−72. This is multiplying, not adding or subtracting: 6 × 12. Same signs give a positive, different signs a negative: −72.

(−5)² = ? A. 10 B. −10 C. −25 D. 25 Choose the right answer

D. 25. (−5)² = (−5) × (−5) = 25.

(−1/3) × (+4/5) = □ Answer in simplest form

−4/15. Same signs give a positive, different signs a negative; tops times tops, bottoms times bottoms, in lowest terms: −4/15.

Directed numbers · Ages 12–13

Multiplying directed numbers

Same signs positive, different negative; count the minus signs.

How to do it

Method

Same signs positive, different negative; count the minus signs

(−3) × (−4) = 12

Another way

Repeated adding

3 × (−2) = (−2) + (−2) + (−2) = −6

In full

Same signs multiply to a positive, different signs to a negative: (−3) × (−4) = 12, (−3) × 4 = −12. For several numbers, just count the minus signs: an odd number gives a negative, an even number a positive. Multiplying can also be seen as repeated adding: 3 × (−2) = (−2) + (−2) + (−2) = −6. Careful with powers: (−3)² = (−3) × (−3) = 9, but −3² has no bracket, so only the 3 is squared: −9.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
(−6) × 12 =
Show the answer and working
Answer: −72
This is multiplying, not adding or subtracting: 6 × 12. Same signs give a positive, different signs a negative: −72.
Example 2
(−5)² = ?
- A. 10
- B. −10
- C. −25
- D. 25
Choose the right answer
Show the answer and working
Answer: D. 25
(−5)² = (−5) × (−5) = 25.
Example 3
(−13) × (+45) =
Answer in simplest form
Show the answer and working
Answer: −415
Same signs give a positive, different signs a negative; tops times tops, bottoms times bottoms, in lowest terms: −415.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.(−2) × (−2) =
Answer:
2.(+8) × 7 =
Answer:
3.The result of (−4) × (+9) × (+4) × (−3) is negative.
True or false?
Answer:
4.(−3)² = ?
- A. −9
- B. −6
- C. 6
- D. 9
Choose the right answer
Answer:
5.−6² + 42 =
Answer:

All the answers

1. 4
2. 56
3. False
4. D. 9
5. 6

Free worksheet: Multiplying directed numbersWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

VIP practice notes and papers

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working

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