Fact Families – Linking the Four Operations
A fact family is a group of related number facts that all use the same set of numbers. Understanding fact families shows you how the four operations are connected.
Addition and Subtraction Fact Families
Three numbers — say 3, 5, and 8 — generate four related facts:
3 + 5 = 8 5 + 3 = 8 8 − 3 = 5 8 − 5 = 3
Multiplication and Division Fact Families
Three numbers — say 4, 7, and 28 — generate four related facts:
4 × 7 = 28 7 × 4 = 28 28 ÷ 4 = 7 28 ÷ 7 = 4
More Examples
| Numbers | Four Facts |
|---|---|
| 6, 9, 54 | 6×9=54, 9×6=54, 54÷6=9, 54÷9=6 |
| 8, 7, 56 | 8×7=56, 7×8=56, 56÷8=7, 56÷7=8 |
| 12, 5, 17 | 12+5=17, 5+12=17, 17−12=5, 17−5=12 |
Why Fact Families Matter
- Knowing one fact instantly gives you three more.
- They reveal the inverse relationship between + and −, and between × and ÷.
- Essential for solving simple equations: if x + 5 = 12, then x = 12 − 5 = 7.
Key Takeaways
- A fact family uses three numbers and four related number sentences.
- Addition and subtraction are inverses; multiplication and division are inverses.
- Learning fact families reduces memorisation: one fact becomes four.
Practice Questions
- Write the fact family for 6, 8, and 14.
- Write the fact family for 5, 9, and 45.
- Use a fact family to find x: x + 7 = 15.
- Use a fact family to find x: x × 6 = 42.
- Write the four facts for 3, 11, and 33.