Simplify the following expressions using the commutative and associative properties of addition.

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5. Simplify by applying commutative and associative properties. a) −32 + 32 + 75 Step 1: Apply the associative property of addition, (a+b)+c = a+(b+c), to group terms that sum to zero or are easy to calculate. −32 + 32 + 75 = (−32 + 32) + 75 Step 2: Perform the addition inside the parentheses. 0 + 75 Step 3: Complete the addition. 75 Answer: 75 b) 65 + 80 + (−65) Step 1: Apply the associative property of addition to group terms. 65 + 80 + (−65) = (65 + (−65)) + 80 Step 2: Perform the addition inside the parentheses. 0 + 80 Step 3: Complete the addition. 80 Answer: 80 c) 112 + 50 + (−112) Step 1: Apply the commutative property (a+b=b+a) and associative property ((a+b)+c = a+(b+c)) to rearrange terms. 112 + 50 + (−112) = 112 + (−112) + 50 Step 2: Perform the addition of the inverse terms. 0 + 50 Step 3: Complete the addition. 50 Answer: 50

Simplify the following expressions using the commutative and associative properties of addition.

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Step-by-step solution

Part a· 3 steps

Apply the associative property of addition, $(a+b)+c = a+(b+c)$ , to group terms that sum to zero or are easy to calculate.

Perform the addition inside the parentheses.

Complete the addition.

Part b· 3 steps80

Apply the associative property of addition to group terms.

Perform the addition inside the parentheses.

Complete the addition.

Part c· 3 steps50

Apply the commutative property ( $a+b=b+a$ ) and associative property ( $(a+b)+c = a+(b+c)$ ) to rearrange terms.

Perform the addition of the inverse terms.

Complete the addition.

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Simplify the following expressions using the commutative and associative properties of addition.

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Step-by-step solution

Part a· 3 steps

Apply the associative property of addition, (a+b)+c=a+(b+c)(a+b)+c = a+(b+c)(a+b)+c=a+(b+c), to group terms that sum to zero or are easy to calculate.

Perform the addition inside the parentheses.

Complete the addition.

Part b· 3 steps80

Apply the associative property of addition to group terms.

Perform the addition inside the parentheses.

Complete the addition.

Part c· 3 steps50

Apply the commutative property (a+b=b+aa+b=b+aa+b=b+a) and associative property ((a+b)+c=a+(b+c)(a+b)+c = a+(b+c)(a+b)+c=a+(b+c)) to rearrange terms.

Perform the addition of the inverse terms.

Complete the addition.

Try one yourself

Still stuck on this one?

More Mathematics Questions

Apply the associative property of addition, $(a+b)+c = a+(b+c)$ , to group terms that sum to zero or are easy to calculate.

Apply the commutative property ( $a+b=b+a$ ) and associative property ( $(a+b)+c = a+(b+c)$ ) to rearrange terms.