# HELP: Finding the Percent Change

#### lillybeth

##### Junior Member
Hello everybody!!! I need help with understanding how to find percent change.

My book gives this formula: (amount of change/original amount) * 100%

For a problem that looks like this: 80 to 100, I usually just do 20/80, which is equal to 25% (which my book's answer key tells me I am correct)

Soooo.

For a problem that reads 200 to 100, would you do 100/200, or -100/200??

And one more thing:

The formula our book tells us to use says to multiply the amount of change divided by the original amount by 100% (1.00).

What is the point of multiplying by one??

Thank you guys!!!
All help will be greatly appreciated!!!

Last edited:

#### pka

##### Elite Member
Hello everybody!!! I need help with understanding how to find percent change.
My book gives this formula: (amount of change/original amount) * 100%

For a problem that looks like this: 80 to 100, I usually just do 20/80, which is equal to 25% (which my book's answer key tells me I am correct)

For a problem that reads 200 to 100, would you do 100/200, or -100/200??
It is $$\displaystyle \dfrac{100-200}{200}=-\dfrac{100}{200}=-50\%$$.

It is always $$\displaystyle \dfrac{\text{new price}-\text{old price}}{\text{old price}}$$.

#### Ishuda

##### Elite Member
Percent means 'amount of parts out of 100 parts'. To use your example the change for 80 to 100 fractional change would be $$\displaystyle \frac{100-80}{80} = 0.25$$. So for every one part you had, it would change by 0.25 parts. If you had a hundred parts, it would change by 100*0.25=25 parts which is 25 parts per hundred or 25%.

Thus compute the fractional change, see pka's post, then multiple by 100 to get the percent change. That is what is meant in your equation of "multiply by 100%"

#### lillybeth

##### Junior Member
It is $$\displaystyle \dfrac{100-200}{200}=-\dfrac{100}{200}=-50\%$$.

It is always $$\displaystyle \dfrac{\text{new price}-\text{old price}}{\text{old price}}$$.

Thanks!!! But what about my second question??

#### Subhotosh Khan

##### Super Moderator
Staff member
Thanks!!! But what about my second question??
We multiply by 100% - so that we can have the answer as "%" as opposed to a fraction or a decimal number (without %).

#### lillybeth

##### Junior Member
We multiply by 100% - so that we can have the answer as "%" as opposed to a fraction or a decimal number (without %).
Ok thx!!!!! I was just curious because there seemed no point really to multiply by one.

Thank you soo much!!!