Fact Families

Three numbers, four facts. Make any fact family, practise finding the missing number, and print free fact family triangles and houses.

A fact family is a group of three numbers that make four related facts. The family 3, 5, 8 gives 3 + 5 = 8, 5 + 3 = 8, 8 − 3 = 5 and 8 − 5 = 3.

Multiplication works the same way: 4, 7, 28 gives 4 × 7, 7 × 4, 28 ÷ 4 and 28 ÷ 7.

Fact family maker

Type two numbers and the triangle writes the whole family.

Part Part

8+ −35

3 + 5 = 8
5 + 3 = 8
8 − 3 = 5
8 − 5 = 3

Practice: find the missing number

One number in the triangle is hidden. Use the other two and the family’s facts to find it.

15+ −69

Press Enter to check.

Addition and subtraction fact families

The top of the triangle is the whole (the sum); the two bottom corners are the parts. Adding the parts in either order makes the whole, and taking either part away from the whole leaves the other.

Numbers	The four facts
3, 5, 8	3 + 5 = 8 5 + 3 = 8 8 − 3 = 5 8 − 5 = 3
6, 9, 15	6 + 9 = 15 9 + 6 = 15 15 − 6 = 9 15 − 9 = 6
4, 8, 12	4 + 8 = 12 8 + 4 = 12 12 − 4 = 8 12 − 8 = 4

Multiplication and division fact families

Here the top number is the product and the corners are its two factors. Every division fact is a times-table fact turned around, which is why the division chart is the multiplication chart read backwards.

Numbers	The four facts
4, 7, 28	4 × 7 = 28 7 × 4 = 28 28 ÷ 4 = 7 28 ÷ 7 = 4
6, 8, 48	6 × 8 = 48 8 × 6 = 48 48 ÷ 6 = 8 48 ÷ 8 = 6
3, 9, 27	3 × 9 = 27 9 × 3 = 27 27 ÷ 3 = 9 27 ÷ 9 = 3

Fact families with doubles

When both parts are the same, the family is smaller: 6, 6, 12 has only 6 + 6 = 12 and 12 − 6 = 6, and 7, 7, 49 has only 7 × 7 = 49 and 49 ÷ 7 = 7. Children often find these the easiest families; the doubles facts are a good place to start.

Why fact families help

Subtraction is easier as “think addition”: to work out 13 − 8, ask what goes with 8 to make 13. A child who knows the family 5, 8, 13 knows the answer is 5. Learning one family gives four facts for the price of one, which is why addition and subtraction are taught together, and why number bonds (the same three numbers drawn as a whole and two parts) come first.

Fact family worksheets

Free PDFs with an answer key on page 2. No login, no email.

Fact Family Triangles: Addition and Subtraction

Grades 1–2

Six triangles with sums to 20: write the two addition and two subtraction facts for each.

Download PDF (6 problems · 46 KB)

Fact Family Houses

Grades 1–2

Six houses: the three numbers live in the roof, and the four facts go on the floors.

Download PDF (6 problems · 46 KB)

Fact Family Triangles: Multiplication and Division

Grades 3–4

Six triangles with products to 100: write the two × and two ÷ facts for each.

Download PDF (6 problems · 46 KB)

More: addition worksheets, subtraction worksheets and division worksheets.

When kids learn fact families

1st grade: addition and subtraction fact families within 20, and subtraction as an unknown-addend problem (1st grade math).
2nd grade: fluent addition and subtraction within 20 (2nd grade math).
3rd grade: multiplication and division fact families, and division as an unknown-factor problem (3rd grade math).

From families to fast facts

A 10-question adaptive quiz finds the addition, subtraction or times-table facts your child is slow on and brings them back. Free, no login.

Start a free quiz

Common questions

What is a fact family?

A fact family is three numbers that are related by addition and subtraction, or by multiplication and division. Together they make four facts: 3, 5, 8 gives 3 + 5 = 8, 5 + 3 = 8, 8 − 3 = 5 and 8 − 5 = 3.

What is a fact family triangle?

A triangle with the whole (the sum or product) at the top and the two parts at the bottom corners. Covering any one number shows which fact finds it: cover the top and you add or multiply, cover a corner and you subtract or divide.

How many facts are in a fact family?

Four, unless the two parts are the same. A double like 6, 6, 12 has only two facts: 6 + 6 = 12 and 12 − 6 = 6.

What is the fact family for 4, 7 and 28?

4 × 7 = 28, 7 × 4 = 28, 28 ÷ 4 = 7 and 28 ÷ 7 = 4.

What grade learns fact families?

Addition and subtraction fact families are 1st grade, with fluency within 20 by the end of 2nd grade. Multiplication and division fact families are 3rd grade.