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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