What it says: This property states that the grouping of numbers in an addition or multiplication expression will not change the sum or product. This is important when parenthesis are used in the expression.
In the example below the 9 and the 7 are grouped in the parenthesis. The order of operations states that you do all operations in parenthesis first. Therefore, you will add 9 and 7 to get a sum (answer to an addition expression) of 16 and then add 5 to get a sum of 21. But would the sum be the same if you moved the parenthesis to the 7 and 5 and then added them first?
Click on the MOVE PARENTHESIS button below and see what happens to the sum when the parenthesis are moved to the 7 and 5.
The sum stays the same no matter what how the numbers are grouped. This is the associative property.
Let's see. In the example below, the parenthesis are around the numbers 3 and 4. The order of operations states that we would mulitply these two numbers first. The product (answer to a multiplication expression) would be 12. Then we would multiply 12 by 2 to get a product of 24. Would the product be the same if you moved the parenthesis to the 4 and 2.
Click on the MOVE PARENTHESIS button below and see what happens to the product when the parenthesis are moved to the 4 and 2.