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division

Division fact families

Use multiplication facts to solve related division questions.

Quick answer

Division fact families show how multiplication and division are connected. If you know one multiplication fact, you can use it to find three related division facts.

Learning outcome

By the end of this page, you will understand how to use multiplication facts to solve division problems and create fact families with three related facts. Success signs:
  • You can write three related division facts from one multiplication fact
  • You can solve division problems using your knowledge of multiplication
  • You can explain how multiplication and division are connected
  • You can create your own fact families

Why this matters

Knowing division fact families helps you solve division problems faster. It's like having a secret code that connects multiplication and division. When you understand this connection, you can use what you know about multiplication to help with division. This makes learning both easier and more fun! In real life, you use fact families when sharing things equally, dividing up your pocket money, or sharing snacks with friends. It's also helpful in games, cooking, and sports where you need to divide things fairly.

How it works

Division fact families work with three numbers that are related through multiplication and division. If you have three numbers, like 4, 6, and 24, you can make a fact family using these numbers. First, you write the multiplication fact: 4 × 6 = 24 Then, you can make two division facts from this multiplication fact:
  • 24 ÷ 4 = 6
  • 24 ÷ 6 = 4
These three facts (4 × 6 = 24, 24 ÷ 4 = 6, 24 ÷ 6 = 4) form a division fact family. Let's look at how this works with a few more examples:

Examples you can see

Let's try some examples with different numbers. Example 1: 3 × 7 = 21
  • Multiplication: 3 × 7 = 21
  • Division: 21 ÷ 3 = 7
  • Division: 21 ÷ 7 = 3
Example 2: 5 × 8 = 40
  • Multiplication: 5 × 8 = 40
  • Division: 40 ÷ 5 = 8
  • Division: 40 ÷ 8 = 5
Example 3: 9 × 4 = 36
  • Multiplication: 9 × 4 = 36
  • Division: 36 ÷ 9 = 4
  • Division: 36 ÷ 4 = 9
You can use this pattern to find all the division facts from any multiplication fact. Let's think about this in a more visual way. Imagine you have 12 cookies and you want to share them equally among 3 friends.
  • 12 cookies shared among 3 friends = 4 cookies each
  • This is the division fact: 12 ÷ 3 = 4
  • If you know that 3 × 4 = 12, then you also know that 12 ÷ 3 = 4
  • And you also know that 12 ÷ 4 = 3

Try it as a mini adventure

Adventure: The Cookie Sharing Challenge You are the cookie chef for a birthday party. You have 24 cookies to share equally among 6 friends. 1st step: How many cookies does each friend get?
  • You need to solve: 24 ÷ 6 = ?
2nd step: What multiplication fact can help you?
  • You know that 6 × 4 = 24
3rd step: What are the three fact family members?
  • Multiplication: 6 × 4 = 24
  • Division: 24 ÷ 6 = 4
  • Division: 24 ÷ 4 = 6
4th step: Check your answer
  • Each friend gets 4 cookies
  • 6 friends × 4 cookies = 24 cookies
5th step: What other fact family can you make with 24, 3, and 8?
  • Multiplication: 3 × 8 = 24
  • Division: 24 ÷ 3 = 8
  • Division: 24 ÷ 8 = 3

Common mistakes

  • Mistake: Thinking that 12 ÷ 3 = 4 and 12 ÷ 4 = 3 are not related
    Why it happens: Not understanding that division is the opposite of multiplication
    Fix: Remember that if 3 × 4 = 12, then 12 ÷ 3 = 4 and 12 ÷ 4 = 3
  • Mistake: Forgetting to write all three facts in a fact family
    Why it happens: Rushing through the problem
    Fix: Always check that you have one multiplication fact and two division facts
  • Mistake: Confusing the order of numbers in division
    Why it happens: Not knowing which number is the total and which is the group size
    Fix: Think of division as "how many in each group?" or "how many groups?"

Parent and carer guide

Parents and carers can help by:
  • Using everyday situations to practice fact families (like sharing snacks or toys)
  • Playing games where you make up multiplication facts and then find the related division facts
  • Encouraging children to explain their thinking when solving problems
  • Using physical objects like counters or blocks to model the relationships
  • Reinforcing that multiplication and division are connected, not separate
Here are some ways to support learning in 5-10 minutes:
  • Ask your child to find a fact family using numbers 2, 5, and 10
  • Give a real-life problem: "You have 18 stickers and want to share them equally among 3 friends. How many does each get?"
  • Use a multiplication fact and ask them to write the division facts
  • Play a quick game: say a multiplication fact, and your child says the three related division facts
Remember to celebrate when your child gets it right, and be patient when they're learning. Making mistakes is part of learning!

Practice questions

  1. What multiplication fact helps you solve 36 ÷ 6 = ?
  2. Write the three fact family members for 7 × 8 = 56
  3. What is 42 ÷ 7 = ?
  4. Write the three fact family members for 9 × 5 = 45
  5. What is 24 ÷ 3 = ?
Answers:
  1. 6 × 6 = 36
  2. 7 × 8 = 56, 56 ÷ 7 = 8, 56 ÷ 8 = 7
  3. 6
  4. 9 × 5 = 45, 45 ÷ 9 = 5, 45 ÷ 5 = 9
  5. 8

FAQ

What is a division fact family?

A division fact family is a group of three related facts that use the same three numbers. One fact is multiplication, and the other two are division facts.

How do I find the division facts from a multiplication fact?

If you have a multiplication fact like 4 × 6 = 24, then you can make two division facts: 24 ÷ 4 = 6 and 24 ÷ 6 = 4.

Why are fact families helpful?

Fact families help you understand the connection between multiplication and division. Once you know one fact, you know three related facts.

Can I make fact families with any three numbers?

No, you can only make fact families when one number equals the product of the other two. For example, 3, 4, and 12 work because 3 × 4 = 12.

How can I practice fact families at home?

You can practice by using objects like counters or blocks to model problems, or by making up real-life sharing situations like dividing up snacks or toys.