Multiplying and Dividing Integers

The one sign rule that covers both × and ÷ — same signs give a positive, different signs give a negative — shown as a grid, with exam-style worked examples, a worksheet with memo and a quick quiz.

Good news: multiplying and dividing integers is easier than adding them. There is only one rule, and it works for both operations. The sizes just multiply or divide as normal — all you have to decide is the sign.

1The sign rule

Same signs → positive (+ × + = + and − × − = +)
Different signs → negative (+ × − = − and − × + = −)

The sign grid. Same signs give a positive answer; different signs give a negative one. Exactly the same grid works for division.

2Multiplying

Worked ExampleCalculate: (−6) × (−4) and (−6) × 4

1
(−6) × (−4): sizes 6 × 4 = 24; signs are the same → positive.
Negative times negative is positive.
2
So (−6) × (−4) = 24.
3
(−6) × 4: sizes 24; signs differ → negative → −24.
Negative times positive is negative.

3Dividing

Worked ExampleCalculate: (−20) ÷ 5 and (−20) ÷ (−4)

1
(−20) ÷ 5: sizes 20 ÷ 5 = 4; signs differ → negative → −4.
The same sign rules apply to division.
2
(−20) ÷ (−4): sizes 20 ÷ 4 = 5; same signs → positive → 5.
Negative divided by negative is positive.

4More than two numbers

When several numbers are multiplied, count the negatives: an even number of negatives gives a positive answer, an odd number gives a negative one.

Worked ExampleCalculate: (−2) × (−3) × (−4)

1
Sizes: 2 × 3 × 4 = 24.
Do the numbers first.
2
Count the negatives: three of them — an odd number.
Odd number of negatives → negative answer.
3
Answer: −24.

💡

Keep the two rule-sets apart in your head: adding uses 'same signs add / different signs subtract', while multiplying and dividing uses 'same → +, different → −'. Mixing them up is the most expensive habit in Grade 8.

Practice exercises

Work each one out, then click to reveal the answer.

📄 Worksheet ✅ Memo 📝 Exam paper 🗝️ Marking guide

1
(−5) × 6
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Different signs → −30
2
(−8) × (−3)
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Same signs → 24
3
7 × (−4)
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Different signs → −28
4
(−24) ÷ 6
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Different signs → −4
5
(−36) ÷ (−9)
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Same signs → 4
6
45 ÷ (−5)
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Different signs → −9
7
(−2) × (−5) × (−3)
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Sizes 30; three negatives (odd) → −30
8
(−4) × (−2) × (−1) × (−3)
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Sizes 24; four negatives (even) → 24