How to learn the division facts

A division fact is a times-table fact read backwards. 6 × 8 = 48, so 48 ÷ 6 = 8 and 48 ÷ 8 = 6. A child who knows the times tables already knows the division facts. They only need practice at reading them the other way.

The rule

To work out 48 ÷ 6, ask what 6 has to be multiplied by to make 48. That number is the answer.

How to work one out

Read the division as a question about the times table. 48 ÷ 6 asks how many 6s make 48.
Go to the times table of the number you are dividing by, here the 6 times table, and find 48 in it. 6 × 8 = 48.
The number you multiplied by, 8, is the answer. 48 ÷ 6 = 8.
If it does not come straight away, start from a fact you know. 6 × 10 = 60 is too big and 6 × 5 = 30 is too small, so the answer is between 5 and 10.
Check by multiplying back. 8 × 6 = 48, so the answer is right.

Worked examples

12 sweets are shared between 3 children. How many does each child get?

12 ÷ 3 = 4

Hand the sweets out one at a time, one to each child, until they are all gone. Each child ends up with 4, because 3 × 4 = 12.

How many 3s are there in 12?

3, 6, 9, 12
four 3s

Count up in 3s until you reach 12. That takes four steps, so 12 ÷ 3 = 4. It is the same division as the sweets, asked the other way round.

What is 56 ÷ 8?

8 × 7 = 56
56 ÷ 8 = 7

7, because 8 × 7 = 56. The 8 times table finds it, and so does the pattern 5, 6, 7, 8, which says 56 = 7 × 8.

Which four facts go with 6, 8 and 48?

6 × 8 = 48
8 × 6 = 48
48 ÷ 6 = 8
48 ÷ 8 = 6

One times-table fact gives two division facts. The biggest number, 48, is always the one being divided, and the answer is one of the other two.

Sharing and grouping

12 ÷ 3 can be two different stories. Sharing: 12 sweets shared between 3 children, how many does each child get? Grouping: 12 sweets put into bags of 3, how many bags? Both answers are 4.

Schools teach both, because word problems come in both shapes. In America they are often called partitive and quotative division, or sharing and measurement.

Tricks that work backwards

÷2: halve the number. ÷4: halve it twice, so 28 ÷ 4 is 14, then 7. ÷8: halve it three times, so 56 ÷ 8 is 28, 14, then 7.

÷10: take the 0 off the end, so 70 ÷ 10 = 7. ÷5: double the number, then divide by 10, so 35 ÷ 5 is 70 ÷ 10, which is 7.

÷9: in the 9 times table the tens digit is one less than the number you multiplied by. So for 63 ÷ 9, add 1 to the 6: the answer is 7.

Why it works, and why 0 is different

Dividing undoes multiplying. Put 8 sweets in each of 6 bags and you have 48. Ask how many go in each bag and the answer is the 8 you started with. That is why every division fact is a times-table fact backwards: 48 ÷ 6 = 8 because 6 × 8 = 48.

So 12 ÷ 0 asks: 0 times what makes 12? Nothing does, because 0 times any number is 0. There is no answer, and that is why you cannot divide by 0. Put 12 sweets in bags of 0 and you could fill bags for ever without using a single sweet.

0 ÷ 3 is fine. Share nothing between 3 children and each gets nothing, so 0 ÷ 3 = 0, because 3 × 0 = 0.

Where mistakes happen

Swapping the numbers round. 6 × 8 = 8 × 6, but 48 ÷ 6 and 6 ÷ 48 are not the same. The number being divided comes first.
Saying 12 ÷ 0 = 0, or 12 ÷ 0 = 12. Dividing by 0 has no answer at all. It is 0 ÷ 12 = 0 that is fine.
Mixing up dividing by 1 and by the number itself. Dividing by 1 leaves a number as it is, 12 ÷ 1 = 12. Dividing a number by itself gives 1, 12 ÷ 12 = 1.
Counting up from the start every time. For 72 ÷ 9, counting 9, 18, 27 and on works, but it is slow. Start from a fact you know instead: 9 × 10 = 90, then 9 × 9 = 81, then 9 × 8 = 72, so the answer is 8.

Questions people ask

What are the numbers in a division called?

In 48 ÷ 6 = 8, 48 is the dividend, 6 is the divisor, and 8 is the quotient.

What if it does not divide exactly?

Then something is left over, the remainder. 50 ÷ 6 = 8 remainder 2, because 6 × 8 = 48 and 2 are left. The division facts are the ones with nothing left over. Remainders come up in long division.

Should division be learned with the times tables?

Yes, at the same time. Schools in England teach the division facts alongside each table, starting with the 2, 5 and 10 in Year 2.

What does goes into mean?

"6 goes into 48 eight times" is another way of saying 48 ÷ 6 = 8. It is the grouping question: how many 6s fit into 48.

How can I tell if a bigger number will divide exactly?

The divisibility rules tell you without dividing. For example, a number divides by 3 when its digits add up to a multiple of 3.