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Learn Index · Arithmetic and Operations Grade 1–2

Addition and subtraction fact families

Addition and subtraction facts that use the same three numbers.

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Three numbers, four facts

A fact family is a group of number sentences that use the same three numbers. Take 3, 5 and 8:

Addition Subtraction
3 + 5 = 8 8 − 3 = 5
5 + 3 = 8 8 − 5 = 3

All four are related facts. If you know one, you can work out the other three.

The whole and the parts

In every fact family:

  • The biggest number is the whole (the sum).
  • The two smaller numbers are the parts (the addends).

Addition puts the parts together to make the whole. Subtraction starts with the whole and takes away one part to find the other (the difference).

Inverse operations

Addition and subtraction are inverse operations: one undoes the other.

  • Start with 3. Add 5 → 8. Subtract 5 → back to 3.

That’s why you can check subtraction with addition: 12 − 7 = 5 because 5 + 7 = 12.

Fact family triangles

A fact triangle shows the three numbers with the whole at the top. Cover any one number and use the other two to find it.

  • Cover the top (whole): add the two bottom numbers.
  • Cover a bottom number: subtract the visible bottom number from the top.

Families with doubles

When both parts are the same, like 6, 6 and 12, there are only two facts:

  • 6 + 6 = 12
  • 12 − 6 = 6

Using fact families to solve problems

Fact families help with missing numbers:

  • 4 + __ = 11. Think: 11 − 4 = 7. So the missing number is 7.
  • __ − 5 = 9. Think: 9 + 5 = 14. So the missing number is 14.

Worked examples

Example 1: Write the fact family for 4, 6 and 10.

4 + 6 = 10, 6 + 4 = 10, 10 − 4 = 6, 10 − 6 = 4.

Example 2: You know 7 + 8 = 15. What is 15 − 8?

Same family: 7.

Example 3: Which number does not belong in the family 5, 9, 14? Fact: 14 − 9 = 6.

That fact is wrong: 14 − 9 = 5. The 6 does not belong.

Common mistakes

  • Putting the whole in the wrong place in a subtraction: 5 − 8 = 3 is not in the family.
  • Using a number that isn’t in the family.
  • Forgetting to check subtraction by adding back.

Try it yourself

  1. Write the fact family for 2, 7, 9.
  2. You know 6 + 9 = 15. What is 15 − 6?
  3. Solve 8 + __ = 13.
  4. Solve __ − 4 = 6.

Answers: 1) 2 + 7 = 9, 7 + 2 = 9, 9 − 2 = 7, 9 − 7 = 2 2) 9 3) 5 4) 10

Quick recap

  • A fact family uses three numbers to make four related facts.
  • Addition and subtraction are inverse operations.
  • The biggest number is always the sum, and it comes first in subtraction.