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Show the associative property for addition holds for integers with specific examples.

Mathematics

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Here's how to show the associative property for addition holds for integers:

Part a· 6 steps

If a=4,b=−5,c=3a=4, b=-5, c=3

The associative property is (a+b)+c=a+(b+c)(a+b)+c = a+(b+c).

Left side: (a+b)+c(a+b)+c

  1. Substitute the values into the expression.

    (4+(−5))+3(4 + (-5)) + 3

  2. Perform the addition inside the parenthesis.

    (−1)+3(-1) + 3

  3. Perform the final addition.

    22

    Right side: a+(b+c)a+(b+c)

  4. Substitute the values into the expression.

    4+((−5)+3)4 + ((-5) + 3)

  5. Perform the addition inside the parenthesis.

    4+(−2)4 + (-2)

  6. Perform the final addition.

    22

    Since 2=22 = 2, the property holds.

Part b· 6 steps

If a=2,b=9,c=−4a=2, b=9, c=-4

The associative property is (a+b)+c=a+(b+c)(a+b)+c = a+(b+c).

Left side: (a+b)+c(a+b)+c

  1. Substitute the values into the expression.

    (2+9)+(−4)(2 + 9) + (-4)

  2. Perform the addition inside the parenthesis.

    11+(−4)11 + (-4)

  3. Perform the final addition.

    77

    Right side: a+(b+c)a+(b+c)

  4. Substitute the values into the expression.

    2+(9+(−4))2 + (9 + (-4))

  5. Perform the addition inside the parenthesis.

    2+52 + 5

  6. Perform the final addition.

    77

    Since 7=77 = 7, the property holds.

Part c· 6 steps

If a=−8,b=1,c=2a=-8, b=1, c=2

The associative property is a+(b+c)=(a+b)+ca+(b+c) = (a+b)+c.

Left side: a+(b+c)a+(b+c)

  1. Substitute the values into the expression.

    (−8)+(1+2)(-8) + (1 + 2)

  2. Perform the addition inside the parenthesis.

    (−8)+3(-8) + 3

  3. Perform the final addition.

    −5-5

    Right side: (a+b)+c(a+b)+c

  4. Substitute the values into the expression.

    ((−8)+1)+2((-8) + 1) + 2

  5. Perform the addition inside the parenthesis.

    (−7)+2(-7) + 2

  6. Perform the final addition.

    −5-5

    Since −5=−5-5 = -5, the property holds.

Part d· 6 steps

If a=−2,b=11,c=12a=-2, b=11, c=12

The associative property is a+(b+c)=(a+b)+ca+(b+c) = (a+b)+c.

Left side: a+(b+c)a+(b+c)

  1. Substitute the values into the expression.

    (−2)+(11+12)(-2) + (11 + 12)

  2. Perform the addition inside the parenthesis.

    (−2)+23(-2) + 23

  3. Perform the final addition.

    2121

    Right side: (a+b)+c(a+b)+c

  4. Substitute the values into the expression.

    ((−2)+11)+12((-2) + 11) + 12

  5. Perform the addition inside the parenthesis.

    9+129 + 12

  6. Perform the final addition.

    2121

    Since 21=2121 = 21, the property holds.

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