A fact family is a group of four statements each of which represent the same meaning. All the four statements have the same meanings. Fact families contain 3
numbers and 2 types of operations. There are 2 types of fact families: addition and subtraction fact families; multiplication and division fact families.

To see the fact families we need to understand the meaning of following words:

Addends: The numbers being added in an addiotion operation. Like 2 and 3 in 2 + 3 = 5

Multiplicands: The numbers being multiplied in a multiplication operation. Like 4 and 5 in 4 x 5 = 20

Inverse operation: Reverse of an operation like inverse operation of addition is subtraction and inverse of multiplication is division.

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Learning Addition and subtraction fact families

This family consists of two addition and two subtraction problems. First we take an addition operation. Like 2 + 4 = 6. In the next operation the addends are reversed. 4 + 2 = 6. Now we can write
the inverse operations of both.

6 - 4 = 2; 6 - 2 = 4;

Example 1: What are the four members of the fact family of 8 + 2 = 10?

Answer: 8 + 2 = 10;

Reversing the addends: 2 + 8 = 10;

Inverse operations: 10 - 2 = 8;

10 - 8 = 2;

Example 2: Write the four facts of the family with numbers 7, 6 and 13.

Answer:

7 + 6 = 13;

6 + 7 = 13;

13 - 7 = 6;

13 - 6 = 7;

Example 3: Write the four facts of the family with numbers 7 , 7 and 0.

Answer:

7 + 0 = 7

0 + 7 = 7

7 - 7 = 7

7 - 7 = 0

When 2 of the numbers are same , then we have only 2 facts. Because 1st two and last two facts are same.

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Learning Multiplication and division fact families

This family consists of two multiplication and two division problems. Fist we take a multiplication fact like 3 x 4 = 12. The next fact is made by turning
the multiplicands around. 4 x 3 =12. Then inverse operations of both which is division is taken.

12 ÷ 4= 3; 12 ÷ 3 = 4

Example 1: What are the 4 members of the fact family of 5 x 6 = 30?

The multiplication fact: 5 x 6 = 30

Turning the multiplicands around: 6 x 5 = 30;

Inverse operations: 30 ÷ 6 = 5

30 ÷ 5 = 6

Example 2: What are the four facts of the numbers 8, 4 and 32.

8 x 4 = 32

4 x 8 = 32

32 ÷ 4 = 8

32 ÷ 8 = 4

Example 2: What are the four facts of the numbers 9, 5 and 45.

9 x 5 = 45

5 x 9 = 45

45 ÷ 5 = 9

45 ÷ 9 = 5

Thus learning fact families become easy from this discusion.