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Using the associative property of addition, evaluate the following expressions:

Mathematics

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30 steps

Here are the calculations using the associative property:

Part a· 3 steps

  1. Apply the associative property.

    [(−6)+(4+2)]=[(−6)+4]+2[(-6) + (4 + 2)] = [(-6) + 4] + 2

  2. Perform the addition inside the first set of parentheses.

    =(−2)+2= (-2) + 2

  3. Perform the final addition.

    =0= \boxed{0}

Part b· 3 steps

  1. Apply the associative property.

    [3+7+(−5)]=(3+7)+(−5)[3 + 7 + (-5)] = (3 + 7) + (-5)

  2. Perform the addition inside the parentheses.

    =10+(−5)= 10 + (-5)

  3. Perform the final addition.

    =5= \boxed{5}

Part c· 3 steps

  1. Apply the associative property.

    [(6+4)+(−2)]=6+[4+(−2)][(6 + 4) + (-2)] = 6 + [4 + (-2)]

  2. Perform the addition inside the second set of parentheses.

    =6+2= 6 + 2

  3. Perform the final addition.

    =8= \boxed{8}

Part d· 3 steps

  1. Apply the associative property.

    [(−3)+7+5]=[(−3)+7]+5[(-3) + 7 + 5] = [(-3) + 7] + 5

  2. Perform the addition inside the first set of parentheses.

    =4+5= 4 + 5

  3. Perform the final addition.

    =9= \boxed{9}

Part e· 3 steps

  1. Apply the associative property.

    [(−4)+(6+2)]=[(−4)+6]+2[(-4) + (6 + 2)] = [(-4) + 6] + 2

  2. Perform the addition inside the first set of parentheses.

    =2+2= 2 + 2

  3. Perform the final addition.

    =4= \boxed{4}

Part f· 3 steps

  1. Apply the associative property.

    [3+(−7)+5]=[3+(−7)]+5[3 + (-7) + 5] = [3 + (-7)] + 5

  2. Perform the addition inside the first set of parentheses.

    =(−4)+5= (-4) + 5

  3. Perform the final addition.

    =1= \boxed{1}

Part g· 3 steps

  1. Apply the associative property.

    [(−9)+(3+11)]=[(−9)+3]+11[(-9) + (3 + 11)] = [(-9) + 3] + 11

  2. Perform the addition inside the first set of parentheses.

    =(−6)+11= (-6) + 11

  3. Perform the final addition.

    =5= \boxed{5}

Part h· 3 steps

  1. Apply the associative property.

    [(12+13)+(−10)]=12+[13+(−10)][(12 + 13) + (-10)] = 12 + [13 + (-10)]

  2. Perform the addition inside the second set of parentheses.

    =12+3= 12 + 3

  3. Perform the final addition.

    =15= \boxed{15}

Part h(i)· 6 steps

  1. Apply the associative property.

    [(−3)+(9+11)]=[(−3)+9]+11[(-3) + (9 + 11)] = [(-3) + 9] + 11

  2. Perform the addition inside the first set of parentheses.

    =6+11= 6 + 11

  3. Perform the final addition.

    =17= \boxed{17}

    j)

  4. Apply the associative property.

    [(−12)+(13+10)]=[(−12)+13]+10[(-12) + (13 + 10)] = [(-12) + 13] + 10

  5. Perform the addition inside the first set of parentheses.

    =1+10= 1 + 10

  6. Perform the final addition.

    =11= \boxed{11}
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