Question

Determine whether the two expressions are equivalent. If so, tell what property is applied. If not, explain why. (35+17)+43 and 35+(17+43)

Answer 1

Yes, the expressions (35+17)+43 and 35+(17+43) are equivalent, and the property being applied is the Associative Property of Addition.

Step-by-step explanation:

Yes, the expressions (35+17)+43 and 35+(17+43) are equivalent. This is because of the Associative Property of Addition, which states that changing the grouping of numbers being added does not change the sum. In this case, the numbers are being grouped differently.

Let's see this step-by-step:

• Step 1: (35+17)+43
• Step 2: 52+43 (addition within the parentheses)
• Step 3: 95 (final sum)

Now let's evaluate the other expression:

• Step 1: 35+(17+43)
• Step 2: 35+60 (addition within the parentheses)
• Step 3: 95 (final sum)

As you can see, both expressions simplify to the same sum of 95, confirming that they are equivalent. The property being applied here is the Associative Property of Addition.