Multiplication and division fact families
A multiplication and division fact family is two multiplication facts and two division facts that use the same three numbers. For 4, 6 and 24: 4 × 6 = 24, 6 × 4 = 24, 24 ÷ 4 = 6 and 24 ÷ 6 = 4.
A multiplication and division fact family is a set of two multiplication facts and two division facts that use the same three numbers: two factors and one product. For 4, 6 and 24 the family is 4 × 6 = 24, 6 × 4 = 24, 24 ÷ 4 = 6 and 24 ÷ 6 = 4.
What is a multiplication and division fact family?
Multiplication joins equal groups. Division splits a total back into equal groups or finds how many groups there are. They are inverse operations, which means each one undoes the other. That is why the same three numbers appear in all four facts.
In the array, 3 rows with 4 dots in each row make 12 dots. Count by rows and you get 3 × 4 = 12. Turn the array and count by columns and you get 4 × 3 = 12. Share the 12 dots into 3 equal rows and each row has 12 ÷ 3 = 4. Share them into 4 equal columns and each has 12 ÷ 4 = 3.
Multiplication and division fact family examples
- 2 × 9 = 18
- 9 × 2 = 18
- 18 ÷ 2 = 9
- 18 ÷ 9 = 2
- 3 × 8 = 24
- 8 × 3 = 24
- 24 ÷ 3 = 8
- 24 ÷ 8 = 3
- 4 × 7 = 28
- 7 × 4 = 28
- 28 ÷ 4 = 7
- 28 ÷ 7 = 4
- 5 × 6 = 30
- 6 × 5 = 30
- 30 ÷ 5 = 6
- 30 ÷ 6 = 5
- 6 × 6 = 36
- 36 ÷ 6 = 6
- 2 × 12 = 24
- 12 × 2 = 24
- 24 ÷ 2 = 12
- 24 ÷ 12 = 2
Build your own multiplication and division family
Multiplication and division fact family calculator
Type any two numbers. The third number and all the facts appear.
- 4 × 6 = 24
- 6 × 4 = 24
- 24 ÷ 4 = 6
- 24 ÷ 6 = 4
Use fact families to divide
Division is easier when you connect it to a multiplication fact you know. To solve 56 ÷ 7, follow these steps.
- Write the division problem: 56 ÷ 7 = ?
- Turn it into a missing factor problem: 7 × ? = 56.
- Use the times table. 7 × 8 = 56, so the missing factor is 8.
- Write the family: 7 × 8 = 56, 8 × 7 = 56, 56 ÷ 7 = 8 and 56 ÷ 8 = 7.
Teacher tip: this is the thinking behind Common Core standard 3.OA.B.6, which treats division as an unknown-factor problem. Ask “7 times what is 56?” and children use the multiplication facts they already know.
Fact families for every times table
Each times table has its own set of fact families. Open the table you are working on to see every family at once.
Squares, zero and one
- Square numbers have two equal factors, so the family has only two different facts. 6 × 6 = 36 and 36 ÷ 6 = 6.
- Multiplying by 1 gives the same number. The family 1, 8 and 8 is 1 × 8 = 8, 8 × 1 = 8, 8 ÷ 1 = 8 and 8 ÷ 8 = 1.
- Multiplying by 0 always gives 0. You cannot divide by 0, so the zero facts do not make a full family.
Tips for learning multiplication and division facts
- Start with the easy tables: 2, 5 and 10. Then build up to the harder ones.
- Use fact family triangles as flash cards. Cover one corner and ask for the hidden number.
- Practice with multiplication and division fact family worksheets.
- Mix multiplication and division questions so children see them as one idea.
Frequently asked questions
What is the fact family for 3, 7 and 21?
3 × 7 = 21, 7 × 3 = 21, 21 ÷ 3 = 7 and 21 ÷ 7 = 3.
Is division the inverse of multiplication?
Yes. Multiplying by a number and then dividing by the same number returns you to where you started.
What grade learns multiplication and division fact families?
Usually third grade. See the 3rd grade fact families page.