Multiplication and Division of Integers

Lessons

Primary 6 · Mathematics

Multiplication and Division of Integers

5 lessons

Lesson 4 of 5

Dividing integers

30 min

Let's begin

Over 3 cold nights, the temperature at a mountain camp dropped a total of 12 °C, the same amount each night. Mugisha writes the total change as −12 and wants to find the change for one night. He needs ( − 12) ÷ 3.

Dividing on the number line

( − 12) ÷ 3 asks: if we split the journey from 0 to −12 into 3 equal jumps, how big is each jump?

0 → −4 → −8 → −12. Each jump is 4 to the left, so ( − 12) ÷ 3 = −4. The temperature dropped 4 °C each night.

Division undoes multiplication

Every division has a multiplication “partner”. Use it to find the answer and the sign.

Because 3 × ( − 4) = −12, we know ( − 12) ÷ 3 = −4 and ( − 12) ÷ ( − 4) = 3.
Because ( − 3) × ( − 4) = 12, we know 12 ÷ ( − 3) = −4 and 12 ÷ ( − 4) = −3.
( − 12) ÷ ( − 3) asks: “what times −3 gives −12?” The answer is 4, because 4 × ( − 3) = −12. So ( − 12) ÷ ( − 3) = 4.

The sign rules are the same as for multiplying

Signs	Answer	Example
Same signs	Positive	( − 81) ÷ ( − 9) = 9
Different signs	Negative	( − 56) ÷ 8 = −7 and 45 ÷ ( − 5) = −9

Worked example

( − 72) ÷ ( − 8)

Divide the sizes: 72 ÷ 8 = 9.
Same signs, so the answer is positive: 9.
Check with multiplication: 9 × ( − 8) = −72. ✔

Mixed multiplication and division

Work from left to right. ( − 24) ÷ 6 × ( − 2) = ( − 4) × ( − 2) = 8.

Zero

0 divided by any non-zero integer is 0: 0 ÷ ( − 5) = 0.
You can never divide by 0. No number times 0 gives −12, so ( − 12) ÷ 0 has no answer.

Tip

Check with the partner. After dividing, multiply your answer by the number you divided by. You must get back the number you started with, sign and all.

✦

Try it yourself

Work each one in your exercise book first, then tap Show answer to check.

1

( − 35) ÷ 7

Show answerHide answer

Answer: −5. Different signs, so negative. Check: ( − 5) × 7 = −35.

2

( − 48) ÷ ( − 6)

Show answerHide answer

Answer: 8. Same signs, so positive. Check: 8 × ( − 6) = −48.

3

54 ÷ ( − 9)

Show answerHide answer

Answer: −6. Check: ( − 6) × ( − 9) = 54.

4

( − 30) ÷ ( − 5) × ( − 2)

Show answerHide answer

Answer: −12. Left to right: ( − 30) ÷ ( − 5) = 6, then 6 × ( − 2) = −12.

Quick check

What you learned today

Division undoes multiplication, so you can check every answer by multiplying back.
Same signs give a positive answer; different signs give a negative answer.
You can never divide by zero.

Sources and credits

Grade 7, Unit 5, Lesson 11: Dividing Rational Numbers, IM 6–8 Math, authored by Illustrative Mathematics and originally developed by Open Up Resources, licensed under CC BY 4.0. Adapted by Ganzaa.
3.5 Multiply and Divide Integers, from Prealgebra 2e by Lynn Marecek, MaryAnne Anthony-Smith and Andrea Honeycutt Mathis, OpenStax (read on LibreTexts), licensed under CC BY 4.0. Adapted by Ganzaa.
Mathematics Grade 8, 2.2 Calculations with integers, Siyavula, licensed under CC BY 3.0 (licence notice read on the page, 23 September 2026). Adapted by Ganzaa.

The stories, Rwandan worked examples and practice questions were written by Ganzaa.

1Dividing on the number line

2Division undoes multiplication

3The sign rules are the same as for multiplying

4Mixed multiplication and division

5Zero

Try it yourself

Dividing on the number line

Division undoes multiplication

The sign rules are the same as for multiplying

Mixed multiplication and division

Zero