Learning Fact Families

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.

 

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. 

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.