Fact Family Examples With Answers

Fact family examples show how three numbers make four facts. For 5, 7 and 12 the facts are 5 + 7 = 12, 7 + 5 = 12, 12 − 5 = 7 and 12 − 7 = 5. This page has worked examples for addition, subtraction, multiplication and division, including doubles, zero and missing numbers.

Addition and subtraction fact family examples

Each card shows the three numbers in a triangle and the four facts beside it.

2 + 3 = 5
3 + 2 = 5
5 − 2 = 3
5 − 3 = 2

5 + 7 = 12
7 + 5 = 12
12 − 5 = 7
12 − 7 = 5

8 + 9 = 17
9 + 8 = 17
17 − 8 = 9
17 − 9 = 8

4 + 6 = 10
6 + 4 = 10
10 − 4 = 6
10 − 6 = 4

9 + 9 = 18
18 − 9 = 9

0 + 5 = 5
5 + 0 = 5
5 − 0 = 5
5 − 5 = 0

Here is how to build the third example. The parts are 8 and 9, so the whole is 8 + 9 = 17. The facts are 8 + 9 = 17, 9 + 8 = 17, 17 − 8 = 9 and 17 − 9 = 8.

Multiplication and division fact family examples

2 × 6 = 12
6 × 2 = 12
12 ÷ 2 = 6
12 ÷ 6 = 2

3 × 7 = 21
7 × 3 = 21
21 ÷ 3 = 7
21 ÷ 7 = 3

4 × 8 = 32
8 × 4 = 32
32 ÷ 4 = 8
32 ÷ 8 = 4

5 × 9 = 45
9 × 5 = 45
45 ÷ 5 = 9
45 ÷ 9 = 5

3 × 5 = 15
5 × 3 = 15
15 ÷ 3 = 5
15 ÷ 5 = 3

7 × 7 = 49
49 ÷ 7 = 7

Take the family for 3, 5 and 15. The factors are 3 and 5 and the product is 15. The facts are 3 × 5 = 15, 5 × 3 = 15, 15 ÷ 3 = 5 and 15 ÷ 5 = 3. If you were asked for the fact family of 15, 5 and 3, this is the answer.

Fact family examples with doubles

A double has two equal parts, so the family has just two different facts. The family 9, 9 and 18 gives 9 + 9 = 18 and 18 − 9 = 9. The family 7, 7 and 49 gives 7 × 7 = 49 and 49 ÷ 7 = 7.

Fact family examples with 0 and 1

Zero and one behave in a special way. Adding zero changes nothing, and multiplying by one changes nothing.

0 + 6 = 6
6 + 0 = 6
6 − 0 = 6
6 − 6 = 0

1 × 8 = 8
8 × 1 = 8
8 ÷ 1 = 8
8 ÷ 8 = 1

Zero in multiplication needs care. 0 × 6 = 0 and 6 × 0 = 0 are true, but you cannot divide by zero, so there is no fact that says 0 ÷ 0 or 6 ÷ 0 gives a number you can use.

Find the missing number in a fact family

Missing number questions are the most common fact family homework. Try each one, then open the answer.

1. A fact family has the numbers 8, 6 and a whole. What is the whole?

The parts are 8 and 6, so the whole is 8 + 6 = 14. The facts are 8 + 6 = 14, 6 + 8 = 14, 14 − 8 = 6 and 14 − 6 = 8.

2. A fact family has the whole 15 and one part 9. What is the other part?

Use subtraction: 15 − 9 = 6. The other part is 6, and the facts are 9 + 6 = 15, 6 + 9 = 15, 15 − 9 = 6 and 15 − 6 = 9.

3. A fact family has the factor 7 and the product 42. What is the other factor?

Use division: 42 ÷ 7 = 6. The other factor is 6, and the facts are 7 × 6 = 42, 6 × 7 = 42, 42 ÷ 7 = 6 and 42 ÷ 6 = 7.

4. Complete the family of facts: 5, 5, 10.

The two parts are the same, so there are two facts: 5 + 5 = 10 and 10 − 5 = 5.

Fact family examples from word problems

Maya has 12 stickers and gives 5 to a friend. She has 12 − 5 = 7 stickers left. The numbers 5, 7 and 12 are a fact family, so 7 + 5 = 12 lets Maya check her answer.

A baker puts 6 muffins in each of 4 boxes. That is 4 × 6 = 24 muffins. If she has 24 muffins and packs 6 in each box, then 24 ÷ 6 = 4 boxes. The same three numbers, 4, 6 and 24, answer both questions.

Practice with fact family examples

Use the fact family calculator to check any three numbers, or print a fresh set from the fact family worksheet maker. New to the idea? Start with what is a fact family.