Pernah bingung nggak ketika mengalikan atau membagi bilangan bulat? Apalagi kalo angkanya negatif. Nah, di artikel Matematika kelas 7 ini, bakal dibahas sifat operasi serta contoh mudahnya biar kamu paham!
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Kamu pasti udah nggak asing lagi kan dengan operasi penjumlahan dan pengurangan bilangan bulat. Dua operasi ini sering banget kita temui pada soal-soal matematika dasar di sekolah. Nah, ternyata selain penjumlahan dan pengurangan, ada dua operasi dasar lain yang nggak kalah penting, yaitu perkalian dan pembagian bilangan bulat.
Kenapa sih kita perlu belajar dan memahaminya? Karena operasi perkalian dan pembagian bilangan bulat sering muncul dalam kehidupan sehari-hari. Misalnya, ketika kamu ingin menghitung total harga beberapa barang yang sama, atau saat membagi rata makanan dengan teman.
Oleh karena itu, yuk, kita pelajari bersama cara menyelesaikan perkalian dan pembagian bilangan bulat! Artikel ini juga diserta sifat-sifat dan contoh soal supaya kamu semakin paham!
1. Operasi Perkalian Bilangan Bulat
Operasi ini biasanya dilambangkan dengan tanda silang (×) atau tanda titik (∙). Secara konsep, perkalian itu sebenarnya bisa dianggap sebagai bentuk penjumlahan berulang. Contohnya nih, kamu ingin menjumlahkan beberapa bilangan bulat yang sama, seperti:
Angka 3, dijumlahkan sebanyak 5 kali. Maka:
3 + 3 + 3 + 3 + 3 = 15
Nah, kamu bisa menubahnya ke dalam bentuk perkalian, menjadi:
3 × 5 = 15
Baca Juga: Penjelasan Lengkap KPK dan FPB, Apa Bedanya Ya?
Aturan Tanda dalam Operasi Perkalian Bilangan Bulat
Sebelum memahami sifat-sifat perkalian bilangan bulat, kita ingat dulu yuk, kalo:
-
Bilangan bulat positif adalah bilangan yang nilainya lebih dari nol (a > 0).
-
Bilangan bulat negatif adalah bilangan yang nilainya kurang dari nol (a < 0).
-
Bilangan nol (0) juga termasuk bilangan bulat.
Artinya, kalo kedua bilangan punya tanda yang sama, hasilnya positif. Tapi, kalo kedua bilangan punya tanda berbeda, hasilnya negatif.
Contoh:
- 5 × 3 = 15 (positif ketemu positif, hasilnya positif)
- (–5) × (–3) = 15 (negatif ketemu negatif, hasilnya positif)
- (–5) × 3 = –15 (negatif ketemu positif, hasilnya negatif)
- 5 × (–3) = –15 (positif ketemu negatif, hasilnya negatif)
Sifat-Sifat Operasi Perkalian Bilangan Bulat
Paham sampai sini? Kita lanjut ya…
Operasi perkalian bilangan bulat itu punya sifat-sifat yang akan membantu kamu menghitung lebih cepat. Berikut sifat-sifat perkalian yang perlu kamu pahami:
1. Tertutup
Artinya, kalau kita mengalikan dua bilangan bulat, hasilnya pasti tetap berupa bilangan bulat.
Contoh: 5 × (–2) = –10 (masih bilangan bulat)
2. Identitas
Dalam perkalian, angka 1 disebut unsur netral. Kenapa? Karena setiap bilangan bulat yang dikalikan dengan 1, hasilnya akan tetap bilangan itu sendiri.
Contoh: (–7) × 1 = –7
3. Komutatif (Pertukaran)
Dalam perkalian bilangan bulat, urutan faktor tidak mempengaruhi hasil. Jadi, jika bilangan pertama dan bilangan kedua ditukar posisinya, hasilnya akan tetap sama.
Contoh: 6 × (–3) hasilnya akan sama dengan (–3) × 6, yaitu –18.
4. Asosiatif (Pengelompokan)
Kalau ada lebih dari dua bilangan bulat yang dikalikan, urutan pengelompokan bilangan juga tidak akan mempengaruhi hasil. Jadi, kamu bisa mengelompokkan bilangan dengan tanda kurung dalam urutan apapun, dan hasilnya akan tetap sama.
Contoh: (2 × –4) × 3 hasilnya akan sama dengan 2 × (–4 × 3), yaitu –24.
Baca Juga: Cara Menyelesaikan Bentuk-Bentuk Aljabar
5. Distribusi Perkalian terhadap Penjumlahan
Jadi, kalo ada bilangan bulat dikalikan dengan jumlah dari dua bilangan, kita bisa mengalikan bilangan itu ke masing-masing anggota penjumlahan, lalu menjumlahkan hasilnya.
Contoh: 2 × (3 + 5) = (2 × 3) + (2 × 5) = 6 + 10 = 14
6. Perkalian dengan Nol
Apapun bilangan bulatnya, kalau dikalikan dengan 0, hasilnya pasti 0. Sifat ini sangat mudah diingat karena berlaku untuk semua bilangan, baik bilangan positif maupun negatif.
Contoh: (–8) × 0 = 0
2. Operasi Pembagian Bilangan Bulat
Invers, atau lawan dari operasi perkalian adalah operasi pembagian. Jadi, pembagian bisa disebut sebagai “kebalikan” dari perkalian.
Operasi pembagian biasanya disimbolkan dengan tanda titik dua (÷ atau 🙂 atau tanda garis miring (/). Nah, kalau perkalian adalah penjumlahan berulang, maka pembagian bisa kita pahami sebagai pengurangan berulang sampai habis.
Contoh:
12 ÷ 3 = 4, karena 12 bisa dikurangi dengan 3 sebanyak 4 kali hingga habis, atau:
12 – 3 – 3 – 3 – 3 = 0
Syarat Operasi Pembagian Bilangan Bulat
Nah, ada satu aturan yang sangat penting dalam menyelesaikan operasi pembagian. Jika sebuah bilangan bulat a dibagi dengan bilangan bulat b, maka b tidak boleh nol (b ≠ 0).
Kenapa? Karena kalau b = 0, hasilnya akan tidak terdefinisi. Artinya, pembagian dengan nol tidak punya jawaban yang sah secara matematika.
Contoh:
10 ÷ 2 = 5
10 ÷ 0 = tidak terdefinisi nilainya
Baca Juga: Aturan Penulisan Bentuk Baku Bilangan Matematika
Aturan Tanda dalam Operasi Pembagian Bilangan Bulat
Aturannya mirip dengan perkalian, kalo kedua bilangan punya tanda yang sama, hasilnya positif. Tapi, kalo kedua bilangan punya tanda berbeda, hasilnya negatif.
Contoh:
- 12 ÷ 3 = 4 (positif ketemu positif, hasilnya positif)
- (–12) ÷ (–3) = 4 (negatif ketemu negatif, hasilnya positif)
- 12 ÷ (–3) = –4 (positif ketemu negatif, hasilnya negatif)
- (–12) ÷ 3 = –4 (negatif ketemu positif, hasilnya negatif)
Sifat-Sifat Operasi Pembagian Bilangan Bulat
Operasi pembagian juga punya aturan dan sifat yang berbeda. Supaya kamu nggak salah langkah, yuk kita bahas satu per satu sifat-sifat pembagian bilangan bulat:
1. Tidak Bersifat Komutatif
Kalau pada perkalian, kita bisa menukar posisi bilangan tanpa mengubah hasil (misalnya 3 × 4 = 4 × 3), hal itu tidak berlaku dalam pembagian. Pada pembagian, posisi bilangan sangat menentukan hasil akhirnya.
Contoh: 12 ÷ 3 = 4
Tapi, kalau dibalik, hasilnya menjadi 3 ÷ 12 = 0,25.
2. Tidak Bersifat Asosiatif
Dalam perkalian, kita juga bebas mengelompokkan bilangan tanpa mengubah hasil (misalnya (2 × 3) × 4 = 2 × (3 × 4)). Tapi dalam pembagian, cara mengelompokkan bilangan tetap mempengaruhi hasil akhir.
Contoh:
(12 ÷ 6) ÷ 2 = 2 ÷ 2 = 1.
Tetapi jika dikelompokkan, hasilnya akan berbeda, yaitu: 12 ÷ (6 ÷ 2) = 12 ÷ 3 = 4.
3. Identitas
Dalam operasi pembagian, angka 1 juga menjadi unsur identitas karena membagi bilangan berapapun dengan 1 akan menghasilkan bilangan itu sendiri.
Contoh: (–9) ÷ 1 = –9
4. Pembagian dengan Diri Sendiri, Hasilnya 1
Setiap bilangan bulat, jika dibagi dengan dirinya sendiri, hasilnya selalu 1. Namun, hati-hati! Kalau 0 ÷ 0, hasilnya tidak terdefinisi, sehingga aturan ini tidak berlaku untuk nol.
Contoh: 15 ÷ 15 = 1.
5. Hubungan dengan Perkalian
Pembagian bisa dianggap sebagai kebalikan dari perkalian. Artinya, kalau kamu tahu hasil perkalian, maka kamu bisa menemukan hasil pembagian.
Contoh: 20 ÷ 4 = 5, karena kita tahu 4 × 5 = 20.
Dengan kata lain, pembagian adalah cara mencari bilangan yang dikalikan untuk mendapatkan hasil tertentu.
Baca Juga: Mengenal Bilangan Rasional dan Irasional
Contoh Soal dan Pembahasan
1. Harga 1 kodi kain adalah Rp300.000, berapa harga 5 helai kain yang sama?
- Rp60.000
- Rp65.000
- Rp70.000
- Rp75.000
Jawaban: D
Pembahasan:
Untuk menjawab soal di atas, pertama-tama, kita cari tau dulu harga satu helai kainnya.
1 kodi kain = 20 helai kain
Maka, harga 1 helai kain = Rp 300.000 ÷ 20 = Rp15.000,00
Harga 5 helai kain = Harga 1 helai kain × 5
Harga 5 helai kain = Rp15.000 × 5
Harga 5 helai kain = Rp75.000
Jadi, harga 5 helai kain adalah Rp75.000. Jawaban yang tepat yaitu D.
2. Seorang pemborong dapat menyelesaikan bangunan pos keamanan selama 20 hari dengan total pekerja sebanyak 9 orang. Agar pekerjaan itu selesai dalam waktu 15 hari, berapa tambahan pekerja yang dibutuhkan?
- 12 orang
- 6 orang
- 5 orang
- 3 orang
Jawaban: D
Pembahasan:
Diketahui:
- Jumlah pekerja awal = 9 orang
- Lama kerja awal = 20 hari
- Lama kerja baru = 15 hari
- Jumlah pekerja baru = ?
Nah, kalo kamu menemukan tipe soal ini, kamu dapat menyelesaikannya menggunakan konsep perbandingan. Kamu juga perlu paham bahwa, ‘jika jumlah hari diperkecil, maka jumlah pekerja harus diperbesar, begitu juga sebaliknya’.
Sehingga,
Jadi, tambahan pekerja yang diperlukan adalah 12 – 9 = 3 orang. Jawaban yang tepat yakni D.
—
Itulah pembahasan mengenai operasi perkalian dan pembagian bilangan bulat. Bagaimana? Apakah menurutmu pembahasan di atas sudah jelas?
Kalo kamu masih ingin belajar lebih banyak lagi? Boleh banget! Yuk, cobain download dan belajar bareng Master Teacher di ruangbelajar! Ada fitur konsep kilat yang bisa membantu kamu mempelajari ringkasan, dan juga video Adapto yang bisa menyesuaikan kemampuanmu menerima materi! Ayo, gabung belajar di ruangbelajar, yuk!
Referensi:
As’ari A.R, Tohir M, Valentino E, Imron Z, Taufiq I. (2017) Matematika SMP/MTs Kelas VII Semester I. Pusat Kurikulum dan Perbukuan, Balitbang, Kemendikbud.
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<h1 class="content-title">
Operasi Perkalian dan Pembagian pada Bilangan Bulat | Matematika Kelas 7 </h1>
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<p class="content-author"><a href="https://www.ruangguru.com/blog/author/hani-ammariah" class="">Hani Ammariah</a> </p>
<p class="content-info"><span>August 13, 2025 • </span> <span>6 minutes read</span></p>
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<p style="text-align: justify;"><img decoding="async" class="aligncenter" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/2d966a3a-9ac8-442e-97ff-6d06ed2a36c7.png" alt="cara menyelesaikan operasi perkalian dan pembagian bilangan bulat" width="820" /></p>
<blockquote>
<p style="text-align: center;"><em>Pernah bingung nggak ketika mengalikan atau membagi bilangan bulat? Apalagi kalo angkanya negatif. Nah, di <strong><a href="https://www.ruangguru.com/blog/c/matematika/matematika-smp-kelas-7">artikel Matematika kelas 7</a></strong> ini, bakal dibahas sifat operasi serta contoh mudahnya biar kamu paham!</em></p>
</blockquote>
<p style="text-align: center;">—</p>
<p> </p>
<p style="text-align: justify;">Kamu pasti udah nggak asing lagi kan dengan <strong><a href="https://www.ruangguru.com/blog/pengertian-dan-contoh-bilangan-bulat">operasi penjumlahan dan pengurangan bilangan bulat</a></strong>. Dua operasi ini sering banget kita temui pada soal-soal matematika dasar di sekolah. Nah, ternyata selain penjumlahan dan pengurangan, ada dua operasi dasar lain yang nggak kalah penting, yaitu <strong>perkalian dan pembagian bilangan bulat</strong>.</p>
<p style="text-align: justify;">Kenapa sih kita perlu belajar dan memahaminya? Karena operasi perkalian dan pembagian bilangan bulat sering muncul dalam kehidupan sehari-hari. Misalnya, ketika kamu ingin menghitung total harga beberapa barang yang sama, atau saat membagi rata makanan dengan teman.</p>
<p style="text-align: justify;">Oleh karena itu, yuk, kita pelajari bersama cara menyelesaikan perkalian dan pembagian bilangan bulat! Artikel ini juga diserta sifat-sifat dan contoh soal supaya kamu semakin paham!</p>
<p> </p>
<h2 style="text-align: justify;"><span style="font-size: 18pt;">1. Operasi Perkalian Bilangan Bulat</span></h2>
<p style="text-align: justify;">Operasi ini biasanya dilambangkan dengan <strong>tanda silang (×) atau tanda titik (∙)</strong>. Secara konsep, perkalian itu sebenarnya bisa dianggap sebagai bentuk <strong>penjumlahan berulang</strong>. Contohnya nih, kamu ingin menjumlahkan beberapa bilangan bulat yang sama, seperti:</p>
<p style="text-align: justify;">Angka 3, dijumlahkan sebanyak 5 kali. Maka:</p>
<p style="text-align: center;">3 + 3 + 3 + 3 + 3 = 15</p>
<p> </p>
<p style="text-align: justify;">Nah, kamu bisa menubahnya ke dalam bentuk perkalian, menjadi:</p>
<p style="text-align: center;">3 × 5 = 15</p>
<p> </p>
<p><strong>Baca Juga: <a href="https://www.ruangguru.com/blog/matematika-kelas-7-mengingat-kembali-apa-itu-kpk-dan-fpb">Penjelasan Lengkap KPK dan FPB, Apa Bedanya Ya?</a></strong></p>
<p> </p>
<h3 style="text-align: justify;"><span style="font-size: 14pt;">Aturan Tanda dalam Operasi Perkalian Bilangan Bulat</span></h3>
<p style="text-align: justify;">Sebelum memahami sifat-sifat perkalian bilangan bulat, kita ingat dulu yuk, kalo:</p>
<ul>
<li style="text-align: justify;"><strong>Bilangan bulat positif</strong> adalah bilangan yang nilainya lebih dari nol (a > 0).</li>
<li style="text-align: justify;"><strong>Bilangan bulat negatif</strong> adalah bilangan yang nilainya kurang dari nol (a < 0).</li>
<li style="text-align: justify;"><strong>Bilangan nol (0)</strong> juga termasuk bilangan bulat.</li>
</ul>
<p> </p>
<p><img decoding="async" class="aligncenter size-medium" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/239a1b74-1cd3-4280-a229-c95744d83517.png" alt="aturan tanda dalam operasi perkalian bilangan bulat" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Artinya, kalo kedua bilangan punya <strong>tanda yang sama, hasilnya positif</strong>. Tapi, kalo kedua bilangan punya <strong>tanda berbeda, hasilnya negatif</strong>.</p>
<p style="text-align: justify;">Contoh:</p>
<ul>
<li style="text-align: justify;">5 × 3 = 15 (positif ketemu positif, hasilnya positif)</li>
<li style="text-align: justify;">(–5) × (–3) = 15 (negatif ketemu negatif, hasilnya positif)</li>
<li style="text-align: justify;">(–5) × 3 = –15 (negatif ketemu positif, hasilnya negatif)</li>
<li style="text-align: justify;">5 × (–3) = –15 (positif ketemu negatif, hasilnya negatif)</li>
</ul>
<p> </p>
<h3 style="text-align: justify;"><span style="font-size: 14pt;">Sifat-Sifat Operasi Perkalian Bilangan Bulat</span></h3>
<p style="text-align: justify;">Paham sampai sini? Kita lanjut ya…</p>
<p style="text-align: justify;">Operasi perkalian bilangan bulat itu punya sifat-sifat yang akan membantu kamu menghitung lebih cepat. Berikut sifat-sifat perkalian yang perlu kamu pahami:</p>
<p> </p>
<h4 style="text-align: justify;">1. Tertutup</h4>
<p style="text-align: justify;">Artinya, kalau kita <strong>mengalikan dua bilangan bulat</strong>, <strong>hasilnya</strong> pasti tetap berupa <strong>bilangan bulat</strong>.</p>
<p style="text-align: justify;">Contoh: 5 × (–2) = –10 (masih bilangan bulat)</p>
<p> </p>
<h4 style="text-align: justify;">2. Identitas</h4>
<p style="text-align: justify;">Dalam perkalian, angka 1 disebut unsur netral. Kenapa? Karena <strong>setiap bilangan bulat yang dikalikan dengan 1, hasilnya akan tetap bilangan itu sendiri</strong>.</p>
<p style="text-align: justify;">Contoh: (–7) × 1 = –7</p>
<p> </p>
<h4 style="text-align: justify;">3. Komutatif (Pertukaran)</h4>
<p style="text-align: justify;">Dalam perkalian bilangan bulat, <strong>urutan faktor tidak mempengaruhi hasil</strong>. Jadi, jika bilangan pertama dan bilangan kedua ditukar posisinya, hasilnya akan tetap sama.</p>
<p style="text-align: justify;">Contoh: 6 × (–3) hasilnya akan sama dengan (–3) × 6, yaitu –18.</p>
<p> </p>
<h4 style="text-align: justify;">4. Asosiatif (Pengelompokan)</h4>
<p style="text-align: justify;">Kalau ada lebih dari dua bilangan bulat yang dikalikan, <strong>urutan pengelompokan bilangan</strong> juga <strong>tidak akan mempengaruhi hasil</strong>. Jadi, kamu bisa mengelompokkan bilangan dengan tanda kurung dalam urutan apapun, dan hasilnya akan tetap sama.</p>
<p style="text-align: justify;">Contoh: (2 × –4) × 3 hasilnya akan sama dengan 2 × (–4 × 3), yaitu –24.</p>
<p><strong>Baca Juga: <a href="https://www.ruangguru.com/blog/penyelesaian-bentuk-bentuk-aljabar">Cara Menyelesaikan Bentuk-Bentuk Aljabar</a></strong></p>
<p> </p>
<h4 style="text-align: justify;">5. Distribusi Perkalian terhadap Penjumlahan</h4>
<p style="text-align: justify;">Jadi, kalo ada bilangan bulat <strong>dikalikan dengan jumlah dari dua bilangan</strong>, kita bisa <strong>mengalikan bilangan itu ke masing-masing anggota penjumlahan</strong>, lalu <strong>menjumlahkan hasilnya</strong>.</p>
<p style="text-align: justify;">Contoh: 2 × (3 + 5) = (2 × 3) + (2 × 5) = 6 + 10 = 14</p>
<p> </p>
<h4 style="text-align: justify;">6. Perkalian dengan Nol</h4>
<p style="text-align: justify;">Apapun bilangan bulatnya, kalau <strong>dikalikan dengan 0, hasilnya pasti 0</strong>. Sifat ini sangat mudah diingat karena berlaku untuk semua bilangan, baik bilangan positif maupun negatif.</p>
<p style="text-align: justify;">Contoh: (–8) × 0 = 0</p>
<p> </p>
<h2 style="text-align: justify;"><span style="font-size: 18pt;">2. Operasi Pembagian Bilangan Bulat</span></h2>
<p style="text-align: justify;">Invers, atau lawan dari operasi perkalian adalah operasi pembagian. Jadi, pembagian bisa disebut sebagai “kebalikan” dari perkalian.</p>
<p style="text-align: justify;">Operasi pembagian biasanya disimbolkan dengan <strong>tanda titik dua (÷ atau 🙂 atau tanda garis miring (/)</strong>. Nah, kalau perkalian adalah penjumlahan berulang, maka pembagian bisa kita pahami sebagai <strong>pengurangan berulang sampai habis</strong>.</p>
<p>Contoh:</p>
<p>12 ÷ 3 = 4, karena 12 bisa dikurangi dengan 3 sebanyak 4 kali hingga habis, atau:</p>
<p>12 – 3 – 3 – 3 – 3 = 0</p>
<p> </p>
<h3><span style="font-size: 14pt;">Syarat Operasi Pembagian Bilangan Bulat</span></h3>
<p style="text-align: justify;">Nah, ada satu aturan yang sangat penting dalam menyelesaikan operasi pembagian. Jika sebuah bilangan bulat a dibagi dengan bilangan bulat b, maka <strong>b tidak boleh nol (b ≠ 0)</strong>.</p>
<p style="text-align: justify;">Kenapa? Karena kalau <strong>b = 0, hasilnya akan tidak terdefinisi</strong>. Artinya, pembagian dengan nol tidak punya jawaban yang sah secara matematika.</p>
<p style="text-align: justify;">Contoh:</p>
<p style="text-align: justify;">10 ÷ 2 = 5</p>
<p style="text-align: justify;">10 ÷ 0 = tidak terdefinisi nilainya</p>
<p> </p>
<p><strong>Baca Juga: <a href="https://www.ruangguru.com/blog/matematika-kelas-7-aturan-penulisan-bentuk-baku-bilangan-matematika">Aturan Penulisan Bentuk Baku Bilangan Matematika</a></strong></p>
<p> </p>
<h3 style="text-align: justify;"><span style="font-size: 14pt;">Aturan Tanda dalam Operasi Pembagian Bilangan Bulat</span></h3>
<p><img decoding="async" class="aligncenter size-medium" src="https://cdn-web-2.ruangguru.com/landing-pages/assets/a02086df-8326-4cba-a189-8bf6f0075bd1.png" alt="aturan tanda dalam operasi pembagian bilangan bulat" width="600" /></p>
<p> </p>
<p style="text-align: justify;">Aturannya mirip dengan perkalian, kalo kedua bilangan punya <strong>tanda yang sama, hasilnya positif</strong>. Tapi, kalo kedua bilangan punya <strong>tanda berbeda, hasilnya negatif</strong>.</p>
<p style="text-align: justify;">Contoh:</p>
<ul>
<li>12 ÷ 3 = 4 (positif ketemu positif, hasilnya positif)</li>
<li>(–12) ÷ (–3) = 4 (negatif ketemu negatif, hasilnya positif)</li>
<li>12 ÷ (–3) = –4 (positif ketemu negatif, hasilnya negatif)</li>
<li>(–12) ÷ 3 = –4 (negatif ketemu positif, hasilnya negatif)</li>
</ul>
<p> </p>
<h3 style="text-align: justify;"><span style="font-size: 14pt;">Sifat-Sifat Operasi Pembagian Bilangan Bulat</span></h3>
<p style="text-align: justify;">Operasi pembagian juga punya aturan dan sifat yang berbeda. Supaya kamu nggak salah langkah, yuk kita bahas satu per satu sifat-sifat pembagian bilangan bulat:</p>
<p> </p>
<h4 style="text-align: justify;">1. Tidak Bersifat Komutatif</h4>
<p style="text-align: justify;">Kalau pada perkalian, kita bisa menukar posisi bilangan tanpa mengubah hasil (misalnya 3 × 4 = 4 × 3), hal itu tidak berlaku dalam pembagian. Pada pembagian, <strong>posisi bilangan sangat menentukan hasil akhirnya</strong>.</p>
<p style="text-align: justify;">Contoh: 12 ÷ 3 = 4</p>
<p style="text-align: justify;">Tapi, kalau dibalik, hasilnya menjadi 3 ÷ 12 = 0,25.</p>
<p> </p>
<h4 style="text-align: justify;">2. Tidak Bersifat Asosiatif</h4>
<p style="text-align: justify;">Dalam perkalian, kita juga bebas mengelompokkan bilangan tanpa mengubah hasil (misalnya (2 × 3) × 4 = 2 × (3 × 4)). Tapi dalam pembagian, <strong>cara mengelompokkan bilangan tetap mempengaruhi hasil akhir</strong>.</p>
<p style="text-align: justify;">Contoh:</p>
<p style="text-align: justify;">(12 ÷ 6) ÷ 2 = 2 ÷ 2 = 1.</p>
<p style="text-align: justify;">Tetapi jika dikelompokkan, hasilnya akan berbeda, yaitu: 12 ÷ (6 ÷ 2) = 12 ÷ 3 = 4.</p>
<p> </p>
<h4 style="text-align: justify;">3. Identitas</h4>
<p style="text-align: justify;">Dalam operasi pembagian, <strong>angka 1 juga menjadi unsur identitas</strong> karena membagi bilangan berapapun dengan 1 akan menghasilkan bilangan itu sendiri.</p>
<p style="text-align: justify;">Contoh: (–9) ÷ 1 = –9</p>
<p> </p>
<h4 style="text-align: justify;">4. Pembagian dengan Diri Sendiri, Hasilnya 1</h4>
<p style="text-align: justify;">Setiap bilangan bulat, <strong>jika dibagi dengan dirinya sendiri, hasilnya selalu 1</strong>. Namun, hati-hati! Kalau 0 ÷ 0, hasilnya tidak terdefinisi, sehingga aturan ini <strong>tidak berlaku untuk nol</strong>.</p>
<p style="text-align: justify;">Contoh: 15 ÷ 15 = 1.</p>
<p> </p>
<h4 style="text-align: justify;">5. Hubungan dengan Perkalian</h4>
<p style="text-align: justify;">Pembagian bisa dianggap sebagai kebalikan dari perkalian. Artinya, kalau kamu <strong>tahu hasil perkalian</strong>, maka kamu <strong>bisa menemukan hasil pembagian</strong>.</p>
<p style="text-align: justify;">Contoh: 20 ÷ 4 = 5, karena kita tahu 4 × 5 = 20.</p>
<p style="text-align: justify;">Dengan kata lain, pembagian adalah cara mencari bilangan yang dikalikan untuk mendapatkan hasil tertentu.</p>
<p><strong>Baca Juga: <a href="https://www.ruangguru.com/blog/matematika-kelas-7-mengenal-bilangan-rasional-dan-irasional">Mengenal Bilangan Rasional dan Irasional</a></strong></p>
<p> </p>
<h2 style="text-align: justify;"><span style="font-size: 18pt;">Contoh Soal dan Pembahasan</span></h2>
<p style="text-align: justify;">1. Harga 1 kodi kain adalah Rp300.000, berapa harga 5 helai kain yang sama?</p>
<ol style="list-style-type: upper-alpha;">
<li>Rp60.000</li>
<li>Rp65.000</li>
<li>Rp70.000</li>
<li>Rp75.000</li>
</ol>
<p> </p>
<p> </p>
<p> </p>
<p style="text-align: justify;"><strong>Jawaban: D</strong></p>
<p><strong>Pembahasan:</strong></p>
<p>Untuk menjawab soal di atas, pertama-tama, kita cari tau dulu harga satu helai kainnya.</p>
<p style="text-align: justify;">1 kodi kain = 20 helai kain</p>
<p style="text-align: justify;">Maka, harga 1 helai kain = Rp 300.000 ÷ 20 = Rp15.000,00</p>
<p style="text-align: justify;">Harga 5 helai kain = Harga 1 helai kain × 5</p>
<p style="text-align: justify;">Harga 5 helai kain = Rp15.000 × 5</p>
<p style="text-align: justify;">Harga 5 helai kain = Rp75.000</p>
<p>Jadi, harga 5 helai kain adalah Rp75.000. Jawaban yang tepat yaitu D.</p>
<p> </p>
<p style="text-align: justify;">2. Seorang pemborong dapat menyelesaikan bangunan pos keamanan selama 20 hari dengan total pekerja sebanyak 9 orang. Agar pekerjaan itu selesai dalam waktu 15 hari, berapa tambahan pekerja yang dibutuhkan?</p>
<ol style="list-style-type: upper-alpha;">
<li>12 orang</li>
<li>6 orang</li>
<li>5 orang</li>
<li>3 orang</li>
</ol>
<p> </p>
<p> </p>
<p> </p>
<p style="text-align: justify;"><strong>Jawaban: D</strong></p>
<p><strong>Pembahasan:</strong></p>
<p>Diketahui:</p>
<ul>
<li>Jumlah pekerja awal = 9 orang</li>
<li>Lama kerja awal = 20 hari</li>
<li>Lama kerja baru = 15 hari</li>
<li>Jumlah pekerja baru = ?</li>
</ul>
<p> </p>
<p style="text-align: justify;">Nah, kalo kamu menemukan tipe soal ini, kamu dapat menyelesaikannya menggunakan <strong><a href="https://www.ruangguru.com/blog/perbandingan">konsep perbandingan</a></strong>. Kamu juga perlu paham bahwa, ‘jika jumlah hari diperkecil, maka jumlah pekerja harus diperbesar, begitu juga sebaliknya’.</p>
<p style="text-align: justify;">Sehingga,</p>
<p style="text-align: justify;"><img decoding="async" class="aligncenter" src="https://cdn-web.ruangguru.com/landing-pages/assets/hs/vcbbb.png" alt="vcbbb.png" /></p>
<p> </p>
<p style="text-align: justify;">Jadi, tambahan pekerja yang diperlukan adalah 12 – 9 = 3 orang. Jawaban yang tepat yakni D.</p>
<p style="text-align: center;">—</p>
<p style="text-align: justify;">Itulah pembahasan mengenai operasi perkalian dan pembagian bilangan bulat. Bagaimana? Apakah menurutmu pembahasan di atas sudah jelas?</p>
<p style="text-align: justify;">Kalo kamu masih ingin belajar lebih banyak lagi? Boleh <em>banget!</em> <em>Yuk</em>, cobain download dan belajar bareng <em>Master Teacher</em> di ruangbelajar! Ada fitur konsep kilat yang bisa membantu kamu mempelajari ringkasan, dan juga video Adapto yang bisa menyesuaikan kemampuanmu menerima materi! Ayo, gabung belajar di <strong><a href="https://www.ruangguru.com/promo">ruangbelajar</a></strong>, <em>yuk!</em></p>
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<p style="text-align: justify;"><strong>Referensi:</strong></p>
<p style="text-align: left;">As’ari A.R, Tohir M, Valentino E, Imron Z, Taufiq I. (2017) Matematika SMP/MTs Kelas VII Semester I. Pusat Kurikulum dan Perbukuan, Balitbang, Kemendikbud.</p>
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<li><a href="https://www.ruangguru.com/privacy-policy">Kebijakan Privasi</a></li>
<li><a href="https://www.ruangguru.com/about-us">Tentang Kami</a></li>
<li><a href="https://www.ruangguru.com/contact-us">Kontak Kami</a></li>
<li><a href="https://www.ruangguru.com/press">Press Kit</a></li>
<li><a href="https://www.ruangguru.com/bantuan">Bantuan</a></li>
<li><a href="https://career.ruangguru.com/">Karier</a></li>
</ul>
</nav>
</div>
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<nav class="footer-menu">
<p class="title">Produk Lainnya</p>
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</div>
<div class="col-6 col-md-3">
<nav class="footer-menu">
<p class="title"> Coba GRATIS Aplikasi Ruangguru</p>
<div class="download-list">
<ul>
<li>
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</a>
</li>
<li>
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<img src="https://cdn-web-2.ruangguru.com/static/googleplay.png" loading="lazy" alt="Button Google Play Footer " />
</a>
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<img src="https://cdn-web-2.ruangguru.com/static/huawei.png" loading="lazy" alt="Button AppGallery Footer " />
</a>
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<div class="d-lg-none text-center">
<nav class="footer-menu social">
<p class="title">Ikuti Kami</p>
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<picture>
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<img src="https://cdn-web-2.ruangguru.com/static/instagram.png" loading="lazy" alt="Logo Instagram Footer" width="32px" height="32px" />
</picture>
</a>
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<picture>
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</a>
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</picture>
</a>
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</div>
<p class="footer-copyright">
© 2026 All Rights Reserved PT. Ruang Raya Indonesia
</p>
</div>
<style>
.bantuan-container {
position: relative;
}
.bantuan-element {
position: fixed;
z-index: 999;
display: flex;
align-items: flex-end;
justify-content: flex-end;
cursor: pointer;
transition: all 0.6s ease;
}
.bantuan-top {
bottom: 11rem;
right: 2rem;
}
.bantuan-bottom {
bottom: 2rem;
right: 2rem;
}
.bantuan-top-2 {
bottom: 15rem;
right: 2rem;
}
.bantuan-top-3 {
bottom: 19rem;
right: 2rem;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 2rem;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 2rem;
}
@media (min-width: 768px) {
.bantuan-element img {
width: auto;
transition: all 0.4s ease;
}
.bantuan-top img {
width: 140px;
}
.bantuan-bottom img {
width: 140px;
}
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 140px;
}
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 140px;
}
.bantuan-element.clicked {
bottom: 9rem;
right: 2.5rem;
}
.bantuan-element.clicked img {
width: auto;
height: 64px;
}
}
@media (max-width: 767px) {
.bantuan-top {
bottom: 8rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom {
bottom: 2rem;
right: 1.25rem;
align-items: center;
}
.bantuan-top-2 {
bottom: 12rem;
right: 1rem;
align-items: center;
}
.bantuan-top-3 {
bottom: 16rem;
right: 1rem;
align-items: center;
}
.bantuan-bottom-2 {
bottom: 5rem;
right: 1.25rem;
align-items: center;
}
.bantuan-bottom-3 {
bottom: 8rem;
right: 1.25rem;
align-items: center;
}
.bantuan-element img {
width: auto;
}
.bantuan-top img,
.bantuan-top-2 img,
.bantuan-top-3 img {
width: 96px;
}
.bantuan-bottom img,
.bantuan-bottom-2 img,
.bantuan-bottom-3 img {
width: 96px;
}
}
.bantuan-element:hover {
transform: scale(1.05);
}
.bantuan-element img {
max-width: 100%;
height: auto;
}
</style>
<div id="bantuan-divs-container" style="position: relative" data-product="ruangguru" data-table="rg_floating_icon"></div>
<script>
class FloatingDivsComponent {
constructor(product = 'ruangguru', table = 'rg_floating_icon') {
this.container = document.getElementById('bantuan-divs-container');
this.floatingElements = [];
this.product = product;
this.table = table;
// Configuration
this.config = {
baseApiUrl: 'https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/rg_banner/views/',
apiKey: 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
maxElements: 2,
zIndexBase: 100,
};
// Build dynamic API URL based on table parameter
this.config.apiUrl = this.buildApiUrl();
this.init();
}
buildApiUrl() {
const baseUrl = this.config.baseApiUrl;
const tableName = this.table || 'rg_floating_icon';
const queryParams =
'offset=0&limit=99999&sort=rankPosition&where=(type,eq,floating)~and(showIn,anyof,blog)~and(hide,is,false)~and(product,eq,' +
this.product +
')&nested%5Bcta%5D%5Bfields%5D=Id,name,ctaId,imageUrl,ctaLink,targetUrl';
return `${baseUrl}${tableName}?${queryParams}`;
}
async init() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to initialize floating divs component:', error);
}
}
async fetchFloatingElements() {
try {
const options = {
method: 'GET',
headers: {
'xc-token': this.config.apiKey || 'vLyK3dJrDBRmOwueX2OJXibMkgsUbBk0WS4ua2p1',
},
};
const urlNoco = this.config.apiUrl;
const response = await fetch(urlNoco, options);
if (!response.ok) {
throw new Error(`HTTP error! status: ${response.status}`);
}
const data = await response.json();
this.floatingElements = this.processApiResponse(data);
} catch (error) {
console.error('Error fetching floating elements:', error);
throw error;
}
}
processApiResponse(data) {
if (!data || !data.list || !Array.isArray(data.list)) {
return [];
}
console.log(data.list);
// Ensure we only get maximum 2 elements
const limitedElements = data.list.slice(0, this.config.maxElements);
return limitedElements;
}
renderFloatingElements() {
if (!this.container || this.floatingElements.length === 0) {
return;
}
// Additional safeguard: ensure we never render more than maxElements
const elementsToRender = this.floatingElements.slice(0, this.config.maxElements);
// Clean up existing elements and their event listeners
this.cleanupExistingElements();
// Clear existing content
this.container.innerHTML = '';
elementsToRender.forEach((element, index) => {
const floatingDiv = this.createFloatingDiv(element, index);
this.container.appendChild(floatingDiv);
});
}
cleanupExistingElements() {
// Clear existing elements (no need for event listener cleanup with CSS approach)
const existingElements = this.container.querySelectorAll('[data-floating-element]');
existingElements.forEach(element => {
element.remove();
});
}
createFloatingDiv(element, index) {
const div = document.createElement('div');
const cta = element.cta[0]; // Use the first CTA
// Add data attribute for cleanup tracking
div.setAttribute('data-floating-element', 'true');
// Apply CSS classes based on rankPosition
const positionClass = this.getPositionClass(element.rankPosition, index);
div.className = `bantuan-element ${positionClass}`;
div.style.zIndex = this.config.zIndexBase + index;
// Create the link and image
const link = document.createElement('a');
link.href = 'https://cta.ruangguru.com/' + cta.ctaId || '#';
link.target = '_blank';
// Add tracking attributes
link.setAttribute('data-tracking-event-type', 'landing_page__core__item_click');
link.setAttribute(
'data-tracking-context',
JSON.stringify({
product_name: this.product,
cta_action: 'redirection',
cta_action_detail: link.href,
item_type: 'floating',
item_name: element.name || 'Floating element',
item_category: 'payment',
item_position: index,
item_serial: null,
section_type: 'floating_item',
section_position: 'body',
section_name: 'floating_item',
})
);
const img = document.createElement('img');
img.src = element.imageUrl + '?h=200&convert=webp';
img.alt = element.name || 'Floating element';
img.loading = 'lazy';
// Add click tracking
link.addEventListener('click', () => {
this.trackClick(element, cta);
});
link.appendChild(img);
div.appendChild(link);
return div;
}
getPositionClass(rankPosition, index) {
// Define positioning classes based on rankPosition
if (rankPosition === 1) {
return 'bantuan-top'; // Top position
} else if (rankPosition === 2) {
return 'bantuan-bottom'; // Bottom position
} else {
// For additional elements, distribute them evenly
return `bantuan-${index % 2 === 0 ? 'top' : 'bottom'}-${Math.floor(index / 2) + 1}`;
}
}
trackClick(element, cta) {
// Implement click tracking logic here
console.log('Floating element clicked:', {
elementId: element.Id,
elementName: cta.name,
ctaId: cta.ctaId,
targetUrl: cta.targetUrl,
});
}
// Public method to manually refresh
async refresh() {
try {
await this.fetchFloatingElements();
this.renderFloatingElements();
} catch (error) {
console.error('Failed to refresh floating elements:', error);
throw error;
}
}
// Public method to get current floating elements
getFloatingElements() {
return [...this.floatingElements];
}
}
// Initialize the component when DOM is ready
document.addEventListener('DOMContentLoaded', () => {
// Get product and table parameters from data attributes
const container = document.getElementById('bantuan-divs-container');
const product = container.getAttribute('data-product') || 'ruangguru';
const table = container.getAttribute('data-table') || 'rg_floating_icon';
new FloatingDivsComponent(product, table);
});
// Export for use in other modules if needed
if (typeof module !== 'undefined' && module.exports) {
module.exports = FloatingDivsComponent;
}
</script> <div id="wp-install-nudge" style="
position: fixed;
bottom: 0rem;
right: 0;
z-index: 999;
cursor: pointer;
"></div>
<script>
(function (w, d, s, o, f, js, fjs) {
w['Sales-Nudge-Widget'] = o; w[o] = w[o] || function () { (w[o].q = w[o].q || []).push(arguments) };
js = d.createElement(s), fjs = d.getElementsByTagName(s)[0];
js.id = o; js.src = f; js.async = 1; fjs.parentNode.insertBefore(js, fjs);
}(window, document, 'script', 'wpInstallNudge', 'https://cdn-web-2.ruangguru.com/sales-nudge/6198a95130/dist/widget.js'));
wpInstallNudge('init', { targetElementId: 'wp-install-nudge', clientTarget: 'ruangguru_blog' });
</script>
<script>
// note: disabled due to auto reload page
// var lastScrollTop = 0;
// $(window).scroll(function(event){
// var st = $(this).scrollTop();
// if (st > lastScrollTop){
// $('#wp-install-nudge').slideDown( "slow", function() {});
// } else {
// $('#wp-install-nudge').slideUp( "slow", function() {});
// }
// lastScrollTop = st;
// });
// $(document).ready(function () {
// $("#wp-install-nudge").hide();
// });
$('#wp-install-nudge').click(function(){
Analytics.track("promotion__install_nudge__click",
{
user_email: "ruangguru@blog.com",
cta_link: widgetData.dataConfig.target_link
}).catch((err) => {
console.log("tracker error", err);
});
});
</script>
</footer>
<div id="__next"></div>
<script type="speculationrules">
{"prefetch":[{"source":"document","where":{"and":[{"href_matches":"\/blog\/*"},{"not":{"href_matches":["\/blog\/wp-*.php","\/blog\/wp-admin\/*","\/blog\/wp-content\/uploads\/*","\/blog\/wp-content\/*","\/blog\/wp-content\/plugins\/*","\/blog\/wp-content\/themes\/ruangguru\/*","\/blog\/*\\?(.+)"]}},{"not":{"selector_matches":"a[rel~=\"nofollow\"]"}},{"not":{"selector_matches":".no-prefetch, .no-prefetch a"}}]},"eagerness":"conservative"}]}
</script>
<script>
async function getCtaDetails(ctaIds) {
const endpoint =
" https://gw.ruangguru.com/api/v3/rdb/p_ddgy8hjx5dxsqx/CTA/views/CTA?offset=0&limit=10&where=(ctaId,in," + ctaIds.toString() + ")";
try {
const response = await fetch(endpoint, {
headers: {
"xc-token": "-hG2nBDJzSj0agSgNtcJx97M4F02y54nUMoY6plJ",
},
});
const data = await response.json();
const ctaList = data?.list || [];
const ctaMap = new Map();
for (const ctaData of ctaList) {
ctaMap.set(ctaData.ctaId, ctaData);
}
return ctaMap;
} catch (error) {
console.error("Error fetching CTA details:", error);
return new Map();
}
}
async function replaceCTA() {
const regex = /{{cta\((‘(.*?)’|“(.*?)”)\)}}/g;
const bodyHTML = document.body.innerHTML;
const matches = Array.from(bodyHTML.matchAll(regex));
const ctaIds = matches.map((match) => {
let ctaId = match[2] ?? match[3];
return ctaId;
});
const ctaMap = await getCtaDetails(ctaIds);
const replacedHTML = bodyHTML.replace(regex, (match, _inner, ctaId1, ctaId2) => {
const ctaId = ctaId1 ?? ctaId2;
const ctaData = ctaMap.get(ctaId);
if (ctaData) {
return `<a href="https://cta.ruangguru.com/${ctaData.ctaId}" target="_${ctaData.targetType}" style="position:relative;display:inline-block;">
<img src="${ctaData.imageUrl}" loading="lazy" alt="${ctaData.altText}" />
</a>`;
} else {
return match;
}
});
document.body.innerHTML = replacedHTML;
}
</script>
<meta name="author" content="Ruangguru Tech Team">
<!-- Google Tag Manager (noscript) -->
<noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PVNLZFT" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>
<!-- Tracker -->
<script type="text/javascript" src="https://cdn-web-2.ruangguru.com/landing-page-web/public/staticpages/global-assets/js/cta.js"></script>
<script src="https://unpkg.com/@dotlottie/player-component@latest/dist/dotlottie-player.mjs" type="module"></script>
</body>
</html>