Question

Determine the sum. Do the addition in the parentheses first. a. \(34+(15+71)\) b. \((34+15)+71\) c. Are the sums in parts a and b the same? d. What property of addition is demonstrated?

Short answer

Answer: Associative Property

Step-by-step solution

Perform addition inside the parentheses first for part a

In part a, we have the expression \(34+(15+71)\). First, add the numbers inside the parentheses. We get \((15+71) = 86\). Now substitute 86 back into the expression and perform the addition: \(34 + 86 = 120\).

Perform addition with parentheses removed for part b

In part b, we have the expression \((34+15)+71\). Since there is no operation inside the parentheses, we can remove them and perform the addition from left to right. First, add 34 and 15: \(34 + 15 = 49\). Now, add 71 to the result: \(49 + 71 = 120\).

Compare sums in parts a and b

Now, let's compare the sums obtained in parts a and b. In part a, we obtained a sum of 120, and in part b, we also obtained a sum of 120. These sums are the same.

Identify the property of addition demonstrated

The property of addition demonstrated here is the Associative Property, which states that for any numbers a, b, and c, \((a+b)+c = a+(b+c)\). In this exercise, the associative property helps confirm that the order in which addition operations are grouped does not affect the final sum.