# Really stupid order of operations question **URL:** \ **Category:** Factual Questions\ **Created:** [January 24, 2011, 6:49pm UTC](https://boards.straightdope.com/t/really-stupid-order-of-operations-question/568821 "2011-01-24T18:49:07Z")\ **Posts on this page:** 7\ **Page:** 3
**Author:** ![Darth\_Panda](https://avatars.discourse-cdn.com/v4/letter/d/ee7513/32.png) [@Darth\_Panda](https://boards.straightdope.com/u/Darth_Panda)\ **Post date:** [January 25, 2011, 7:52pm UTC](https://boards.straightdope.com/t/really-stupid-order-of-operations-question/568821/41 "2011-01-25T19:52:43Z")
Just think of all subtraction as adding a negative number, and then add in any order you like. 1 - 2 + 3 - 5 - 3 + 8 = 1 + (-2) + 3 + (-5) + (-3) + 8 = 8 + 1 + 3 + (-2) + (-5) + (-3) etc. but I’m not sure where the confusing part is honestly 9+7+5-6-2+8-6 -\> 9+7 = 16, 16+5 =21, 21-6=15, 15-2=13, 13+8=21, 21-6=15 now backwards -6+8=2, 2-2=0, 0-6=-6, -6+5=-1, -1+7=6, 6+9=15 adding in multiplication is easy, just multiply first, and then move on: 2+3\*-7-6_2+3+8-6_-7 3\*-7=-21, 6_2= 12, 6_-7=-42 sub in the results to the formula 2±21-12+3+8–42 apply any signs to one another (when you have a subtraction sign in front of a number that is multiplied by another number, you can choose whether to bring the negative sign with you into multiplication question and bring the result back as addition (of a possibly negative number) or do what I do and leave the negative sign behind and bring back the result as subtraction (alos, possibly of a negative number). -\> 2-21-12+3+8+42 now we can add them in some random order, -21+3 = -18 42-12=30 2+8=10 and then, 10+30=40 40-18=22 A really dumb way to do the problem, but you get the right answer. More straightfoward way -\> 2+3\*-7-6_2+3+8-6_-7 = 2+(-21)-(12)+3+8-(-42) 2-21=-19, -19-12=-31, -31+3=-28, -28+8=-20, -20+42=22 ---
**Author:** ![Zsofia](https://avatars.discourse-cdn.com/v4/letter/z/7bcc69/32.png) [@Zsofia](https://boards.straightdope.com/u/Zsofia)\ **Post date:** [January 25, 2011, 8:38pm UTC](https://boards.straightdope.com/t/really-stupid-order-of-operations-question/568821/42 "2011-01-25T20:38:14Z")
> [@UncleRojelio](#): > > My kids were required to get [graphing calculators](http://www.google.com/products/catalog?q=ti+graphing+calculator&oe=utf-8&rls=org.mozilla:en-US:official&client=firefox-a&um=1&ie=UTF-8&cid=4537577764080176352&ei=dyg_Te3fGYbfgQe4ssXiCA&sa=X&oi=product_catalog_result&ct=result&resnum=1&ved=0CDoQ8wIwAA#) for their first middle school algebra classes. They were taught to enter complicated expressions into them in order to check their work. Later, when they took physics in high school, being able to rapidly key stuff into the calculator was a godsend. You might want to look into getting one. Oh, god, back in the day my TI-82 was grafted onto my body like some sort of futuristic shackle. Wonder what happened to that bastard? ---
**Author:** ![panamajack](https://avatars.discourse-cdn.com/v4/letter/p/47e85d/32.png) [@panamajack](https://boards.straightdope.com/u/panamajack)\ **Post date:** [January 25, 2011, 8:39pm UTC](https://boards.straightdope.com/t/really-stupid-order-of-operations-question/568821/43 "2011-01-25T20:39:22Z")
I’ve heard of a method similar to what **Darth Panda** is getting at. If you treat each +/- term as being associated with its operator, then the method would be to group all terms of one kind together. For example: 16 - 8 + 3 Group all the additive terms together and add them, and group and add all the subtractive terms. (And by group, I mean put in parentheses) : (16 + 3) - (8) = 19 - 8 = 11 Or for one with more terms : 5 - 2 + 4 + 1 - 3 (5 + 4 + 1) - ( 2 + 3) = 10 - 5 = 5 You could also do this if you rearrange, and then perform your steps more similar to the mnemonic, i.e. : Rearrange 5 + 4 + 1 - 2 - 3 Do additions: =10 - 2 - 3 Then subtractions: 10 -2 -3 = 8 - 3 = 5 This grouping works even at higher levels, to avoid minus-sign distribution errors. ---
**Author:** ![needscoffee](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/needscoffee/32/1076_2.png) [@needscoffee](https://boards.straightdope.com/u/needscoffee)\ **Post date:** [January 26, 2011, 7:36am UTC](https://boards.straightdope.com/t/really-stupid-order-of-operations-question/568821/44 "2011-01-26T07:36:16Z")
Zsophia, if you have trouble remembering to distribute the minus sign, you could also do (less elegantly): 4x-(2x-3)=0 _Now add (2x-3) to both sides of the equation_ 4x = 2x-3 _Now subtract 2x from each side of the equation_ 2x = -3 x = -3/2 ---
**Author:** ![Zsofia](https://avatars.discourse-cdn.com/v4/letter/z/7bcc69/32.png) [@Zsofia](https://boards.straightdope.com/u/Zsofia)\ **Post date:** [January 26, 2011, 2:32pm UTC](https://boards.straightdope.com/t/really-stupid-order-of-operations-question/568821/45 "2011-01-26T14:32:06Z")
Oh, you know, I bet that’s how they wanted me to do that. ---
**Author:** ![needscoffee](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/needscoffee/32/1076_2.png) [@needscoffee](https://boards.straightdope.com/u/needscoffee)\ **Post date:** [January 28, 2011, 2:18am UTC](https://boards.straightdope.com/t/really-stupid-order-of-operations-question/568821/46 "2011-01-28T02:18:01Z")
Need any help with your homework tonight? ---
**Author:** ![CookingWithGas](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cookingwithgas/32/485_2.png) [@CookingWithGas](https://boards.straightdope.com/u/CookingWithGas)\ **Post date:** [January 28, 2011, 2:37am UTC](https://boards.straightdope.com/t/really-stupid-order-of-operations-question/568821/47 "2011-01-28T02:37:57Z")
My 8th grade algebra teacher said, “My dear Aunt Sally is dead!” (At this point most of us had never heard of “my dear Aunt Sally” and were bit taken aback.) “And she’s buried in a gray box on page 17.” The gray box on a page of our text described order of operations, pointing out that multiplication and division were of equal precedence and should be executed left to right. Same for addition and subtraction. > [@pulykamell](#): > > Here’s [Wikipedia’s take](http://en.wikipedia.org/wiki/Order_of_operations): > > > [@](#): > > > > There is a new mnemonic featured in Danica McKellar’s books Math Doesn’t Suck[2] and Kiss My Math[3] that does address this very issue: “Pandas Eat: Mustard on Dumplings, and Apples with Spice.” After they eat that, they shoot and leave. 😉 [Previous page](https://boards.straightdope.com/t/really-stupid-order-of-operations-question/568821.md?page=2)