MHB Algebra rearranging operations help

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The formula SPI = EV / PV can be rearranged to EV = SPI * PV by multiplying both sides by PV. This operation effectively eliminates PV from the denominator, simplifying the equation. The change from division to multiplication occurs because division is equivalent to multiplying by the reciprocal. Thus, the transformation maintains the equality of the equation. Understanding this concept is essential for mastering algebraic rearrangements.
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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.
 
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We begin with:

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

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

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