LEARN · PRACTISE · DISCOVER
Fact Families: Multiplication and Division Together
Here is a secret: if you know your times tables, you already know your division facts! Multiplication and division are linked in groups called fact families. In this lesson you will learn to use fact families to divide quickly and check your answers.
What is a fact family?
A fact family is a set of related facts that use the same three numbers. For the numbers 3, 6 and 18, the fact family is:
| Multiplication | Division |
|---|---|
| 3 × 6 = 18 | 18 ÷ 6 = 3 |
| 6 × 3 = 18 | 18 ÷ 3 = 6 |
Four facts, one family! The largest number (the product) is always the number being divided.
The triangle picture
Draw a triangle. Put the product at the top and the two factors at the bottom corners. Cover the top number and multiply the bottom two. Cover a bottom number and divide the top number by the other bottom number.
Using multiplication to divide
To solve a division problem, ask yourself a multiplication question.
- 35 ÷ 5 = ? Think: 5 times what makes 35? 5 × 7 = 35, so the answer is 7.
- 48 ÷ 8 = ? Think: 8 times what makes 48? 8 × 6 = 48, so the answer is 6.
- 63 ÷ 9 = ? Think: 9 times what makes 63? 9 × 7 = 63, so the answer is 7.
This is often called thinking multiplication.
Example
Mr Ortiz has 56 chairs to set out in rows of 8. How many rows will there be? He thinks, “8 times what is 56?” He knows 8 × 7 = 56, so there will be 7 rows. He checks with the fact family: 7 × 8 = 56. Correct!
Checking your work
Fact families let you check any division answer. Multiply your answer by the divisor. If you get the dividend, you are right.
| Division | Check | Correct? |
|---|---|---|
| 42 ÷ 6 = 7 | 7 × 6 = 42 | Yes |
| 36 ÷ 4 = 8 | 8 × 4 = 32 | No, the answer should be 9 |
Square numbers have small families
When both factors are the same, like 5 × 5 = 25, the family has only two facts: 5 × 5 = 25 and 25 ÷ 5 = 5. Numbers like 25 are called square numbers, because the array makes a square.
Key takeaways
- A fact family uses the same three numbers in multiplication and division facts.
- Every multiplication fact gives you two division facts.
- To divide, think “what times the divisor gives the total?”
- Check division by multiplying the quotient by the divisor.
Practice
- Write the fact family for 4, 9 and 36.
- 54 ÷ 6
- 72 ÷ 8
- Is 45 ÷ 5 = 8 correct? Check with multiplication.
Answers: 1 is 4 × 9 = 36, 9 × 4 = 36, 36 ÷ 9 = 4, 36 ÷ 4 = 9. 2 is 9. 3 is 9. 4 is no, because 8 × 5 = 40; the correct answer is 9.