How to learn the subtraction facts

Subtraction facts are the take-aways that go with the addition facts, from 2 − 1 up to 18 − 9. They are what every column of a long subtraction is made of. There is nothing new to memorise for them, because each one is an addition fact read backwards.

The rule

Every subtraction fact is an addition fact backwards. To find 13 − 6, ask what you add to 6 to make 13.

How to work one out

If you are taking away 1, 2 or 3, count back. For 11 − 3, start at 11 and say 10, 9, 8.
If the two numbers are close together, count on from the smaller one instead. For 12 − 9, say 10, 11, 12. That is three steps, so the answer is 3.
Otherwise, go through 10. Take away enough to get down to 10, then take away the rest: 13 − 6 = 13 − 3 − 3 = 7.
If you know the addition fact, use it. 6 + 7 = 13, so 13 − 6 = 7.
Check by adding back. The answer plus the number you took away should give the number you started with.

Worked examples

What is 10 − 7?

7 + 3 = 10
10 − 7 = 3

3. Every number bond to 10 is also a take-away from 10. 7 and 3 make 10, so 10 − 7 = 3 and 10 − 3 = 7.

What is 13 − 6?

13 − 6
= 13 − 3 − 3
= 10 − 3
= 7

Split the 6 into 3 and 3. The first 3 takes 13 down to 10, and the second takes 10 down to 7. So 13 − 6 = 7.

What is 12 − 9?

9 → 10 → 11 → 12, three jumps

9 and 12 are close, so count on from 9 to 12. That is 3 jumps, so 12 − 9 = 3. Counting back 9 from 12 would take nine steps.

What is 15 − 8?

7 + 8 = 15
15 − 8 = 7

Think of the addition fact. 7 + 8 = 15, so taking the 8 away leaves 7, and 15 − 8 = 7. The same fact gives 15 − 7 = 8 as well.

Taking away and finding the difference

13 − 6 can be read two ways. Take 6 away from 13 and see what is left. Or find the difference between 6 and 13, which is how far apart they are. Both give 7.

Counting back suits the first way, and counting on suits the second. A child who can pick between them is never stuck with a long count. Counting on is also how a shopkeeper counts out change.

Fact families

6, 7 and 13 make a fact family: four facts from the same three numbers. 6 + 7 = 13, 7 + 6 = 13, 13 − 6 = 7 and 13 − 7 = 6.

The biggest number is always the total in the additions and the starting number in the take-aways. Learning facts in families means one addition fact gives two subtraction facts with it.

Why the addition facts are enough

Taking away undoes adding. Put 6 counters with 7 counters and you have 13. Take the 6 back out and the 7 are left. So 13 − 6 asks which number goes with 6 to make 13, and that is an addition fact you already know.

Going through 10 works because 10 is the easiest number to take away from: 10 − 3 is a number bond. Taking the 6 away in two parts, 3 and then 3, takes away the same 6 as taking it all at once.

Counting on gives the same answer as counting back because the gap between two numbers is the same whichever end you start from. From 9 up to 12 is 3, and from 12 down to 9 is 3.

Where mistakes happen

Counting the number you start on. For 11 − 3, the count is 10, 9, 8, so the answer is 8. Saying 11, 10, 9 gives 9, one too many.
Counting back a long way. 12 − 9 counted back is nine steps, and it is easy to lose count. Counted on from 9 it is three.
Swapping the numbers round. 6 + 7 and 7 + 6 are the same, but 13 − 6 and 6 − 13 are not. Only adding lets you change the order.
Splitting the wrong number when going through 10. In 13 − 6 it is the 6 that is split, so that the first part takes 13 down to exactly 10.

Questions people ask

Why does my child find taking away harder than adding?

Counting backwards is harder than counting forwards, and the order of the numbers matters. Learning each subtraction fact as an addition fact backwards takes most of that difficulty away, because there is nothing new to remember.

What does inverse mean?

It means one undoes the other. Taking away is the inverse of adding. Add 6 and then take 6 away, and you are back where you started. Schools in England teach the word in Year 2, and it is the reason fact families work.

How do I check a subtraction?

Add it back. For 13 − 6 = 7, check that 7 + 6 = 13.

Can the answer be less than 0?

Yes, 3 − 5 is −2. At primary school the first number is nearly always the bigger one, so the answers to the subtraction facts are never below 0.