# What is the answer to this maths question? **URL:** \ **Category:** Miscellaneous and Personal Stuff I Must Share\ **Created:** [July 27, 2016, 11:00am UTC](https://boards.straightdope.com/t/what-is-the-answer-to-this-maths-question/761017 "2016-07-27T11:00:50Z")\ **Posts on this page:** 8\ **Page:** 1
**Author:** ![Atomic\_Alex](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/atomic_alex/32/175_2.png) [@Atomic\_Alex](https://boards.straightdope.com/u/Atomic_Alex)\ **Post date:** [July 27, 2016, 11:00am UTC](https://boards.straightdope.com/t/what-is-the-answer-to-this-maths-question/761017/1 "2016-07-27T11:00:50Z")
There was something of a heated debate about the correct answer to this question at work yesterday and the ‘correct’ answer isn’t what I thought it would be. 9 - 3 ÷ 1/3 + 1 = ? I thought it was 19, apparently the correct answer is 1, but it seems to me that answer is achieved by adding parenthesis and changing the order of operations, not what is actually written and asked which seems perfectly straightforward I’m somewhat confused, as I thought maths was supposed to be unambiguous, not like the written word. ---
**Author:** ![yellowjacketcoder](https://avatars.discourse-cdn.com/v4/letter/y/4bbf92/32.png) [@yellowjacketcoder](https://boards.straightdope.com/u/yellowjacketcoder)\ **Post date:** [July 27, 2016, 12:29pm UTC](https://boards.straightdope.com/t/what-is-the-answer-to-this-maths-question/761017/2 "2016-07-27T12:29:41Z")
The acronym to remember (which I had drilled into me in 7th grade - thanks Mrs. Mac) is PEMDAS Parenthesis - do whatever is in parenthesis first Exponentiation - handle exponents next Multiplication/Division - these are handled with the same precedence as they’re just inverses of each other, right to left Addition/Subtraction - against, same precedence as they are essentially the same operation, right to left. There are no parenthesis or exponents, so handle multiplication/division first 9 - 3 ÷ 1/3 + 1 = 9 - 9 + 1 (division) 9 - 9 + 1 = 0 + 1 (substraction, left first) 0 + 1 = 1 (only one left) The thing that confuses most people is that dividing by a fraction is the same as multiplying by it’s inverse. So three divided by one third equals nine. EDIT: it doesn’t seem you made that mistake. Your mistake was in doing all operations right to left with the same precedence, instead of doing the division first and the addition/subtraction next. ---
**Author:** ![Bill\_Door](https://avatars.discourse-cdn.com/v4/letter/b/50afbb/32.png) [@Bill\_Door](https://boards.straightdope.com/u/Bill_Door)\ **Post date:** [July 27, 2016, 12:32pm UTC](https://boards.straightdope.com/t/what-is-the-answer-to-this-maths-question/761017/3 "2016-07-27T12:32:10Z")
The order of operations is PEMDAS, which stands for parenthesis, exponents, multiply, divide, add, subtract. So in the expression 9 - 3 ÷ 1/3 + 1 = ? you first divide 3 by 1/3 getting 9, subtract that from 9 getting zero, and add in the 1 ending up with 1. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [July 27, 2016, 12:38pm UTC](https://boards.straightdope.com/t/what-is-the-answer-to-this-maths-question/761017/4 "2016-07-27T12:38:51Z")
We just had a thread on that [here](http://boards.straightdope.com/sdmb/showthread.php?t=792862). Basically, it boils down to whether you interpret the “1/3” as a single unit mean “one third” or just one divided by three. In other words, whether you interpret 9 - 3 ÷ 1/3 + 1 = as 9 - 3 / (1/3) + 1 = 1 or 9 - 3 / 1 / 3 + 1 = 9 Given that a “÷” sign is used, my interpretation is that that sign means division and “/” is being used to show a fraction. Also, given the spacing, where everywhere else there is a space before and after the operand, except the “/”. ETA: And, yeah, 19 is just right out. You’re just doing it left to right with no regard for order of operations, which is not how it’s conventionally done. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [July 27, 2016, 12:47pm UTC](https://boards.straightdope.com/t/what-is-the-answer-to-this-maths-question/761017/5 "2016-07-27T12:47:23Z")
There is no standard order of operations. PEDMAS is commonly used, but not universally. Unless operator precedence is specified any such expression is ambiguous. In the age of computers even the operators aren’t standard in their meaning. It’s common practice now in programming to use as many parentheses as necessary to make the order of evaluation clear. ---
**Author:** ![amanset](https://avatars.discourse-cdn.com/v4/letter/a/8dc957/32.png) [@amanset](https://boards.straightdope.com/u/amanset)\ **Post date:** [July 27, 2016, 1:37pm UTC](https://boards.straightdope.com/t/what-is-the-answer-to-this-maths-question/761017/6 "2016-07-27T13:37:25Z")
IN the UK this was taught as BODMAS Brackets Order Divide Multiply Add Subtract So, yes, using that the answer is clearly 1. You get used to this when writing computer programs, although I tend to add brackets everywhere for clarity. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [July 27, 2016, 2:54pm UTC](https://boards.straightdope.com/t/what-is-the-answer-to-this-maths-question/761017/7 "2016-07-27T14:54:18Z")
[We’ve done this exact question before](http://boards.straightdope.com/sdmb/showthread.php?t=792862), except with a link to a YouTube video that clarifies the notation somewhat. On preview: oops—ninja’d by **pulykamell**. ---
**Author:** ![absurdistan1](https://avatars.discourse-cdn.com/v4/letter/a/278dde/32.png) [@absurdistan1](https://boards.straightdope.com/u/absurdistan1)\ **Post date:** [August 4, 2016, 1:36am UTC](https://boards.straightdope.com/t/what-is-the-answer-to-this-maths-question/761017/8 "2016-08-04T01:36:23Z")
yup got 1, even in a rather inebriated state. 3 divided by 1/3 is 9. There are other notations too, like prefix and postfix. The conventional way, with the operator between the numbers, is i think called infix…