I’m writing a letter to the editor about the crime rate going down and it requires math that I can’t remember how to do. If the crime rate was 1207 (per 100,000) and is now 757, how much of a reduction is that?
The crime rate was 1207 (per 100,000). It is now 757 (per 100,000). That’s a reduction of 450 (per 100,000).
As a percentage, the crime rate is now only (757/1207) = 62.72% of what it once was–in other words, the crime rate has been reduced by (450/1207) = 37.28%.
Thank you! I thought that was right, but I just don’t trust my math.
Simple arithmetic like Zut’s gets the answer here, but in other problems you may need to watch out for reciprocation.
I recall the Asian financial crisis. When baht-per-dollar rose from 26 to 39, both the English-language papers in Bangkok stated repeatedly that “the baht [had] fallen 50%” or even “[had] lost half its value.” The baht-per-dollar ratio then went all the way to 52, but newspapers did not follow through and speak of a 100% fall, or loss of all value. 
On a similar note, it needs to be remembered that a 50% increase followed by a 50% decrease, or such a decrease followed by such an increase, will not yield the same amount as before either change. In both cases you’ll get 75% of the original, or a 25% overall decrease, because the 50% increase is in relation to a smaller value than the 50% decrease.
100 -> 150 -> 75 or 100 -> 50 -> 75
Good point. When someone says “Playing the stock market for two years, my portfolio gained 20% during each of 13 months and lost 20% during each of 11 months,” commiserations are in order, not congratulations.