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Math Help - I need the right steps to dividing fractions with different denominators

  1. #1
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    I need the right steps to dividing fractions with different denominators

    I need help solving (10/9) divided by 1/2
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  2. #2
    Super Member Quacky's Avatar
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    Quote Originally Posted by nykhris22 View Post
    I need help solving (10/9) divided by 1/2
    There is a neat trick that you can use when dividing fractions: flip the second fraction, and then multiply them together!

    So here, instead of trying to fathom:

    \frac{10}{9}\div\frac{1}{2}

    Flip the second, and multiply:


    \frac{10}{9}\times\frac{2}{1}

    Can you manage from here?

    Essentially, you can think of this as "doing the opposite twice" - you invert the fraction, and then invert the operation, so the result is the same.
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    MHF Contributor Also sprach Zarathustra's Avatar
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    10/9 : 1/2 = 10/9 x 2 = 20/9
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    Quote Originally Posted by nykhris22 View Post
    I need help solving (10/9) divided by 1/2
    Hi nykhris22,

    We don't care so much about denominators when we're dividing or multiplying fractions.

    Remember that dividing is the same as multiplying a number by its multiplicative inverse or reciprocal.

    For instance, 4 \div 2 = 4 \times \frac{1}{2}

    \frac{1}{2} is the multiplicative inverse (reciprocal) of 2.

    To divide two fractions like \frac{2}{3} \div \frac{3}{4}, we just multiply \frac{2}{3} \times \frac{4}{3}=\frac{8}{9}

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  5. #5
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    Quote Originally Posted by nykhris22 View Post
    I need help solving (10/9) divided by 1/2
    \frac{\left(\frac{10}{9}\right)}{\left(\frac{1}{2}  \right)}=\frac{\frac{1}{2}\left(\frac{20}{9}\right  )}{\left(\frac{1}{2}\right)}

    =\frac{0.5\left(\frac{20}{9}\right)}{0.5}=\frac{20  }{9}
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  6. #6
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    Quote Originally Posted by nykhris22 View Post
    I need help solving (10/9) divided by 1/2
    The "stay, change, flip" method works well, but it helps if you realise that "divided by" means "how many" or "how much".

    So it's asking "How many halves in 10/9".

    Well, 10/9 = 1 + 1/9. Since there are two halves in 1, so you know the answer will be slightly more than 2.
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