# 1.2 Rules for multiplication and division of signed numbers

You’ve just established the following rules that you can use when faced with multiplication or division involving negative numbers:

- negative × positive or positive × negative = negative
- negative ÷ positive or positive ÷ negative = negative
- negative × negative = positive
- negative ÷ negative = positive.

When you used your calculator, you found that 4 × (–2) = –8. This is the same as asking what four lots of (–2) are, or answering the calculation (–2) + (–2) + (–2) + (–2), both of which give an answer of –8. So you can see that it makes sense that positive × negative = negative.

You also found that the product of any two negative numbers is positive; for example, (–2) × (–4) = 8.

Why is this? Consider (–6) ÷ 2 = (–3). An alternative way of considering this problem is to say: ‘What do I have to multiply 2 by to get (–6)?’ Since 2 is positive and –6 is negative, the answer must be negative. Because 2 × (–3) = (–6), then (–6) ÷ 2 = (–3).

Similarly, to answer the calculation (–6) ÷ (–2) you would need to multiply (–2) by 3 to get (–6). Therefore, you can deduce that (–6) ÷ (–2) = 3.

Now you’ll get some practice **without** your calculator. Look back at the rules if you need to.

## Activity 4 Multiplying and dividing negative numbers

Work out the answers to the following questions.

- a.(–3) × 5

Hint: remember: negative × positive = negative.

### Answer

Since negative × positive = negative, (–3) × 5 = –15.

- b.(–3) × (–5)

Hint: remember: negative × negative = positive.

### Answer

Since negative × negative = positive, (–3) × (–5) = 15.

- c.(–10) ÷ 5

Hint: remember: negative ÷ positive = negative.

### Answer

Since negative ÷ positive = negative, (–10) ÷ 5 = –2.

- d.(–10) ÷ (–2)

Hint: remember: negative ÷ negative = positive.

### Answer

Since negative ÷ negative = positive, (–10) ÷ (–2) = 5.

Now that you’re familiar with these rules, see if you can use negative numbers to help solve Activity 5 in the next section. Hopefully, you’ll be able to see how useful it is to have clear rules in place – we’ve summarised them for you below.

## When multiplying or dividing:

- Combining two numbers of the same sign gives a positive.
- Combining two numbers of the opposite sign gives a negative.

NB: these rules are for multiplying and dividing – you need to use the different ones, covered last week, for adding and subtracting.