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Fill in the blanks using the commutative and additive identity properties. a) (-27) + (-52) = (-52) + b) (-27) + = (-27)

Mathematics

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2 steps
  1. Solve part a) using the commutative property of addition.

    The commutative property of addition states that for any two integers aa and bb, a+b=b+aa + b = b + a.
    Given the equation:

    (−27)+(−52)=(−52)+‾(-27) + (-52) = (-52) + \underline{\hspace{1cm}}

    Comparing this to a+b=b+aa + b = b + a, where a=−27a = -27 and b=−52b = -52, the blank must be aa.

    (−27)+(−52)=(−52)+(−27)(-27) + (-52) = (-52) + (-27)

    So, the blank is −27\boxed{-27}.

  2. Solve part b) using the additive identity property.

    The additive identity property states that for any integer aa, a+0=aa + 0 = a.
    Given the equation:

    (−27)+‾=(−27)(-27) + \underline{\hspace{1cm}} = (-27)

    Comparing this to a+0=aa + 0 = a, where a=−27a = -27, the blank must be 0.

    (−27)+0=(−27)(-27) + 0 = (-27)

    So, the blank is 0\boxed{0}.

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