How to move a fraction to the bottom of a fraction

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July 14th 2012, 01:53 PM
daigo

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
July 14th 2012, 02:17 PM
Soroban

Re: How to move a fraction to the bottom of a fraction

Hello, daigo!

Quote:

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

$\text{How can I make it look like: }\:\frac{x}{y \cdot \frac{1}{z}}$ . 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 $\frac{z}{z}\!:$

. . . $\dfrac{x\cdot\frac{1}{z}}{y} \cdot \frac{z}{z} \;=\;\frac{x\cdot\frac{1}{z}\cdot z}{y\cdot z} \;=\;\frac{x}{yz}$
July 14th 2012, 02:19 PM
Plato

Re: How to move a fraction to the bottom of a fraction

Quote:

Originally Posted by daigo

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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