# Associative property of addition

The associative property of addition states that how the numbers in an addition are grouped doesn't change the result of the problem.

This can be generalized as:

a + (b + c) = (a + b) + c

Example

4 + 7 + 12 + 15 + 48 = 86

Using parentheses to indicate order of operation, we can group the above addition problem in a number of ways:

Group 1:

(4 + 7) + (12 + 15 + 48) = 86

(11) + (75) = 86

Group 2:

(4 + 7 + 12) + 15 + 48 = 86

(23) + 15 + 48 = 86

Group 3:

(4 + 7) + 12 + (15 + 48) = 86

(11) + 12 + (63) = 86

There are more ways to group the above numbers than what is shown above, but in all cases, the result of the addition will still be 86. This is the nature of the associative property of addition. Addition is an operation such that the way the numbers are added up and which order they are written in doesn't change the result. This is also true of multiplication. It is not true of subtraction or division however, where how numbers are grouped changes the outcome.