Welcome to our community

Be a part of something great, join today!

Algebra division formula help

falcios

New member
Jul 31, 2013
3
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

Administrator
Staff member
Feb 24, 2012
13,775
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
Jul 31, 2013
3
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

Administrator
Staff member
Feb 24, 2012
13,775
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

"Read Euler, read Euler." - Laplace
MHB Math Helper
Feb 29, 2012
342
Hello! I'm invading another thread. :eek:

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. :D

Cheers!