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Math Help - A simple simplification problem

  1. #1
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    A simple simplification problem

    I thought I know this one but the answer stumps me:

    (3a - 3b) / (6a - 6b)

    Answer key: 1/2

    After cancelling out the "a" and "b", I would think I have (3 - 3) in the numerator and (6 - 6) in the denominator and the answer would be 0. How did the answer turns out to 1/2.

    I think I'm missing some concept here. Pls help. Thanks.
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  2. #2
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    Quote Originally Posted by shenton View Post
    I thought I know this one but the answer stumps me:

    (3a - 3b) / (6a - 6b)

    Answer key: 1/2

    After cancelling out the "a" and "b", I would think I have (3 - 3) in the numerator and (6 - 6) in the denominator and the answer would be 0. How did the answer turns out to 1/2.

    I think I'm missing some concept here. Pls help. Thanks.

    (3*a - 3*b)/(6*a - 6*b) = 1/2

    Indeed, your answer key is correct.

    I can see why you think it is 0. You are thinking the problem is:

    (3*a)/(6*b) - (3*a)/(6*b) = 0.

    However, this problem is:

    (3*a)/(6*a - 6*b) - (3*b)/(6*a - 6*b)

    Do you see they each have a common denominator. Now you can cancel to get:

    (3*a)/(6*a - 6*b) = a/[2(a - b)] and:

    (3*b)/(6*a - 6*b) = b/[2(a - b)]

    Thus, a/[2(a - b)] - b/[2(a - b)] = (a - b)/[2(a - b)]

    Cancel the (a - b) from the numerator and denominator. Note that there is a "1 times (a - b)" at the top; thus, you are left with 1/2.

    Do you see why it isn't 0?
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  3. #3
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    Thanks for the detailed explanation.

    Things certainly does not look as simple as it seems.
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  4. #4
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    Quote Originally Posted by shenton View Post
    I thought I know this one but the answer stumps me:

    (3a - 3b) / (6a - 6b)

    Answer key: 1/2

    After cancelling out the "a" and "b", I would think I have (3 - 3) in the numerator and (6 - 6) in the denominator and the answer would be 0. How did the answer turns out to 1/2.

    I think I'm missing some concept here. Pls help. Thanks.
    A simpler explanation is this (but it involves factoring):
    \frac{3a - 3b}{6a - 6b} = \frac{3(a-b)}{6(a-b)} = \frac{3}{6} = \frac{1}{2} (Requires b \neq a!)

    -Dan
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  5. #5
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    Why can't we have a = b? We can use that guys new nullity number and divide by 0!
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by AfterShock View Post
    Why can't we have a = b? We can use that guys new nullity number and divide by 0!
    (groans in great agony)

    -Dan
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