Integers
Multiplying and dividing integers
Multiplying by a negative flips the sign. That single idea gives you every rule in this section.
Why a negative times a positive is negative
Multiplying is repeated adding. 3 × 4 = 3 + 3 + 3 + 3 = 12 −3 × 4 = −3 + −3 + −3 + −3 = −12 5 × −2 = −2 + −2 + −2 + −2 + −2 = −10 So the product of a positive and a negative is always NEGATIVE.
Working it out
Ignore the signs, multiply the numbers, then decide the sign. 6 × −4: work out 6 × 4 = 24, so 6 × −4 = −24. −9 × 3: work out 9 × 3 = 27, so −9 × 3 = −27. The answer 12 is called the PRODUCT of 3 and 4.
Dividing
Division is the inverse of multiplication, so the same sign rule applies. −3 × 4 = −12, so −12 ÷ 4 = −3. When one number is positive and the other negative, the answer is negative: −48 ÷ 6 = −8 and 63 ÷ −7 = −9
Brackets first
Do whatever is inside the brackets before you multiply. 5 × (1 + −4) First: 1 + −4 = −3 Then: 5 × −3 = −15
Worked examples
−3 × 4 by repeated addition
- −3 × 4 means −3 + −3 + −3 + −3.
- That totals −12.
Answer: −12
6 × −4
- Ignore the signs: 6 × 4 = 24.
- One number is negative, so the answer is negative.
Answer: −24
−48 ÷ 6
- Ignore the signs: 48 ÷ 6 = 8.
- One number is negative, so the answer is negative.
Answer: −8
63 ÷ −7
- 63 ÷ 7 = 9.
- One negative, so the answer is negative.
Answer: −9
5 × (1 + −4)
- Brackets first: 1 + −4 = −3.
- Then 5 × −3.
Answer: −15
Checking a division with multiplication
- −3 × 4 = −12.
- So −12 ÷ 4 must give back −3.
Answer: −3 — division is the inverse of multiplication
Where you see this in real life
- A diver descends 3 m each minute. After 4 minutes their depth is −3 × 4 = −12 m relative to the surface.
- A shop loses £6 on each of 7 items sold at a discount: −6 × 7 = −£42 in total.
Key words
- Product
- the result of multiplying numbers together
- Inverse operation
- the operation that undoes another
- Sign
- whether a number is positive or negative
- Brackets
- grouping symbols — work out what is inside them first
- Quotient
- the result of a division