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.

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.