# Fact Families: Multiplication and Division Together

- Link: https://thecuriosi.com/lessons/fact-families/
- Published: 2026-10-31T14:56:10+05:30
- Author: MAHENDRA MANCHIKALAPATI

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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

 1. Write the fact family for 4, 9 and 36.
 2. 54 ÷ 6
 3. 72 ÷ 8
 4. 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.

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 [ Previous lesson What Is Division? Sharing and Grouping ](https://thecuriosi.com/lessons/what-is-division/)
[ Next lesson Division with Remainders ](https://thecuriosi.com/lessons/division-with-remainders/)

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