# Division and Remainders

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

### Example: There are 7 bones to share with 2 pups.

But 7 cannot be divided exactly into 2 groups,
so each pup gets 3 bones,
and there is 1 left over: We say:

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

And we write:

7 ÷ 2 = 3 R 1

### As a Fraction

It is also possible to cut the remaining bone in half, so each pup gets 3 ½ bones:

7 ÷ 2 = 3 R 1 = 3 ½

"7 divided by 2 equals 3 remander 1 equals 3 and a half"

## Play with the Idea

Try changing the values here ... sometimes there will be a remainder:

## Check by Multiplying

If we look at it "the other way around" we can check our answer:

2 × 3 + 1 = 7

"2 groups of 3, plus 1 extra, equals 7"

## Another Example 19 cannot be divided exactly by 5. The closest we 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

### As a Fraction

We 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