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Math Help - How to move a fraction to the bottom of a fraction

  1. #1
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    How to move a fraction to the bottom of a fraction

    Say I have:

    \frac{x \cdot \frac{1}{z}}{y}

    How can I make it look like:

    \frac{x}{y \cdot \frac{1}{z}}

    I'm trying to figure out the algebraic rule(s) for this
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  2. #2
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    Re: How to move a fraction to the bottom of a fraction

    Hello, daigo!

    \text{Say I have: }\:\frac{x \cdot \frac{1}{z}}{y}

    \text{How can I make it look like: }\:\frac{x}{y \cdot \frac{1}{z}} . You can't

    It looks like you're making up your own rules:
    . . "Just pick it up and move it down."


    You can multiply the fraction by \frac{z}{z}\!:

    . . . \dfrac{x\cdot\frac{1}{z}}{y} \cdot \frac{z}{z} \;=\;\frac{x\cdot\frac{1}{z}\cdot z}{y\cdot z} \;=\;\frac{x}{yz}
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  3. #3
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    Re: How to move a fraction to the bottom of a fraction

    Quote Originally Posted by daigo View Post
    Say I have:

    \frac{x \cdot \dfrac{1}{z}}{y}

    How can I make it look like:

    \frac{x}{y \cdot \frac{1}{z}}
    The short answer is: you cannot, because they are not equal.

    \frac{x \cdot \dfrac{1}{z}}{y}=\frac{x}{y\cdot z}
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