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Calculate (75 + 16) + 5.
Calculate 75 plus 16 plus five.
To add these together without using a calculator or even really without writing much down, we can use some properties of addition to help us. Do you notice that 75 and five both end in fives? I know that I could easily mentally add 75 and five together. So I wanna regroup this problem and group 75 and five together, add those first, and then add the 16.
Why are we allowed to move this problem around like this? The associative property of addition tells us that when we’re dealing with addition, we can group our numbers in any way that we want. In our case, we can add 75 and five together, which equals 80, and then add 16 to 80, which equals 96.
By moving around the five and the 16, we were able to solve this problem mentally, thanks to the associative property of addition. When we calculate 75 plus 16 plus five or if we move it around, either way, the final answer is 96.
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