Evaluate 27 plus 29 plus 73 using the commutative and associative properties.
The community property allows us to change something from 𝑎 plus 𝑏 to 𝑏 plus 𝑎, switch around the order. The associative property allows us to add different numbers together first, but still with the same total.
So we can take 𝑎 plus parenthesis 𝑏 plus 𝑐 or we would need to add 𝑏 and 𝑐 together first. And it will actually be the exact same thing as taking 𝑎 plus 𝑏 inside the parenthesis, adding those together first then adding 𝑐. And we would still get the same number.
So here we have our expression: 27 plus 29 plus 73. So we’re supposed to evaluate this using the commutative and associative properties. So let’s first begin by using the commutative property.
Using the commutative property, we can use the commutative property to switch the order of adding the 73 and 29. So instead of having 27 plus 29 plus 73, we can have 27 plus 73 plus 29. And the associative property states as long as we’re adding or multiplying — but in this case we’re adding — we can add whichever two numbers together we would like first.
So looking at the original expression, we would think we would add 27 and 29 together first. But here we can see we’re actually going to be adding 27 and 73 first, because they’re inside the parentheses. So, 27 plus 73 is equal to 100, and 100 plus 29 is equal to 129. Therefore, 129 will be our final answer.