terdapat beberapa contoh lain penjumlahan model 3 ini.

{{#ev:youtube| watch?v=bul1s5UjLsA }}

model 4 : Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -2\frac{2}{5} + 3\frac{3}{7} }

Pada model ini pecahan campuran negatif ditambah pecahan campuran negatif.

Contoh : Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -2 \frac{5}{7} + 3 \frac{3}{8} }

• Langkah pertama: jumlahkan bilangan bulatnya

-2 + 3 = 1

• Langkah kedua : jumlahkan pecahannya (ingat $-2{\frac {5}{7}}=-2-{\frac {5}{7}}$

${\begin{array}{lcl}-{\frac {5}{7}}+{\frac {3}{8}}&=&{\frac {-5\times 8}{7\times 8}}+{\frac {7\times 3}{7\times 8}}\\&=&{\frac {-5\times 8+7\times 3}{7\times 8}}\\&=&{\frac {-40+21}{56}}\\&=&{\frac {-19}{56}}\end{array}}$

• Langkah ketiga : Jumlahkan bilangan bulat dan hasil pecahan

$1{\frac {-19}{56}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{37}{56} }

Jadi

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -2 \frac{5}{7} + 3 \frac{3}{8} } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{37}{56} }

Dalam video ini terdapat beberapa contoh lain penjumlahan model 4 ini.

{{#ev:youtube| watch?v=0Kw7CmMXKoI }}

Multiplication Fraction

Pembahasan perkalian pecahan akan kita bagi dalam 4 bagian

• Perkalian bilangan bulat dengan pecahan
• Perkalian pecahan dengan bilangan bulat
• Perkalian pecahan dengan pecahan
• Perkalian pecahan majemuk

Whole number x Fraction

Perkalian pecahan menggunakan dasar konsep perkalian yang sudah dipelajari sebelumnya.

Dalam perkalian kita tentu masih ingat bahwa 3 x 2 artinya 3 kotak isi 2, yaitu konkretnya ada 3 kotak yang masing-masing isinya 2.

Jadi hasilnya (abstrak) adalah 3 x 2 = 3▢2 = = 2 + 2 + 2 = 6.

Sekarang bagaimana dengan 2 x ${\frac {1}{2}}$ ?

2 x Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} artinya 2 kotak isi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}}

Konkretnya ada 2 kotak yang masing-masing berisi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}}

Error creating thumbnail: Unable to save thumbnail to destination

Jadi, abstraknya adalah

2 x ${\frac {1}{2}}$ = 2▢${\frac {1}{2}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} = ${\frac {2}{2}}$ = 1

Begitu pula

3 x ${\frac {1}{2}}$ = 3▢${\frac {1}{2}}$ = ${\frac {1}{2}}$ + ${\frac {1}{2}}$ + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{2}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{2}}

Kongkretnya digambarkan sebagai 3 kotak masing-masing berisi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{2}}

Lakukan kegiatan eksplorasi perkalian bilangan bulat dengan pecahan seperti di atas dengan berbagai soal sehingga siswa menemukan pola bagaimana mendapatkan hasilnya dengan cepat, yaitu dengan mengalikan bilangan bulat dengan pembilang.

Contohnya

3 x ${\frac {2}{5}}$ = 3▢${\frac {2}{5}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{5}} + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{5}} + Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{5}} = ${\frac {3\times 2}{5}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{6}{5}}

Cara cepat

Fraction x whole number

Bagaimana dengan perkalian bilangan pecahan dengan bilangan bulat seperti Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} x 6 ?

${\frac {1}{2}}$ x 6 artinya Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} kotak isi 6.

Jadi konkretnya ada 6 kue dalam suatu kotak lalu kita bagi kotak tersebut menjadi 2 bagian yang sama besar (sehingga banyaknya kue dalam tiap bagian sama). lalu kita hitung berapa isi kotak yang setengah itu?

Hasilnya adalah 3

Jadi ${\frac {1}{2}}$ x 6 = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} ▢6 = 3

Sekarang bagaimana dengan ${\frac {1}{3}}$ x 6 = ?

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3}} x 6 artinya Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3}} kotak isi 6, jadi konkretnya ada 6 kue dalam suatu kotak lalu kita bagi kotak tersebut menjadi 3 bagian yang sama besar (sehingga banyaknya kue dalam tiap bagian sama). Lalu kita hitung berapa isi satu bagian kotak itu?

Hasilnya adalah 2

Jadi ${\frac {1}{3}}$ x 6 = ${\frac {1}{3}}$▢6 = 2

Bagaimana dengan ${\frac {1}{3}}$ x 9 = ?

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3}} x 9 artinya Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3}} kotak isi 9, jadi konkretnya ada 9 kue dalam suatu kotak lalu kita bagi kotak tersebut menjadi 3 bagian yang sama besar (sehingga banyaknya kue dalam tiap bagian sama). Lalu kita hitung berapa isi satu bagian kotak itu?

Hasilnya adalah 3

Jadi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3}} x 9 = ${\frac {1}{3}}$▢9 = 3

Perhatikan hasil-hasil yang kita peroleh

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} x 6 hasilnya sama dengan 6÷2 yaitu 3

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3}} x 6 hasilnya sama dengan 6÷3 yaitu 2

${\frac {1}{3}}$ x 9 hasilnya sama dengan 9÷3 yaitu 3

Kesimpulan apa yang kita peroleh?

Kita lihat bahwa perkalian pecahan dengan bilangan bulat sama dengan pembagian bilangan bulat itu dengan penyebut.

Bagaimana dengan ${\frac {2}{3}}$ x 9 = ?

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{3}} artinya 2 x ${\frac {1}{3}}$

Jadi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{3}} x 9 = 2 x Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3}} x 9 = 2 x 3 = 6

Jadi disini kita hitung dulu 9 ÷ 3 kemudian hasilnya dikalikan dengan 2.

Secara kongkret ini dapat digambarkan sebagai berikut. Hasilnya adalah 6 kue yang ada dalam daerah yang diarsir.

Berikut ini beberapa contoh perkalian pecahan dengan bilangan bulat

a) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{4}} x 12 = ?

${\frac {3}{4}}$ artinya 3 x ${\frac {1}{4}}$

Jadi ${\frac {3}{4}}$ x 12 = 3 x ${\frac {1}{4}}$ x 12 = 3 x 3 = 9

Error creating thumbnail: Unable to save thumbnail to destination

b) ${\frac {5}{6}}$ x 30 = ?

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{5}{6}} artinya 5 x Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{6}}

Jadi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{5}{6}} x 30 = 5 x Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{6}} x 30 = 5 x 5 = 25

c) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{5}{7}} x 49 = ?

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{5}{7}} artinya 5 x ${\frac {1}{7}}$

Jadi ${\frac {5}{7}}$ x 49 = 5 x ${\frac {1}{7}}$ x 49 = 5 x 7 = 35

Error creating thumbnail: Unable to save thumbnail to destination

d) ${\frac {7}{9}}$ x 18 = ?

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{7}{9}} artinya 7 x Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{9}}

Jadi ${\frac {7}{9}}$ x 18 = 7 x Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{9}} x 18 = 7 x 2 = 14

Error creating thumbnail: Unable to save thumbnail to destination

Video berikut menunjukan beberapa contoh perkalian bilangan pecahan dengan bilangan bulat.

Video

Fraction x Fraction

Pada bab ini kita akan belajar tentang perkalian pecahan biasa dengan pecahan biasa, seperti Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{5} \times \frac{3}{7}}

Kita akan gunakan papan pecahan sebagai alat bantu.

Misalkan kita akan menghitung Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} × ${\frac {1}{2}}$

Ini adalah pecahan ${\frac {1}{2}}$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2} \times \frac{1}{2}} artinya Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} kotak isinya ${\frac {1}{2}}$

Jadi disini kotak ${\frac {1}{2}}$ kita bagi menjadi dua bagian yang sama besar.

Kita cari dipapan pecahan, pecahan mana yang besarnya Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} tetapi terbagi atas dua bagian.

Jawabnya adalah pecahan ${\frac {1}{4}}$

Jadi kita lihat bahwa kalau Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} dibagi 2, hasilnya adalah Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{4}}

Dengan demikian Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2} \times \frac{1}{2}} = ${\frac {1}{4}}$

Perhatikan beberapa contoh berikut

a) ${\frac {1}{2}}\times {\frac {1}{3}}$

• Pertama kita buat dulu pecahan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3} }
• Kemudian pecahan tersebut dibagi menjadi dua bagian yang sama besar.
• Salah satu bagian ini nilainya adalah Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2} \times \frac{1}{3}}

• Kalau kita perhatikan pada gambar diatas Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2} \times \frac{1}{3}} adalah nilai satu bagian dari satu kelompok yang terdiri dari 6 bagian yang sama besar. Ini adalah definisi ${\frac {1}{6}}$

Error creating thumbnail: Unable to save thumbnail to destination

• Sehingga bisa disimpulkan bahwa ${\frac {1}{2}}\times {\frac {1}{3}}$ = ${\frac {1}{6}}$

b) ${\frac {1}{3}}\times {\frac {1}{2}}$

• Pertama kita buat dulu pecahan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2} }
• Kemudian pecahan tersebut dibagi menjadi tiga bagian yang sama besar.
• Salah satu bagian ini nilainya adalah Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3} \times \frac{1}{2}}

• Kalau kita perhatikan pada gambar diatas Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3} \times \frac{1}{2}} adalah nilai satu bagian dari satu kelompok yang terdiri dari 6 bagian yang sama besar. Ini adalah definisi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{6} }

• Sehingga bisa disimpulkan bahwa ${\frac {1}{3}}\times {\frac {1}{2}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{6} }

c) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2} \times \frac{2}{3}}

• Pertama kita buat dulu pecahan ${\frac {2}{3}}$

Error creating thumbnail: Unable to save thumbnail to destination

• Kemudian pecahan tersebut dibagi menjadi dua bagian yang sama besar.
• Salah satu bagian ini nilainya adalah ${\frac {1}{2}}\times {\frac {2}{3}}$

• Kalau kita perhatikan pada gambar diatas ${\frac {1}{2}}\times {\frac {2}{3}}$ adalah nilai dua bagian dari satu kelompok yang terdiri dari 6 bagian yang sama besar. Ini adalah definisi Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{6} }

• Sehingga bisa disimpulkan bahwa Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2} \times \frac{2}{3}} = ${\frac {2}{6}}$

Lakukan eksplorasi ini berulang-ulang, sampai siswa melihat pola bahwa pada perkalian pecahan dengan pecahan, maka hasilnya diperoleh dengan mengalikan pembilang dengan pembilang dan penyebut dengan penyebut.

Perhatikan contoh beberapa perkalian pecahan dibawah ini

• a) ${\frac {2}{3}}\times {\frac {3}{5}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2 \times 3}{3 \times 5} } = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{6}{15} } = ${\frac {2}{5}}$

• b) ${\frac {5}{7}}\times {\frac {7}{9}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{5 \times 7}{7 \times 9} } = ${\frac {35}{63}}$ = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{5}{9} }

Cara coret:

Ada kalanya dalam perkalian pecahan kita bisa lakukan cara cepat yaitu dengan membagi pembilang dan penyebut dengan bilangan tertentu sebelum mereka dikalikan.

Perhatikan contoh berikut

a) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{3} \times \frac{3}{5}}

• Langkah pertama adalah mengalikan pembilang dengan pembilang dan penyebut dengan penyebut

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{3} \times \frac{3}{5}} = ${\frac {2\times 3}{3\times 5}}$

• Langkah kedua adalah membagi pembilang dan penyebut dengan 3.

Pembilang 3 ÷ 3 = 1

Penyebut 3 ÷ 3 = 1

• Langkah ketiga adalah kalikan pembilang dengan pembilang dan penyebut dengan penyebut

Pembilang 2 x 1 = 2

Penyebut 1 x 5 = 5

• Hasilnya adalah ${\frac {2}{5}}$

Kalau sudah mahir kita bisa coret diawal seperti pada gambar ini.

Pembilang 2 x 1 = 2

Penyebut 1 x 5 = 5

Hasilnya ${\frac {2}{5}}$

b) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{5}{7} \times \frac{7}{9}}

• Langkah pertama adalah mengalikan pembilang dengan pembilang dan penyebut dengan penyebut

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{5}{7} \times \frac{7}{9}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{5 \times 7}{7 \times 9} }

• Langkah kedua adalah membagi pembilang dan penyebut dengan 7.

Pembilang 7÷7 = 1

Penyebut 7÷7 = 1

• Langkah ketiga adalah kalikan pembilang dengan pembilang dan penyebut dengan penyebut

Pembilang 5 x 1 = 5

Penyebut 1 x 9 = 9

• Hasilnya adalah ${\frac {5}{9}}$

Error creating thumbnail: Unable to save thumbnail to destination

Kalau sudah mahir kita bisa coret diawal seperti pada gambar ini.

Error creating thumbnail: Unable to save thumbnail to destination

Pembilang 5 x 1 = 5

Penyebut 1 x 9 = 9

Hasilnya ${\frac {5}{9}}$

c) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{16}{15} \times \frac{9}{4}}

Kita bisa selesaikan soal ini dengan mengalikan pembilang dengan pembilang dan penyebut dengan penyebut. Kemudian kita sederhanakan seperti ditunjukan pada gambar ini.

Error creating thumbnail: Unable to save thumbnail to destination

Atau kita melakukan penyederhanaan diawal pembilang dan penyebut dibagi dengan bilangan yang sama.

16 ÷ 4 = 4 (pembilang) dan 4 ÷ 4 = 1 (penyebut)

15 ÷ 3 = 5 (penyebut) dan 9:3 = 3 (pembilang)

Kemudian mengalikan pembilang dengan pembilang dan penyebut dengan penyebut

Pembilang = 4 x 3 = 12

Penyebut = 5 x 1 = 5

Error creating thumbnail: Unable to save thumbnail to destination

Video berikut ini beberapa contoh perkalian pecahan dengan pecahan

Compound x Compound

Pada perkalian pecahan majemuk, kita harus mengubah dulu pecahan majemuk ini menjadi pecahan biasa. Setelah itu kita bisa lakukan perkalian pecahan seperti yang sudah dipelajari sebelumnya.

Perhatikan contoh berikut

a) $2{\frac {4}{7}}\times 3{\frac {2}{4}}$ =

Hasil perhitungan diberikan pada gambar dibawah ini

Error creating thumbnail: Unable to save thumbnail to destination

b) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3 \frac{3}{7} \times 2\frac{12}{15}} =

Hasil perhitungan diberikan pada gambar dibawah ini

c) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1 \frac{4}{8} \times 3\frac{7}{14}} =

Hasil perhitungan dapat dilihat pada gambar dibawah ini

Pada soal diatas kita bisa juga menyederhanakan pecahan lebih awal lagi

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{4}{8} = \frac{1}{2}}

${\frac {7}{14}}={\frac {1}{2}}$

Hasilnya adalah

Video berikut ini memberikan beberapa variasi soal perkalian pecahan majemuk

Video

Division Fraction

Pembahasan pembagian pecahan akan kita bagi dalam 4 bagian

• Pembagian bilangan bulat dengan pecahan
• Pembagian pecahan dengan bilangan bulat
• Pembagian pecahan dengan pecahan
• Pembagian pecahan majemuk

Whole number ÷ Fraction

Pembagian pecahan menggunakan dasar konsep pembagian yang sudah dipelajari sebelumnya.

Dalam pembagian kita tentu masih ingat bahwa 6 ÷ 2 artinya saya punya 6 kue hendak dimasukan dalam 2 kotak, berapa yang diterima tiap kotak.

Kita sudah tahu bahwa jawabnya adalah 3.

Bagaimana dengan pembagian 1 ÷ Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}}  ?

Saya punya kue hendak dimasukan dalam kotak dengan kapasitas atau ukuran Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} , berapa banyak potong kue dapat dimasukan dalam kotak tersebut?

Gambar dibawah ini menggambarkan situasi ketika 1 potong kue sudah masuk kotak.

Ini gambar situasi ketika 2 potong kue sudah masuk kotak.

Jadi total potongan kue yang diterima oleh kotak adalah 2.

Sehingga

1 ÷ ${\frac {1}{2}}$ = 2

Sekarang kita akan hitung 1 ÷ ${\frac {1}{4}}$

Pada gambar diatas kita punya 1 kue, hendak kita masukan dalam kotak dengan kapasitas atau ukuran Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{4}} .

Kue kita bagi menjadi potongan ${\frac {1}{4}}$ agar bisa masuk kotak.

Kita lihat bahwa kotak itu bisa menerima 4 potong kue.

Jadi

1 ÷ Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{4}} = 4

Dengan cara yang sama kita bisa dapatkan bahwa

1 ÷ ${\frac {1}{3}}$ = 3

1 ÷ ${\frac {1}{6}}$ = 6

1 ÷ Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{10}} = 10

Pola apa yang Anda lihat?

Bagaimana kalau 2 ÷ Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} = ?

Karena

1 ÷ ${\frac {1}{2}}$ = 2

maka

2 ÷ Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} = 2 x 2 = 4

Error creating thumbnail: Unable to save thumbnail to destination

Dengan cara yang sama kita bisa peroleh

2 ÷ ${\frac {1}{3}}$ = 2 x 3 = 6

2 ÷ Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{4}} = 2 x 4 = 8

2 ÷ ${\frac {1}{6}}$ = 2 x 6 = 12

2 ÷ Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{10}} = 2 x 10 = 20

Dan dengan pola yang sama kita bisa peroleh

5 ÷ Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3}} = 5 x 3 = 15

9 ÷ ${\frac {1}{4}}$ = 9 x 4 = 36

12 ÷ ${\frac {1}{6}}$ = 12 x 6 = 72

25 ÷ ${\frac {1}{10}}$ = 25 x 10 = 250

Cara cepat

Pembagian bilangan bulat dengan pecahan dapat digambarkan sebagai berikut. Kita mengalikan penyebut dengan bilangan bulat.

Umtuk pembilang lebih dari 1 maka pembagian bilangan bulat dengan pecahan adalah dengan cara berikut

kalikan penyebut dengan bilangan bulat

Bagi hasilnya dengan pembilang dari pecahan

Video berikut menunjukan berbagai contoh pembagian bilangan bulat dengan pecahan.

Fraction x whole number

Bagaimana dengan pembagian bilangan pecahan dengan bilangan bulat seperti Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} ÷ 2 ?

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} ÷ 2 artinya ${\frac {1}{2}}$ kue hendak dimasukan dalam 2 kotak. Berapa isi masing-masing kotak agar pembagian ini adil dan merata.

Yang kita perlu lakukan adalah membagi dua kue ${\frac {1}{2}}$ itu. Kemudian memasukan tiap bagian ke dalam kotak. Kita lihat tiap kotak akan menerima masing-masing ${\frac {1}{4}}$ kue.

Dengan demikian ${\frac {1}{2}}$ ÷ 2 = ${\frac {1}{4}}$

Sekarang bagaimana dengan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3}}  : 2 = ?

Kita bisa gunakan papan pecahan.

Ini pecahan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3}}

Cari di papan pecahan, pecahan yang nilainya Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3}} tapi terbagi 2.

Jawabnya adalah pada gambar ini

Disini terlihat bahwa ${\frac {1}{3}}:2={\frac {1}{6}}$

Bagaimana dengan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} ÷ 5 = ?

Kita bisa gunakan papan pecahan.

Ini pecahan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}}

Cari di papan pecahan, pecahan yang nilainya Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} tapi terbagi 5.

Jawabnya adalah pada gambar ini

Error creating thumbnail: Unable to save thumbnail to destination

Disini terlihat bahwa ${\frac {1}{2}}:5={\frac {1}{10}}$

Perhatikan hasil-hasil yang kita peroleh dibawah ini

${\frac {1}{2}}$ ÷ 6 hasilnya sama dengan Failed to parse (syntax error): {\displaystyle \frac{1}{2×6}} yaitu Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{12}}

${\frac {1}{3}}$ ÷ 4 hasilnya sama dengan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3×4}} yaitu ${\frac {1}{12}}$

${\frac {1}{5}}$ ÷ 7 hasilnya sama dengan Failed to parse (syntax error): {\displaystyle \frac{1}{5×7}} yaitu Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{35}}

Kesimpulan apa yang kita peroleh?

Kita lihat bahwa pembagian pecahan dengan bilangan bulat sama dengan penyebutnya dikalikan dengan bilangan bulat.

Sedangkan pembilang tetap sama.

Video berikut menunjukan beberapa contoh perkalian bilangan pecahan dengan bilangan bulat.

Video

Fraction ÷ Fraction

Pada bab ini kita akan belajar tentang pembagian pecahan biasa dengan pecahan biasa, seperti Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{5} \div \frac{3}{7}}

Kita akan gunakan papan pecahan sebagai alat bantu.

Misalkan kita akan menghitung Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} ÷ ${\frac {1}{4}}$

Ini adalah pecahan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2} \div \frac{1}{4}} artinya ada ${\frac {1}{2}}$ kue hendak dimasukan dalam kotak dengan kapasitas atau ukuran ${\frac {1}{4}}$, ada berapa banyak potongan kue bisa diterima tiap kotak?

Kita cari pada batang pecahan, kotak pecahan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{4}} . Kemudian lihat ada berapa pecahan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{4} } yang jumlah nilainya Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2}} ?

Pada gambar terlihat bahwa ada 2 buah pecahan ${\frac {1}{4}}$ yang jumlahnya ${\frac {1}{2}}$.

Dengan demikian Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2} \div \frac{1}{4}} = 2

Perhatikan beberapa contoh berikut

a) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2} \div \frac{1}{8}}

• Cari di papan pecahan, pecahan ${\frac {1}{2}}$

• Cari di papan pecahan, pecahan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{8}} , kemudian hitung ada berapa pecahan ${\frac {1}{8}}$

yang nilainya Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2} } .

Error creating thumbnail: Unable to save thumbnail to destination

• Kalau kita perhatikan pada gambar diatas jawabnya adalah 4
• Sehingga bisa disimpulkan bahwa ${\frac {1}{2}}\div {\frac {1}{8}}$ = 4.

b) ${\frac {1}{3}}\div {\frac {1}{2}}$

• Pertama kita cari pada papan pecahan, pecahan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3} }

• Tempatkan pecahan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3} } ini ke dalam kotak ${\frac {1}{2}}$

• Perhatikan berapa bagian dari kotak ${\frac {1}{2}}$ ditempati pecahan ${\frac {1}{3}}$?

Gunakan bantuan pecahan Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{6} }

Jawabnya adalah ${\frac {2}{3}}$ (dua bagian dari suatu kelompok yang terdiri dari tiga bagian yang sama besar).

Jadi jawabnya

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{3} \div \frac{1}{2}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{3} }

Pembagian pecahan cara khusus

semuanya penyebut disamakan

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{5}{7} \times \frac{7}{9}}

Video berikut ini beberapa contoh pembagian pecahan dengan pecahan

Compound x Compound

Pada perkalian pecahan majemuk, kita harus mengubah dulu pecahan majemuk ini menjadi pecahan biasa. Setelah itu kita bisa lakukan perkalian pecahan seperti yang sudah dipelajari sebelumnya.

Perhatikan contoh berikut

a) $2{\frac {4}{7}}\times 3{\frac {2}{4}}$ =

Hasil perhitungan diberikan pada gambar dibawah ini

Error creating thumbnail: Unable to save thumbnail to destination

b) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3 \frac{3}{7} \times 2\frac{12}{15}} =

Hasil perhitungan diberikan pada gambar dibawah ini

c) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1 \frac{4}{8} \times 3\frac{7}{14}} =

Hasil perhitungan dapat dilihat pada gambar dibawah ini

Pada soal diatas kita bisa juga menyederhanakan pecahan lebih awal lagi

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{4}{8} = \frac{1}{2}}

${\frac {7}{14}}={\frac {1}{2}}$

Hasilnya adalah

Video berikut ini memberikan beberapa variasi soal perkalian pecahan majemuk

Video

Fraction x whole number

Whole number x Fraction

Fraction x Fraction

Compound x Compound