Mathematics • Year 7 • Unit 1 • Lesson 4
Multiplying and Dividing Integers
Build the sign rule for × and ÷: same signs → positive answer; different signs → negative answer. Multiply or divide the magnitudes as usual, then attach the sign.
1. I do, fully worked example
Read every line. Each step has a short reason on the right so you can see why, not just what.
Problem. Calculate (−8) × (−5).
Step 1, Check the signs.
−8 and −5 → both negative → same signs.
Reason: the sign rule is the FIRST thing to settle before you multiply. Same sign means a positive answer.
Step 2, Multiply the magnitudes.
8 × 5 = 40
Reason: ignore the signs and just multiply like normal whole numbers.
Step 3, Apply the sign.
Same signs → positive answer → +40
Reason: positive × positive = positive, and negative × negative = positive. Two negatives "cancel" each other in multiplication.
Step 4, Sanity check (mini-pattern).
(−1) × (−1) = +1. So adding more negative factors must keep giving positives, confirms our sign.
Reason: count the negative signs. Even number → positive. Odd number → negative. Here we had 2 negatives → positive.
Answer: (−8) × (−5) = +40.
2. We do, fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank line. 4 marks
Problem. Calculate (−6) × 7.
Step 1, Check the signs: −6 and +7 → __________ (same / different) signs.
Step 2, Multiply the magnitudes:
6 × 7 = _______
Step 3, Apply the sign: different signs → __________ (positive / negative) answer.
(−6) × 7 = _______
Step 4, Pattern check: there is ____ negative sign in the question, which is an ____ (even / odd) number, so the answer must be ____ (positive / negative). This matches Step 3.
3. You do, independent practice
Show your working in the space under each problem. The first four are foundation, the middle two are standard, and the last two are extension.
Foundation, single step
3.1 Calculate (−4) × 3. 1 mark
3.2 Calculate (−9) × (−2). 1 mark
3.3 Calculate 20 ÷ (−4). 1 mark
3.4 Calculate (−18) ÷ (−6). 1 mark
Standard, combine two ideas
3.5 Calculate (−3) × (−4) × (−1). Use the "count the negatives" pattern to check your sign. 2 marks
3.6 Calculate (−36) ÷ 9 + 2. 2 marks
Extension, push your thinking
3.7 Evaluate [24 ÷ (−3)] × (−2) + (−4). 3 marks
3.8 Without doing the full multiplication, decide whether each answer is positive or negative. Explain how you decided.
(a) (−2) × (−3) × (−5) × (−7) (b) (−1) × 4 × (−6) × 2 × (−1). 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2, We do ((−6) × 7)
Step 1: different signs (−6 negative, +7 positive).
Step 2: 6 × 7 = 42.
Step 3: different signs → negative; (−6) × 7 = −42.
Step 4: 1 negative sign, an odd number, so the answer must be negative matches Step 3.
3.1, (−4) × 3
Different signs: 4 × 3 = 12, sign negative. Answer: −12.
3.2, (−9) × (−2)
Same signs: 9 × 2 = 18, sign positive. Answer: +18.
3.3-20 ÷ (−4)
Different signs: 20 ÷ 4 = 5, sign negative. Answer: −5.
3.4, (−18) ÷ (−6)
Same signs: 18 ÷ 6 = 3, sign positive. Answer: +3.
3.5, (−3) × (−4) × (−1)
Magnitudes: 3 × 4 × 1 = 12. Count negatives: 3 (odd) → answer negative. Answer: −12. Check by pairing: (−3) × (−4) = +12, then +12 × (−1) = −12. ✓
3.6, (−36) ÷ 9 + 2
Division first: (−36) ÷ 9 = −4 (different signs).
Then add: −4 + 2 = −2.
3.7, [24 ÷ (−3)] × (−2) + (−4)
Brackets first: 24 ÷ (−3) = −8 (different signs, 24 ÷ 3 = 8, sign negative).
Multiply: (−8) × (−2) = +16 (same signs).
Add: 16 + (−4) = 12.
3.8, Count the negatives
(a) (−2) × (−3) × (−5) × (−7) has 4 negative factors → even → answer is positive.
(b) (−1) × 4 × (−6) × 2 × (−1) has 3 negative factors → odd → answer is negative.
Rule: count only the negative factors; whether or not there are positives doesn't change the sign.