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,
but 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

As a Fraction

It is also possible to cut the remaining bone in half, and then each pup would have 3 ½ bones, so:

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

2 × 3 + 1 = 7

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

Another Example

remainder 19 5

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 รท 5 is:

19 ÷ 5 = 3 R 4

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

As a Fraction

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