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 / 2 = 3 R 1  (remainder 1)

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:

images/divide-marbles.js

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

remainder 19 5

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:

so we also have:

19 ÷ 5 = 3 R 4 = 3 4/5

 

1635, 1636, 1637, 1638, 3431, 3432, 3433, 3434, 3435, 3436