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Apply the associative property of addition to solve for the final value in the following problems: a) a = 4, b = -5, c = 3; b) a = 2, b = 9, c = -4; c) a = -8, b = 1, c = 2

Mathematics

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Answers

4 parts
a
2
b
7
c
-5
d
21

Step-by-step solution

16 steps

Okay, Christina, let's continue with these problems, applying the associative property of addition.

The associative property of addition states that for any three numbers aa, bb, and cc, the way in which the numbers are grouped does not affect the sum: (a+b)+c=a+(b+c)(a + b) + c = a + (b + c).

Here are the solutions:

Part a· 4 steps

If: a=4a = 4, b=−5b = -5, c=3c = 3

Equation: (a+b)+c=a+(b+c)(a + b) + c = a + (b + c)

  1. Substitute the values into the equation.

    (4+(−5))+3=4+((−5)+3)(4 + (-5)) + 3 = 4 + ((-5) + 3)

  2. Calculate the Left Hand Side (LHS).

    (4−5)+3=(−1)+3=2(4 - 5) + 3 = (-1) + 3 = 2

  3. Calculate the Right Hand Side (RHS).

    4+(−5+3)=4+(−2)=24 + (-5 + 3) = 4 + (-2) = 2

  4. Verify the equality.

    2=22 = 2

    The final value is 2\boxed{2}.

Part b7

If: a=2a = 2, b=9b = 9, c=−4c = -4

Equation: (a+b)+c=a+(b+c)(a + b) + c = a + (b + c)

  1. Substitute the values into the equation.

    (2+9)+(−4)=2+(9+(−4))(2 + 9) + (-4) = 2 + (9 + (-4))

  2. Calculate the LHS.

    (11)+(−4)=11−4=7(11) + (-4) = 11 - 4 = 7

  3. Calculate the RHS.

    2+(9−4)=2+5=72 + (9 - 4) = 2 + 5 = 7

  4. Verify the equality.

    7=77 = 7

    The final value is 7\boxed{7}.

Part c-5

If: a=−8a = -8, b=1b = 1, c=2c = 2

Equation: a+(b+c)=(a+b)+ca + (b + c) = (a + b) + c

  1. Substitute the values into the equation.

    (−8)+(1+2)=((−8)+1)+2(-8) + (1 + 2) = ((-8) + 1) + 2

  2. Calculate the LHS.

    (−8)+(3)=−8+3=−5(-8) + (3) = -8 + 3 = -5

  3. Calculate the RHS.

    (−7)+2=−5(-7) + 2 = -5

  4. Verify the equality.

    −5=−5-5 = -5

    The final value is −5\boxed{-5}.

Part d21

If: a=−2a = -2, b=11b = 11, c=12c = 12

Equation: a+(b+c)=(a+b)+ca + (b + c) = (a + b) + c

  1. Substitute the values into the equation.

    (−2)+(11+12)=((−2)+11)+12(-2) + (11 + 12) = ((-2) + 11) + 12

  2. Calculate the LHS.

    (−2)+(23)=−2+23=21(-2) + (23) = -2 + 23 = 21

  3. Calculate the RHS.

    (9)+12=21(9) + 12 = 21

  4. Verify the equality.

    21=2121 = 21

    The final value is 21\boxed{21}.

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