A Fact Family Holds Four Related Facts
Three numbers make two multiplications and two divisions. The largest number is the product.
A fact family is three numbers that stay together. 3, 4, and 12 belong to each other because 3 groups of 4 make 12. If you know one sentence, the other three reuse the same numbers. Nothing new is invented when you switch the operation.
The largest number is the product. It is the answer in multiplication, and it is the number being split in division, so it goes first there. The two smaller numbers are the factors. They trade places, but they do not change.
- 3 × 4 = 12
- 4 × 3 = 12
- 12 ÷ 3 = 4
- 12 ÷ 4 = 3
5, 6, and 30 are another family. 5 × 6 = 30 and 6 × 5 = 30. Turn them around: 30 ÷ 5 = 6 and 30 ÷ 6 = 5. 7, 8, and 56 work the same way: 7 × 8 = 56, 8 × 7 = 56, 56 ÷ 7 = 8, 56 ÷ 8 = 7.
Watch out
- Writing 3 ÷ 12 = 4. The largest number has to be divided, not used as the divisor.
- Changing one of the three numbers when the operation changes.
- Putting a factor first in the division.
What family goes with 5 × 6 = 30?
6 × 5 = 30, 30 ÷ 5 = 6, and 30 ÷ 6 = 5.
Where does the largest number go?
It is the product, so it is the answer of both multiplications and the first number of both divisions.
Math practice for Fact Families
Missing number division, tables 1–9
Practice this