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Math Help - subtraction

  1. #1
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    subtraction

    Is there an associative property of subtraction? In other words, is

    A- (B-C)=(A-B)-C

    true for all real numbers A, B, C? Explain your answer. If the equation is always true, explain why; if the equation is not always true, find another expression that is equal to the expression

    A- (B-C)

    and explain why the two expressions are equal.
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  2. #2
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    Quote Originally Posted by recca View Post
    Is there an associative property of subtraction? In other words, is

    A- (B-C)=(A-B)-C

    true for all real numbers A, B, C? Explain your answer. If the equation is always true, explain why; if the equation is not always true, find another expression that is equal to the expression

    A- (B-C)

    and explain why the two expressions are equal.
    I don't think that's possible....not for all real numbers. There is a A+(B+C)=(A+B)+C.....but you are talking about subtraction....

    example:
    A=4
    B=5
    C=6

    A-(B-C)=(A-B)-C
    4-(5-6)=(4-5)-6
    4-(-1)=(-1)-6
    5=-7

    doesn't work obviously.
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  3. #3
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    Quote Originally Posted by recca View Post
    Is there an associative property of subtraction? In other words, is

    A- (B-C)=(A-B)-C

    true for all real numbers A, B, C? Explain your answer. If the equation is always true, explain why; if the equation is not always true, find another expression that is equal to the expression

    A- (B-C)

    and explain why the two expressions are equal.
    Hi, recca. blair_alane is right; his or her counterexample proves the identity false.

    To find an expression that actually is equivalent, I offer a hint: Subtracting a quantity from another number is really the same as adding (-1) times that quantity. Rewrite your expression, and use the distributive property of multiplication over addition (i.e., a(b + c) = ab + ac) to simplify.
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  4. #4
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    Thank you,
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  5. #5
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    Quote Originally Posted by Reckoner View Post
    Hi, recca. blair_alane is right; his or her counterexample proves the identity false.
    I'm a she! but thank you!
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