Question

supply reasons for each of the first three steps given below.
(425 + 36) + 75 = 425 + (36 + 75)
= 425 + (75 + 36)
= (425 + 75) + 36
= 500 + 36
= 536

choose the correct reason to the right of each step.
(425 + 36) + 75 = 425 + (36 + 75)
= 425 + (75 + 36)
= (425 + 75) + 36
= 500 + 36
= 536

Explanation:

Step1: Analyze first step

The first step \((425 + 36)+75=425+(36 + 75)\) changes the grouping of the addends. The associative property of addition states that \((a + b)+c=a+(b + c)\) for any real numbers \(a\), \(b\), and \(c\). So the reason for this step is the Associative Property of Addition.

Step2: Analyze second step

The second step \(425+(36 + 75)=425+(75 + 36)\) swaps the order of \(36\) and \(75\) within the parentheses. The commutative property of addition states that \(a + b=b + a\) for any real numbers \(a\) and \(b\). So the reason for this step is the Commutative Property of Addition.

Step3: Analyze third step

The third step \(425+(75 + 36)=(425 + 75)+36\) changes the grouping of the addends again. Using the associative property of addition \((a + b)+c=a+(b + c)\), we can regroup \(425\) with \(75\) instead of \(36\). So the reason for this step is the Associative Property of Addition.

Answer:

1. For \((425 + 36)+75 = 425+(36 + 75)\): Associative Property of Addition
2. For \(425+(36 + 75)=425+(75 + 36)\): Commutative Property of Addition
3. For \(425+(75 + 36)=(425 + 75)+36\): Associative Property of Addition