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Use the associative property to evaluate the following expressions: a) [(-6) + (4 + 2)] b) [3 + 7 + (-5)] c) [(6 + 4) + (-2)] d) [(-3) + 7 + 5] e) [(-4) + (6 + 2)] f) [3 + (-7) + 5] g) [(-9) + (3 + 11

Mathematics

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Step-by-step solution

20 steps

Here are the calculations for each problem using the associative property:

Part a· 2 steps

[(−6)+(4+2)][(-6) + (4 + 2)]

  1. Calculate the sum inside the parentheses.

    4+2=64 + 2 = 6

  2. Add the result to −6-6.

    −6+6=0-6 + 6 = 0

    The final answer is 0\boxed{\text{0}}

Part b· 2 steps

[3+7+(−5)][3 + 7 + (-5)]

  1. Add the first two numbers.

    3+7=103 + 7 = 10

  2. Add the result to −5-5.

    10+(−5)=510 + (-5) = 5

    The final answer is 5\boxed{\text{5}}

Part c· 2 steps

[(6+4)+(−2)][(6 + 4) + (-2)]

  1. Calculate the sum inside the parentheses.

    6+4=106 + 4 = 10

  2. Add the result to −2-2.

    10+(−2)=810 + (-2) = 8

    The final answer is 8\boxed{\text{8}}

Part d· 2 steps

[(−3)+7+5][(-3) + 7 + 5]

  1. Add the first two numbers.

    −3+7=4-3 + 7 = 4

  2. Add the result to 5.

    4+5=94 + 5 = 9

    The final answer is 9\boxed{\text{9}}

Part e· 2 steps

[(−4)+(6+2)][(-4) + (6 + 2)]

  1. Calculate the sum inside the parentheses.

    6+2=86 + 2 = 8

  2. Add the result to −4-4.

    −4+8=4-4 + 8 = 4

    The final answer is 4\boxed{\text{4}}

Part f· 2 steps

[3+(−7)+5][3 + (-7) + 5]

  1. Add the first two numbers.

    3+(−7)=−43 + (-7) = -4

  2. Add the result to 5.

    −4+5=1-4 + 5 = 1

    The final answer is 1\boxed{\text{1}}

Part g· 2 steps

[(−9)+(3+11)][(-9) + (3 + 11)]

  1. Calculate the sum inside the parentheses.

    3+11=143 + 11 = 14

  2. Add the result to −9-9.

    −9+14=5-9 + 14 = 5

    The final answer is 5\boxed{\text{5}}

Part h· 2 steps

[(12+13)+(−10)][(12 + 13) + (-10)]

  1. Calculate the sum inside the parentheses.

    12+13=2512 + 13 = 25

  2. Add the result to −10-10.

    25+(−10)=1525 + (-10) = 15

    The final answer is 15\boxed{\text{15}}

Part h(i)· 4 steps

[(−3)+(9+11)][(-3) + (9 + 11)]

  1. Calculate the sum inside the parentheses.

    9+11=209 + 11 = 20

  2. Add the result to −3-3.

    −3+20=17-3 + 20 = 17

    The final answer is 17\boxed{\text{17}}

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

  3. Calculate the sum inside the parentheses.

    13+10=2313 + 10 = 23

  4. Add the result to −12-12.

    −12+23=11-12 + 23 = 11

    The final answer is 11\boxed{\text{11}}

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