What is a fact family?
A fact family is a group of math facts that use the same three numbers. The numbers 3, 4 and 7 make 3 + 4 = 7, 4 + 3 = 7, 7 − 3 = 4 and 7 − 4 = 3. Fact families show how addition and subtraction, and multiplication and division, are connected.
A fact family is a group of related math facts that all use the same three numbers. Teachers also call it a family of facts or a number family. The facts belong together because knowing one of them lets you work out the others.
Fact family definition
Every fact family has three numbers. In an addition and subtraction family, two numbers are the parts and the biggest number is the whole. In a multiplication and division family, two numbers are the factors and the biggest number is the product.
Take 3, 4 and 7. The parts are 3 and 4, and the whole is 7. Those three numbers make four facts, and you can see them on the anchor chart below.
Try it yourself. Type any two numbers into the calculator and it builds the whole fact family. Switch to multiplication and division to see that kind of family too.
Fact family calculator
Type any two numbers. The third number and all the facts appear.
- 3 + 4 = 7
- 4 + 3 = 7
- 7 − 3 = 4
- 7 − 4 = 3
Addition and subtraction fact families
An addition and subtraction fact family joins two addition facts with two subtraction facts. The addition facts show the parts coming together to make the whole. The subtraction facts show the whole being split back into its parts.
- 2 + 5 = 7
- 5 + 2 = 7
- 7 − 2 = 5
- 7 − 5 = 2
- 6 + 9 = 15
- 9 + 6 = 15
- 15 − 6 = 9
- 15 − 9 = 6
- 8 + 8 = 16
- 16 − 8 = 8
Want more? Read our guide to addition and subtraction fact families, or see every family that adds up to 10 on the addition fact families to 10 page.
Multiplication and division fact families
A multiplication and division fact family joins two multiplication facts with two division facts. The multiplication facts show two factors making a product. The division facts show the product being shared back into equal groups.
- 3 × 4 = 12
- 4 × 3 = 12
- 12 ÷ 3 = 4
- 12 ÷ 4 = 3
- 6 × 8 = 48
- 8 × 6 = 48
- 48 ÷ 6 = 8
- 48 ÷ 8 = 6
- 5 × 5 = 25
- 25 ÷ 5 = 5
You can find all of these on the multiplication and division fact families page, and the family for each times table on our fact families by number pages.
How to find a fact family
Follow these steps whenever you have three numbers that belong together.
- Find the biggest number. It is the whole in an addition family or the product in a multiplication family.
- Write the first fact. Join the two smaller numbers: 3 + 4 = 7 or 3 × 4 = 12.
- Swap the two smaller numbers. This gives the second fact: 4 + 3 = 7 or 4 × 3 = 12.
- Write the two inverse facts. Start with the biggest number and take away or divide by each small number: 7 − 3 = 4 and 7 − 4 = 3, or 12 ÷ 3 = 4 and 12 ÷ 4 = 3.
- Check. Every fact must use only the same three numbers.
Quick check: if you cannot make all four facts from your three numbers, they are not a fact family. The numbers 3, 4 and 8, for example, do not work, because 3 + 4 is 7 and 3 × 4 is 12, not 8.
Fact families with only two facts
When the two smaller numbers are the same, swapping them changes nothing, so the family has only two different facts. The family 5, 5 and 10 has 5 + 5 = 10 and 10 − 5 = 5. The family 4, 4 and 16 has 4 × 4 = 16 and 16 ÷ 4 = 4.
The fact family triangle and house
Teachers often draw a fact family as a triangle. The biggest number sits at the top and the two smaller numbers sit at the bottom. Another favorite is the fact family house, where the whole is the roof and the two parts are the rooms.
You can make your own with the fact family triangles maker and the fact family house template, then print them for the classroom or the kitchen table.
Why fact families matter
- They show that operations are connected. Addition and subtraction undo each other, and so do multiplication and division.
- They make facts easier to learn. Learning one fact gives you three more for free.
- They help children check their work. If 12 − 5 = 7, then 7 + 5 should be 12.
- They prepare children for algebra. Finding a missing number in 5 + ? = 12 is the same thinking as solving an equation.
Which grade learns fact families?
In the United States, children meet addition and subtraction fact families in first grade. They work with them fluently within 20 in second grade, and they learn multiplication and division fact families in third grade. These steps connect to Common Core standards 1.OA.B.4, 2.OA.B.2, 3.OA.B.6 and 3.OA.C.7. In England, related facts start in Year 1 and the times tables are taught across Years 2 to 4. Exact timing varies by school and state, so check your own curriculum. See our pages for 1st grade, 2nd grade and 3rd grade.
Practice finding fact families
Ten quick questions, one empty circle each. Choose the level that suits your child.
Practice: complete the fact family triangle
Frequently asked questions
What is a family of facts in math?
A family of facts is another name for a fact family. It is a set of addition and subtraction facts, or multiplication and division facts, that use the same three numbers.
How many facts are in a fact family?
Most fact families have four facts. A family with two equal smaller numbers, like 6, 6 and 12, has only two different facts.
Are related facts the same as fact families?
They are very close. Related facts is the term some textbooks use for the facts in a fact family. Our related facts page explains the difference in wording.
Can a fact family use zero?
Yes for addition and subtraction: 0, 6 and 6 gives 0 + 6 = 6, 6 + 0 = 6, 6 − 0 = 6 and 6 − 6 = 0. In multiplication, 0 × 6 = 0, but you cannot divide by zero, so that family has fewer division facts.
What is the difference between a fact family and a number bond?
A number bond shows how a whole splits into two parts. A fact family goes one step further and writes out every addition and subtraction fact that bond supports.