# Algebra division formula help

#### falcios

##### New member
If you rearrange this formula from SPI=EV/PV to EV=SPI*PV. Why is this formula like this: CPI=EV/AC is AC=EV/CPI
Aren't they basically the same.

Thanks for the help.

#### MarkFL

Staff member
We begin with:

$$\displaystyle CPI=\frac{EV}{AC}$$

Now, multiply both sides by $$\displaystyle \frac{AC}{CPI}$$:

$$\displaystyle CPI\cdot\frac{AC}{CPI}=\frac{EV}{AC}\cdot\frac{AC}{CPI}$$

$$\displaystyle AC\cdot\frac{CPI}{CPI}=\frac{EV}{CPI}\cdot\frac{AC}{AC}$$

$$\displaystyle AC\cdot1=\frac{EV}{CPI}\cdot1$$

$$\displaystyle AC=\frac{EV}{CPI}$$

#### falcios

##### New member
I'm still lost aren't the two formulas basically the same why is there 2 different solutions?

Is there a simpler way to calculate for someone who is relearning the basics.

Thanks.

#### MarkFL

Staff member
also $SPI=EV/PV$ to $EV=SPI*PV$

it should be $SPI=EV/PV$ to $EV=SPI/PV$ you divide both sides by $PV$ to isolate $EV$
You want to multiply both sides by $PV$ to isolate $EV$.

#### Fantini

MHB Math Helper

Falcios, you are right. They are mathematically equivalent, as both Mark and Karush have shown you. However, what I think is really the issue here is: why bother with the equivalent versions?

The answer is that each version helps you calculate one quantity in terms of the others. When you write

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

you can find the value of SPI in terms of EV and PV. If, for some reason, you are given SPI and PV, you can find the value of EV in terms of these. Likewise, you can find the value of PV in terms of SPI and EV by doing the calculation

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

In other words, there are not 2 "solutions", but two ways of interpreting results in light of what data you might have.

Hope this has helped.

Cheers!