Division and Remainders

Sometimes when dividing, there is something left over. It is called the remainder.

Example: There are 7 cookies, and 2 people want to share them equally.

But 7 cookies cannot be divided exactly into 2 groups, because there will be 1 left over.

We say:

"7 divided by 2 equals 3 with a remainder of 1"

And we write:

7 ÷ 2 = 3 R 1

Note: It is also possible to cut the remaining cookie in half, and then each person would have 3 ½ cookies, so:

7 ÷ 2 = 3 R 1 = 3 ½

Check by Multiplying

If you look at it "the other way around" you can check your answer:

2 × 3 + 1 = 7

In other words "2 groups of 3, plus 1 extra, equals 7".

19 cannot be divided exactly by 5. The closest you can get (without going over) is:

3 x 5 = 15,

which is 4 less than 19.

So the answer of 19 ÷ 5 is:

19 ÷ 5 = 3 R 4

Check it by multiplying: 5 × 3 + 4 = 19

You can also make a fraction with the remainder on top, and the number you are dividing by on the bottom, so we also have:

19 ÷ 5 = 3 R 4 = 3 ⁴/₅