 Integer Multiplication and Division (Negatives) | KS3 Maths Resources

## What you need to know

Things to remember:

• If you multiply or divide by a negative number, it changes the sign of the number it is multiplying.
• A positive becomes negative.
• A negative becomes positive.

What is the value of $-7\times8$?

Before we start, what is multiplication? Well, it is just a way of writing lots of additions.

$$5\times12=12+12+12+12+12=60$$

So, how does this help us multiply by a negative number? It doesn’t quite yet. We also need to remember that the order of multiplication doesn’t matter.

$$5\times12=60$$

$$12\times5=60$$

$$5\times12=12\times5$$

So now, we can change the order of our multiplication and treat it like lots of additions, or, in this case, subtractions.

$$-7\times8=8\times-7$$

$$8\times-7=-7-7-7-7-7-7-7==-56$$

But, remember that $8\times7=56$. So, really, all that happens when we multiply a positive number by a negative number is that it becomes negative. The sign has changed!

$$-6\times3=-18$$

$$5\times-13=-65$$

The same thing happens when we multiply a negative by a negative, it changes the sign, but this time to a positive.

$$-6\times-3=18$$

$$-5\times-13=65$$

The same thing works when dividing by a negative number too.

Positives become negative.

$$12\div-4=-3$$

$$28\div-2=-14$$

Negatives become positive.

$$-12\div-4=3$$

$$-28\div-2=14$$

## Example Questions

$$7\times-3=-21$$

$$-45\div-9=5$$

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