# Fact Families for Addition and Subtraction

A fact family is a group of math facts using the same numbers. In the case of addition and subtraction, you use three numbers and get four facts.

**For example**, you can form a fact family using the three numbers 3, 10, and 13: 10 + 3 = 13, 3 + 10 = 13, 13 − 10 = 3, and 13 − 3 = 10.

**Addition facts** − Here the sum of two of the three given numbers is the remaining third number. This sum is expressed in two possible orders. Thus, there are two addition facts for any three given numbers

For 3, 10 and 13, the two addition facts are:

3 + 10 = 13;

10 + 3 = 13

**Subtraction facts** − Here the difference of two of the three given numbers is the remaining third number. There are two such differences. Thus, there are two subtraction facts for any three given numbers.

For 3, 10 and 13, the two subtraction facts are:

13 − 10 = 3;

13 − 3 = 10

We use fact families to reinforce the connection between addition and subtraction, and to help students learn and memorize the basic addition & subtraction facts.

Make four related number sentences using each set of 3 numbers.

10, 7, 3:

There should be two additions and two subtractions.

### Solution

10, 7, 3:

**Step 1:**

The addition facts using above three numbers are:

7 + 3 = 10;

3 + 7 = 10;

**Step 2:**

The subtraction facts using above three numbers are:

10 – 7 = 3;

10 – 3 = 7

Make four related number sentences using each set of 3 numbers.

13, 8, 5

There should be two additions and two subtractions.

### Solution

13, 8, 5

**Step 1:**

The addition facts using above three numbers are:

5 + 8 = 13;

8 + 5 = 13;

**Step 2:**

The subtraction facts using above three numbers are:

13 – 5 = 8;

13 − 8 = 5