Associative Property Of Real Numbers

The associative property states that when three or more real numbers are added or multiplied, changing only the grouping does not change the result.

Suppose a company records profits of $2.4 million, $3.6 million, and $1.5 million from three product lines. One way to find the total profit is to add the first two values, then add the third. Another way is to add the first value to the sum of the last two values. Both groupings give the same total profit.

Now, suppose a company is calculating training manual costs for a department with 16 employees, where each employee receives 4 manuals that cost $25 each.

We can first find the total number of manuals, then multiply that by the cost per manual. Or we can first find the manual cost per employee, then multiply that by the number of employees. Both groupings give the same total cost.

The associative property also helps simplify algebraic expressions involving addition and multiplication. The order of the numbers stays the same, but the grouping changes. This makes calculations and algebraic expressions easier to simplify.