# math question (not homework related)
**URL:** https://boards.straightdope.com/t/math-question-not-homework-related/571315
**Category:** Factual Questions
**Created:** [February 14, 2011, 4:19pm UTC](https://boards.straightdope.com/t/math-question-not-homework-related/571315 "2011-02-14T16:19:10Z")
**Posts on this page:** 6
**Page:** 1
### Author:  [@Palo\_Verde](https://boards.straightdope.com/u/Palo_Verde)
#### Post date: [February 14, 2011, 4:19pm UTC](https://boards.straightdope.com/t/math-question-not-homework-related/571315/1 "2011-02-14T16:19:10Z")
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?
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### Author:  [@zut](https://boards.straightdope.com/u/zut)
#### Post date: [February 14, 2011, 4:26pm UTC](https://boards.straightdope.com/t/math-question-not-homework-related/571315/2 "2011-02-14T16:26:19Z")
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%.
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### Author:  [@Palo\_Verde](https://boards.straightdope.com/u/Palo_Verde)
#### Post date: [February 14, 2011, 4:38pm UTC](https://boards.straightdope.com/t/math-question-not-homework-related/571315/3 "2011-02-14T16:38:39Z")
Thank you! I thought that was right, but I just don’t trust my math.
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### Author:  [@septimus](https://boards.straightdope.com/u/septimus)
#### Post date: [February 14, 2011, 4:43pm UTC](https://boards.straightdope.com/t/math-question-not-homework-related/571315/4 "2011-02-14T16:43:36Z")
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. 😃
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### Author:  [@glowacks](https://boards.straightdope.com/u/glowacks)
#### Post date: [February 14, 2011, 4:49pm UTC](https://boards.straightdope.com/t/math-question-not-homework-related/571315/5 "2011-02-14T16:49:43Z")
> [@septimus](#):
>
> 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
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### Author:  [@septimus](https://boards.straightdope.com/u/septimus)
#### Post date: [February 14, 2011, 5:12pm UTC](https://boards.straightdope.com/t/math-question-not-homework-related/571315/6 "2011-02-14T17:12:10Z")
> [@glowacks](#):
>
> 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_.