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Math Help - cancelling in fractions

  1. #1
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    cancelling in fractions

    I am doing this problem a+3 / a - 5 x 2a - 10 / 3a + 9 the answer given is 2/3 but as there are 3 a's in the numerator line and 4 a's in the denominator line how do these cancell out?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by tanch View Post
    I am doing this problem a+3 / a - 5 x 2a - 10 / 3a + 9 the answer given is 2/3 but as there are 3 a's in the numerator line and 4 a's in the denominator line how do these cancell out?
    ok, you need to be more clear as to what you mean. if you can't use latex, type fractions like this:

    (numerator)/(denominator)

    example, type (2x + 5)/(x + 9) to mean \frac {2x + 5}{x + 9}

    i think you mean \frac {a + 3}{a - 5} \times \frac {2a - 10}{3a + 9} but i am not sure. that is certainly not what you typed, but it is probably what you meant
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  3. #3
    Super Member wingless's Avatar
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    Firstly, please use parantheses when you write a problem.

    I assume you are asking for this:

    \frac{a+3}{a-5}\cdot \frac{2a - 10}{3a + 9}

    Factorize 2a-10 and 3a+9.

    \frac{\not a+\not 3}{\not a-\not 5}\cdot \frac{2 (\not a- \not 5)}{3 ( \not a+\not 3)}

    \frac{2}{3}
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  4. #4
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    Quote Originally Posted by tanch View Post
    I am doing this problem a+3 / a - 5 x 2a - 10 / 3a + 9 the answer given is 2/3 but as there are 3 a's in the numerator line and 4 a's in the denominator line how do these cancell out?
    "Cancel"? What is that? Never do that.

    \frac{a+3}{a-5}*\frac{2a-10}{3a+9} =

    \frac{a+3}{a-5}*\frac{2(a-5)}{3(a+3)} = -- That's right, the Distributive Property of Multiplication over Addition

    \frac{a+3}{a-5}*\frac{2}{3}*\frac{a-5}{a+3} = -- What's that? Multiplication?

    \frac{2}{3}*\frac{a+3}{a-5}*\frac{a-5}{a+3} = -- Now we see the Commutative Property of Multiplication.

    \frac{2}{3}*\frac{a+3}{a+3}*\frac{a-5}{a-5} = -- Same thing, but only in the denominators.

    \frac{2}{3}*1*1 = \frac{2}{3} -- At last, an Identity Definition and Identity Property

    There is no "cancelling" going on in there. "Cancelling" is bad. Properties of mathematics will solve math problems. There is a reason why you studied those properties. I dare you to show me a text book that describes the "Property of Cancelling".

    Special Note: This is good only for a \neq 5 and a \neq -3. You tell me why.
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  5. #5
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    Thank you
    That explanation makes it clear, The answer will not work if a = 5 beacause the term a - 5 = 0 yes?
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  6. #6
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    Will you ever use "Cancel" again?

    Right. Even though it does not appear in the final statement, 2/3, it was in the ORIGINAL problem statement and must be considered. Same for -3.

    Good work.
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  7. #7
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    No more cancelling! I think my problem was looking for shortcuts, but short cuts make long delays! thanks again
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