Fact Families

For Elementary Students

What is a Fact Family?

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

Think about it like this: In your family, you have different people who are related. In a math fact family, you have different equations that are related!

Example: The 3, 5, 8 Family

Let's say we have the numbers 3, 5, and 8.

We can write four related facts:

Addition facts:

• 3 + 5 = 8
• 5 + 3 = 8

Subtraction facts:

• 8 - 5 = 3
• 8 - 3 = 5

All four of these use the same three numbers: 3, 5, and 8. They are a fact family!

Why Fact Families Help

If you know one fact, you automatically know three more facts for free!

Example: You know that 4 + 6 = 10.

That means you also know:

• 6 + 4 = 10 (you can switch the order)
• 10 - 6 = 4 (subtract one part from the whole)
• 10 - 4 = 6 (subtract the other part from the whole)

How to Build a Fact Family

1. Start with two parts (the smaller numbers)
2. Add them to find the whole (the largest number)
3. Write all four facts

Try it with 7 and 9:

• Add: 7 + 9 = 16
• Now you know the whole is 16
• Write all four:
  • 7 + 9 = 16
  • 9 + 7 = 16
  • 16 - 7 = 9
  • 16 - 9 = 7

Special Fact Families

Some fact families only have two facts instead of four.

Example: 5, 5, 10

• 5 + 5 = 10
• 10 - 5 = 5

Because both parts are the same, switching them doesn't make a new fact!

For Junior High Students

The Relationship Between Addition and Subtraction

Fact families show that addition and subtraction are opposite operations (also called inverse operations).

• Addition combines two numbers to make a larger number
• Subtraction separates a larger number into two smaller numbers

If you know 12 + 8 = 20, then you automatically know 20 - 8 = 12.

Using Fact Families to Check Your Work

If you solve 15 + 7 = 22, you can check by subtracting:

22 - 7 = 15 ✓ (Correct!)

If the subtraction gives you back one of the original numbers, your addition was right.

Fact Families with Larger Numbers

The same idea works with any three numbers, even big ones.

Example: 45, 38, 83

• 45 + 38 = 83
• 38 + 45 = 83
• 83 - 45 = 38
• 83 - 38 = 45

Algebra Connection (Preview)

Later, you'll learn about variables. Fact families prepare you for solving equations like:

x + 7 = 15

If you know fact families, you know that:

15 - 7 = x

So x = 8. We'll learn more about this later.

Multiplication and Division Fact Families

Fact families also work for multiplication and division! (We'll learn more about this in multiplication lessons.)

Example: 3, 4, 12

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

Just like addition and subtraction, multiplication and division are inverse operations.

Practice