# Thread: subtraction

1. ## 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.

2. Originally Posted by recca
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.

3. Originally Posted by recca
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.

4. Thank you,

5. Originally Posted by Reckoner
Hi, recca. blair_alane is right; his or her counterexample proves the identity false.
I'm a she! but thank you!