Algebra rearranging operations help

[falcios]

How does this formula SPI = EV / PV rearrange to this formula EV = SPI * PV
Why does the operation change from multiply to divide?

Thanks for the help.

 

[MarkFL]

We begin with:

$$SPI=\frac{EV}{PV}$$

If we next multiply both sides by $PV$, we get:

$$SPI\cdot PV=\frac{EV}{PV}\cdot PV=EV\cdot\frac{PV}{PV}=EV\cdot1=EV$$

 

[Deveno]

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The answer to your "why" question is this:

Division is the same as multiplying by a reciprocal, that is:

[math]\frac{a}{b} = a*\frac{1}{b}[/math]