# Fast way to manually calculate percentage increments/decrements

I'm currently studying for the GMAT exam, and I'd like to know if there's a way to manually (and quickly) determine an increment/decrement percent between two numbers.

I know for example, that if I take 5 as my $100%$ reference value and I then compare it against $15$, I find that there was a $200%$ increment with the following formula:

$\text{dPctg}=\frac{15\times100}{5}-100$

However, is there a faster way to get to this fact? Or at least achieve it with less calculations?

Please let me know if there's anything else I may be missing.

Thank you for your time and help!

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If 5 is 100%, then $15=3\times 5$ is $3\times100\%$.Your increase is then $300-200=$... –  Ｊ. Ｍ. Oct 31 '11 at 21:10

Perhaps $\left(\frac{\textrm{new value}}{\textrm{reference value}} - 1\right) \times 100$ is what you need.

Example: $\left(\frac{15}{5}-1\right)\times 100 = (3-1)\times 100 = 200$.

This has the benefit of giving you a fast way to "ballpark" what you're looking for. So if you had, say, 397 as the new value, and 53 as the reference value, then you know that 50 is a little less than 53, so 8*50 is a little less than 8*53. Combine that with the fact that 397 is a little less than 400 = 8*50, and consequently your increase will be a little less than (8-1)*100 = 700.

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Definitely looks easier than my reference formula. Sorry for the late accept. And thanks! –  Jesús Zazueta Aug 27 '13 at 20:36