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:

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

As a Fraction

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

"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 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:

which is 4 less than 19.

So the answer of 19 ÷ 5 is:

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