Number
Multiplying and dividing integers
Multiply and divide positive and negative whole numbers, and get the sign right every time.
Multiplying and dividing integers is two jobs, not one. First you work out the numbers, exactly as you always have. Then you decide the sign, using a rule that has nothing to do with how big the numbers are.
The sign rule
Same signs give a positive answer: 6 × 4 = 24 and -6 × (-4) = 24. Different signs give a negative one: -6 × 4 = -24 and 6 × (-4) = -24. Division follows exactly the same rule, because dividing is undoing a multiplication.
Have a play
This line runs from twelve below zero to twelve above it, in twos. Move along it and see how the two halves mirror each other.
Tap anywhere on the line.
Worked example
What is -56 ÷ 8?
Ignore the signs and divide: 56 ÷ 8 = 7.
The size of the answer never depends on the signs, so getting it out of the way first leaves one decision instead of two.
Try it together
Now let us work out -7 × (-6) ÷ 3 together.
Three numbers, two signs to keep track of. Counting the minus signs first turns the whole thing into an ordinary sum.
1.How many negative numbers are there in -7 × (-6) ÷ 3?
Watch out
-3² and (-3)² are not the same. Without brackets the square only reaches the 3, so -3² is -9; with brackets the whole of -3 is squared, giving 9.
Have a go
Have a go on your own: -9 × (-4) = ?
Hint: Two negatives multiplied together.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.