# 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 remainder 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}