# Thread: How to move a fraction to the bottom of a fraction

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

Say I have:

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

How can I make it look like:

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

I'm trying to figure out the algebraic rule(s) for this

2. ## Re: How to move a fraction to the bottom of a fraction

Hello, daigo!

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

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

. . . $\displaystyle \dfrac{x\cdot\frac{1}{z}}{y} \cdot \frac{z}{z} \;=\;\frac{x\cdot\frac{1}{z}\cdot z}{y\cdot z} \;=\;\frac{x}{yz}$

3. ## Re: How to move a fraction to the bottom of a fraction

Originally Posted by daigo
Say I have:

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

How can I make it look like:

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

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