Times table fact families

Quick answer

Times table fact families show how multiplication and division facts are connected. For example, 6 × 7 = 42, 7 × 6 = 42, 42 ÷ 6 = 7 and 42 ÷ 7 = 42 all belong to the same fact family.

Learning outcome

By the end of this page, you will understand how multiplication and division facts are connected in fact families, and be able to find all the facts in a family for any times table.

• You can write 4 facts that belong to a times table fact family
• You can use one fact to find another fact in the same family
• You can explain why multiplication and division are linked
• You can spot the fact family for any multiplication fact

Why this matters

Fact families help you understand that multiplication and division are linked. This makes it easier to learn and remember your times tables. When you know that 6 × 7 = 42, you also know that 42 ÷ 7 = 6. This means you only need to learn half the facts!

Fact families are useful in real life too. When you're sharing 24 cookies equally between 4 friends, you're using division. When you're making 3 trays with 8 cupcakes each, you're using multiplication. Both are part of the same fact family!

How it works

Fact families are groups of related multiplication and division facts that use the same three numbers.

Here’s how to find a fact family:

1. Choose any two numbers that multiply to make a third number
2. Write the multiplication facts with those numbers
3. Write the division facts using the same numbers
4. Check that all four facts are true

Let’s look at the numbers 6, 7, and 42.

• 6 × 7 = 42
• 7 × 6 = 42
• 42 ÷ 6 = 7
• 42 ÷ 7 = 6

These four facts make up the fact family for 6, 7, and 42.

Examples you can see

Let’s look at a few fact families to help you understand.

Fact family for 3, 4, and 12

• 3 × 4 = 12
• 4 × 3 = 12
• 12 ÷ 3 = 4
• 12 ÷ 4 = 3

Fact family for 5, 8, and 40

• 5 × 8 = 40
• 8 × 5 = 40
• 40 ÷ 5 = 8
• 40 ÷ 8 = 5

Fact family for 9, 6, and 54

• 9 × 6 = 54
• 6 × 9 = 54
• 54 ÷ 9 = 6
• 54 ÷ 6 = 9

Fact family for 0, 5, and 0

• 0 × 5 = 0
• 5 × 0 = 0
• 0 ÷ 5 = 0
• 0 ÷ 0 = ? (undefined)

Notice how in the last example, we can’t divide by zero, so that fact doesn’t work. But the multiplication facts are still true.

Try it as a mini adventure

Imagine you're a space explorer on a mission to collect alien fruits. You find 6 alien trees, and each tree has 7 fruits. How many fruits do you collect?

Step 1: Count how many trees and how many fruits per tree.

Step 2: Multiply to find the total number of fruits.

6 × 7 = 42 fruits

Step 3: Now, if you want to share 42 fruits equally among 6 friends, how many does each get?

42 ÷ 6 = 7 fruits each

Step 4: If you want to share 42 fruits equally among 7 friends, how many does each get?

42 ÷ 7 = 6 fruits each

Step 5: What multiplication fact did you use to find the total?

7 × 6 = 42

You've found a fact family: 6 × 7 = 42, 7 × 6 = 42, 42 ÷ 6 = 7, 42 ÷ 7 = 6.

Common mistakes

• Mistake: Thinking that 6 × 7 = 42 and 6 ÷ 7 = 42 is wrong.
• Why it happens: Confusing multiplication with division.
• Fix: Remember that multiplication makes a bigger number, and division makes a smaller number.

• Mistake: Forgetting to write all four facts in a family.
• Why it happens: Not understanding that a fact family needs four related facts.
• Fix: Always write both multiplication facts and both division facts.

• Mistake: Writing 42 ÷ 6 = 7 but then thinking 42 ÷ 7 = 6 is wrong.
• Why it happens: Not knowing that division is the opposite of multiplication.
• Fix: Use counters or drawings to check your division.

Parent and carer guide

Help your child understand fact families by:

1. Using real objects like counters or toys to show how multiplication and division work together
2. Practicing with simple numbers first, like 3, 4, and 12
3. Encouraging them to write all four facts in a family
4. Using everyday examples like sharing snacks or counting items in groups
5. Being patient if they make mistakes – it's part of learning!

Ask questions like:

• Can you find the fact family for 5 × 6?
• What multiplication fact helps you find 30 ÷ 5?
• Can you show me with counters how 6 × 7 = 42?

Remember: Fact families are a way to understand that multiplication and division are linked. This makes learning times tables easier and more fun!

Practice questions

1. What is the fact family for 4 × 6?
2. Write the fact family for 8 × 5.
3. What multiplication fact helps you find 24 ÷ 4?
4. Find the fact family for 9 × 7.
5. Which fact belongs in the family for 3 × 8?

Answers:

1. 4 × 6 = 24, 6 × 4 = 24, 24 ÷ 4 = 6, 24 ÷ 6 = 4
2. 8 × 5 = 40, 5 × 8 = 40, 40 ÷ 8 = 5, 40 ÷ 5 = 8
3. 4 × 6 = 24
4. 9 × 7 = 63, 7 × 9 = 63, 63 ÷ 9 = 7, 63 ÷ 7 = 9
5. 24 ÷ 8 = 3

FAQ

What is a fact family?

A fact family is a group of related multiplication and division facts that use the same three numbers.

Why are fact families important?

Fact families help you understand how multiplication and division are connected. This makes it easier to learn and remember your times tables.

Can you make a fact family with any three numbers?

No, the numbers must work together. For example, 3, 5, and 15 make a fact family because 3 × 5 = 15 and 15 ÷ 5 = 3.

How many facts are in a fact family?

There are always four facts in a fact family: two multiplication facts and two division facts.

Can zero be part of a fact family?

Yes, but only in multiplication. For example, 0 × 5 = 0 and 5 × 0 = 0. Division by zero is not possible.