What is the correct way to calculate percent increase in math problems?

[TSN79]

Can someone explain to me the following:
If a number increases from 108,7 to 113,7 how much in percent has it increased?

First I tried to do 108,7 / 113,7 = 0,956.
1 - 0,956 = 0,0439. In other words, an increase of 4,39%. This turns out to be wrong. 113,7 / 108,7 = 1,0459 -> an increase of 4,59% is correct, but I fail to see the logic in that the last approach is correct. What am I actually calculating in my first try?

 

[Karlsen]

In your first try you're finding that 108.7 is 0.956*100 = 95.6% out of 113.7.

Look at the increase from 108.7 to 113.7, it's a increase by 5 units. (113.7-108.7). Now, if we want to find how many % 5 is out of 108.7, we do (5/108.7)*100 = 4.59%. So, in general:
If a number increases from a to b, how many percent did it increase?
Answer:
[(b-a)/a]*100%

 

[TSN79]

Aha, thanks a lot Karlsen!

 

[Karlsen]

Always nice to help a fellow citizen.