When performing a single operation on three (or more) numbers, if the result is unchanged by the way the numbers are grouped, then the operation is said to be associative.

Addition and multiplication are associative.

4 + 2 + 1 = 4 + 2 + 1

6 + 1 = 4 + 3

7 = 7 (Both sides have a sum of 7.)

4 × 2 × 1 = 4 × 2 × 1

8 × 1 = 4 × 2

8 = 8 (Both sides have a product of 8.)

 

Subtraction and division are generally NOT associative.

4 − 2 − 1 ≠ 4 − 2 − 1

2 − 1 ≠ 4 − 1

1 ≠ 3

4 ÷ 2 ÷ 2 ≠ 4 ÷ 2 ÷ 2

2 ÷ 2 ≠ 4 ÷ 1

1 ≠ 4