# The Division Sign In Story Problems.

**URL:** <https://boards.straightdope.com/t/the-division-sign-in-story-problems/694947>\
**Category:** Factual Questions\
**Created:** [August 6, 2014, 1:53pm UTC](https://boards.straightdope.com/t/the-division-sign-in-story-problems/694947 "2014-08-06T13:53:06Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![Jim\_B](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jim_b/32/4338_2.png) [@Jim\_B](https://boards.straightdope.com/u/Jim_B)\
**Post date:** [August 6, 2014, 1:53pm UTC](https://boards.straightdope.com/t/the-division-sign-in-story-problems/694947/1 "2014-08-06T13:53:06Z")

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When I was in the 7th grade, my teacher, Mrs. D, taught us a neat little trick. When you come across the word “of” in a story problem in math, 9 times out of 10, it means the multiplication sign. Then you can simply rewrite the story problem as a math problem, substituting × for “of” where appropriate.

I love using this simple rule, because I really hated doing story problems. But I have just one question. If “×” equals “of”, what does the division sign (i.e., ÷) always equal?

:):)🙂

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**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\
**Post date:** [August 6, 2014, 1:58pm UTC](https://boards.straightdope.com/t/the-division-sign-in-story-problems/694947/2 "2014-08-06T13:58:32Z")

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It can be “per”, sometimes “in”, sometimes “between” or “among”.

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**Author:** ![bob\_2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bob_2/32/3341_2.png) [@bob\_2](https://boards.straightdope.com/u/bob_2)\
**Post date:** [August 6, 2014, 2:08pm UTC](https://boards.straightdope.com/t/the-division-sign-in-story-problems/694947/3 "2014-08-06T14:08:46Z")

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I assume that you mean like -

“What is half of a quarter?” = ½ x ¼ = ⅛

The nearest I can think is ‘shared’ -

“what is one, shared among four?” = 1 ÷ 4 = ¼

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**Author:** ![sbunny8](https://avatars.discourse-cdn.com/v4/letter/s/c77e96/32.png) [@sbunny8](https://boards.straightdope.com/u/sbunny8)\
**Post date:** [August 6, 2014, 3:08pm UTC](https://boards.straightdope.com/t/the-division-sign-in-story-problems/694947/4 "2014-08-06T15:08:19Z")

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> [@Jim\_B](#):
>
> When I was in the 7th grade, my teacher, Mrs. D, taught us a neat little trick. When you come across the word “of” in a story problem in math, 9 times out of 10, it means the multiplication sign. Then you can simply rewrite the story problem as a math problem, substituting × for “of” where appropriate.
> 
> I love using this simple rule, because I really hated doing story problems. But I have just one question. If “×” equals “of”, what does the division sign (i.e., ÷) always equal?
> 
> :):)🙂

I won’t say _always_, but “out of” usually means division. For example, “4 out of 5 dentists” would mean 4 ÷ 5 , which is 0.8 or 80%. Another word for division is “per”. For example, “20 parts per million” is 20 ÷ 1,000,000 which is 0.00002, and “75 per cent” is 75 ÷ 100 (because “cent”, short for “centum”, is Latin for 100) and 75 ÷ 100 is 0.75 or 3/4.

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**Author:** ![Ethilrist](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ethilrist/32/4604_2.png) [@Ethilrist](https://boards.straightdope.com/u/Ethilrist)\
**Post date:** [August 6, 2014, 3:36pm UTC](https://boards.straightdope.com/t/the-division-sign-in-story-problems/694947/5 "2014-08-06T15:36:55Z")

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> [@Jim\_B](#):
>
> … 9 times \*\*out of \*\*10

That’d be the irony, Bob…