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Math Help - Dividing fractions

  1. #1
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    Dividing fractions

    when I divide two fractions example

    [1/2] / [3/5] I know that I have to invert and then multiply

    [1/2]*[5/3] so my answer will be 5/6
    My question is why do I invert then multiply inorder to get the correct answer, Why cannot I just say that it is 3/10, why do we need to invert and multiply, why is this the rule that we must invert then multiply?
    Last edited by schinb64; December 2nd 2007 at 02:45 PM. Reason: Clearify question
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by schinb64 View Post
    when I divide two fractions example

    [1/2] / [3/5] I know that I have to invert and then multiply

    [1/2]*[5/3] so my answer will be 5/6 My question is why do I invert then multiply inorder to get the correct answer?
    Lets take the following equation as an example. I'm not entirely sure how to explain using words.

    \frac{4}{1} \div \frac{2}{1} = \frac{4}{2} = \frac{2}{1} I'm sure you understand that.

    \frac{4}{1} \times \frac{1}{2} = \frac{4}{2} = \frac{2}{1}

    Does this make sense? I'm not too good a teacher.
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by schinb64 View Post
    when I divide two fractions example

    [1/2] / [3/5] I know that I have to invert and then multiply

    [1/2]*[5/3] so my answer will be 5/6 My question is why do I invert then multiply inorder to get the correct answer?
    \frac{ \frac{1}{2} }{ \frac{3}{5} }

    We want to clear out the fractions in the numerator and denominator, so we need to multiply top and bottom by the LCM of 2 and 5, which is 10:
    = \frac{ \frac{1}{2} }{ \frac{3}{5} } \cdot \frac{2 \cdot 5}{2 \cdot 5}

    = \frac{ \frac{1}{2} \cdot 2 \cdot 5 }{ \frac{3}{5} \cdot 2 \cdot 5 }

    = \frac{1 \cdot 5}{3 \cdot 2} = \frac{1}{2} \times \frac{5}{3}

    This is, by far, the harder method to do the problem with, but it is the way to prove that the shortcut you learned is correct.

    -Dan
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  4. #4
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    Quote Originally Posted by schinb64 View Post
    when I divide two fractions example

    [1/2] / [3/5] I know that I have to invert and then multiply

    [1/2]*[5/3] so my answer will be 5/6
    My question is why do I invert then multiply inorder to get the correct answer, Why cannot I just say that it is 3/10, why do we need to invert and multiply, why is this the rule that we must invert then multiply?
    Quote Originally Posted by topsquark View Post
    \frac{ \frac{1}{2} }{ \frac{3}{5} }

    We want to clear out the fractions in the numerator and denominator, so we need to multiply top and bottom by the LCM of 2 and 5, which is 10:
    = \frac{ \frac{1}{2} }{ \frac{3}{5} } \cdot \frac{2 \cdot 5}{2 \cdot 5}

    = \frac{ \frac{1}{2} \cdot 2 \cdot 5 }{ \frac{3}{5} \cdot 2 \cdot 5 }

    = \frac{1 \cdot 5}{3 \cdot 2} = \frac{1}{2} \times \frac{5}{3}

    This is, by far, the harder method to do the problem with, but it is the way to prove that the shortcut you learned is correct.

    -Dan
    You guys are good because when I was in 6th and asked why questions my teacher said," don't ever ask why in math. Some old guy said so that's why." In the future my teachers said they didn't know why. I just accepted that it was a rule some old guy that made up the rules and we follow them.
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Itachi888Uchiha View Post
    You guys are good because when I was in 6th and asked why questions my teacher said," don't ever ask why in math. Some old guy said so that's why." In the future my teachers said they didn't know why. I just accepted that it was a rule some old guy that made up the rules and we follow them.
    haha, interesting. well, the rule is, dividing by a fraction is the same as multiplying by its inverse, and this is not just because some old guy said so. it makes sense when you think about it. dividing something by two is the same as making two halves of it. so dividing by 2 is the same as multiplying by 1/2. etc
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Itachi888Uchiha View Post
    You guys are good because when I was in 6th and asked why questions my teacher said," don't ever ask why in math. Some old guy said so that's why." In the future my teachers said they didn't know why. I just accepted that it was a rule some old guy that made up the rules and we follow them.
    Always ask "why?" It's the way you learn this stuff, as opposed to merely being able to do it.

    -Dan
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