How to move a fraction to the bottom of a fraction

[daigo]

Say I have:

[tex]\frac{x \cdot \frac{1}{z}}{y}[/tex]

How can I make it look like:

[tex]\frac{x}{y \cdot \frac{1}{z}}[/tex]

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

 

[HallsofIvy]

Say I have:

[tex]\frac{x \cdot \frac{1}{z}}{y}[/tex]

How can I make it look like:

[tex]\frac{x}{y \cdot \frac{1}{z}}[/tex]

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

Well, you can't make it look exactly like that- they are not the same values, as you can see by putting in some values: if x, y, and z are all equal to 2, for example, the first fraction would have value [tex]\frac{2\frac{1}{2}}{2}= \frac{1}{2}[/tex] while the second would be [tex]\frac{2}{2\frac{1}{2}}= 2[/tex].

What you can say is that multiplying in the numerator of a fraction is the same as multiplying the entire fraction:
[tex]\frac{x\frac{1}{z}}{y}= \frac{x}{y}\frac{1}{z}= \frac{x}{yz}[/tex]