# Math homework - sanity check **URL:** \ **Category:** Factual Questions\ **Created:** [October 30, 2020, 12:41pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310 "2020-10-30T12:41:23Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![iamthewalrus\_3](https://avatars.discourse-cdn.com/v4/letter/i/258eb7/32.png) [@iamthewalrus\_3](https://boards.straightdope.com/u/iamthewalrus_3)\ **Post date:** [October 30, 2020, 9:10pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/41 "2020-10-30T21:10:11Z")
> [@Hari\_Seldon](#): > > Let me just say that any mathematician who wrote that expression without parens would be disbarred. Yes, I know there is a standard order for applying operations, but we don’t count on it being done correctly. Good. As a software developer, I regularly get feedback about adding extraneous parentheses, and I think those people are crazy. Like I want to remember whether bitwise operations bind tighter than dereferencing in whatever language this is. Parentheses are always clear! ---
**Author:** ![Babale](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/babale/32/15666_2.png) [@Babale](https://boards.straightdope.com/u/Babale)\ **Post date:** [October 30, 2020, 9:18pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/42 "2020-10-30T21:18:24Z")
> [@Summerday](#): > > After you completed the second step, I don’t think that the parentheses should’ve been moved to include the 16. > > Once you subtract 2 from 3.5, those parentheses are “eliminated” and we’re left with, 8 + 16 ÷ 1.5. Then we go left to right and the answer is 16. Multiplication and division always come before addition and subtraction. The parentheses are there to show you this, but even without them, you divide before you add ---
**Author:** ![glowacks](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/glowacks/32/5548_2.png) [@glowacks](https://boards.straightdope.com/u/glowacks)\ **Post date:** [October 30, 2020, 9:30pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/43 "2020-10-30T21:30:17Z")
I personally have no idea why the division sign is still in usage at all, given that it’s not easy to type on a standard keyboard, and a slash is far more clear as to what exactly it means. I’ll also note that I was very good at math all the way through elementary school such that I placed 3 years ahead of my nominal grade level entering middle school, and was going to a school that was able to accommodate that because the high school was effectively intermingled with the middle school. Somehow though, I thought that a minus sign implied parentheses around the entire rest of the expression. Presumably it was because I never was given any problems before where more than one term followed a minus sign, and when I initially encountered them at my new school, that sort of thing had already been talked about in lower level classes so it wasn’t talked about at all in my class I was taking then. I was thus able to intuit basically the entire curriculum of those courses OTHER than what to do if multiple terms followed a minus sign. The lesson? Teaching order of operations is hard. Even smart kids that can figure out most of math without lessons in it don’t understand the rules if you don’t teach them correctly. ---
**Author:** ![glowacks](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/glowacks/32/5548_2.png) [@glowacks](https://boards.straightdope.com/u/glowacks)\ **Post date:** [October 30, 2020, 9:38pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/44 "2020-10-30T21:38:27Z")
> [@glowacks](#): > > I personally have no idea why the division sign is still in usage at all, given that it’s not easy to type on a standard keyboard, and a slash is far more clear as to what exactly it means. Ok, maybe it’s not as clear as I hoped, because Excel thinks that 2/3\*4 = 8/3, while most people would interpret that as 1/6, but I suppose what I meant to say is that using a slash makes it much more likely you will use parentheses to show what’s on each side of the slash. Or maybe I’m just horribly mistaken about this. Still, why would anyone use an obelus that’s much harder to type? ---
**Author:** ![Babale](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/babale/32/15666_2.png) [@Babale](https://boards.straightdope.com/u/Babale)\ **Post date:** [October 30, 2020, 9:43pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/45 "2020-10-30T21:43:13Z")
2/3\*4 doesn’t imply 1/6. 2/(3\*4) would be 1/6. So would 2÷(3×4) 2/3\* 4 is the same as 2÷3 \*4, and 8/6 is correct. 2/3\*4 doesn’t imply that the 2 is in the numerator over everything following it and I don’t know anyone who would interpret it as such. 2/3\*4 is not equivalent to _ **2** _\_ 3\*4 Which clearly doesn’t translate well to a messageboard. ---
**Author:** ![Summerday](https://avatars.discourse-cdn.com/v4/letter/s/22d042/32.png) [@Summerday](https://boards.straightdope.com/u/Summerday)\ **Post date:** [October 30, 2020, 9:52pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/46 "2020-10-30T21:52:06Z")
> [@Babale](#): > > > [@Summerday](#): > > > > After you completed the second step, I don’t think that the parentheses should’ve been moved to include the 16. > > > > > Once you subtract 2 from 3.5, those parentheses are “eliminated” and we’re left with, 8 + 16 ÷ 1.5. Then we go left to right and the answer is 16. > > Multiplication and division always come before addition and subtraction. The parentheses are there to show you this, but even without them, you divide before you add I guess I’ll take your word for it…but I take solace in the fact that 16 was most likely the correct answer on the quiz and 18 2/3 wasn’t even listed as an option. 🙂 ---
**Author:** ![glowacks](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/glowacks/32/5548_2.png) [@glowacks](https://boards.straightdope.com/u/glowacks)\ **Post date:** [October 30, 2020, 10:37pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/47 "2020-10-30T22:37:05Z")
> [@Babale](#): > > 2/3\*4 doesn’t imply that the 2 is in the numerator over everything following it and I don’t know anyone who would interpret it as such. Ok, what does 2/3a mean? (2/3)a or 2/(3a)? If the latter, why should 2/3\*4 be different, when the \* is simply implied by juxtaposition? Even if you say the former, I hope you’ll agree that it’s less clear cut. Or at least trust that this person who did a lot of mathematics would never even consider the former what was meant. Not to say that other people who have done lots of mathematics would say the exact same thing, but I’m not coming to this from a position of ignorance. Yes, it really annoys me how Excel interprets this, but at least it means one learns to ALWAYS use parentheses. ---
**Author:** ![Babale](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/babale/32/15666_2.png) [@Babale](https://boards.straightdope.com/u/Babale)\ **Post date:** [October 30, 2020, 10:44pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/48 "2020-10-30T22:44:24Z")
> [@glowacks](#): > > Ok, what does 2/3a mean? (2/3)a or 2/(3a)? If the latter, why should 2/3\*4 be different, when the \* is simply implied by juxtaposition? Even if you say the former, I hope you’ll agree that it’s less clear cut. Or at least trust that this person who did a lot of mathematics would never even consider the former what was meant. Not to say that other people who have done lots of mathematics would say the exact same thing, but I’m not coming to this from a position of ignorance. 2/3a I would read as ‘2, divided by 3a’. 3a is a term in and of itself. 2/3×a [2, divided by 3, times a] is a different expression than 2/3a. 3a is equivalent to (3a). I suppose this is another example of the limits of the PEMDAS mnemonic as pointed out by @LSLGuy ---
**Author:** ![glowacks](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/glowacks/32/5548_2.png) [@glowacks](https://boards.straightdope.com/u/glowacks)\ **Post date:** [October 30, 2020, 10:46pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/49 "2020-10-30T22:46:54Z")
> [@Babale](#): > > I suppose this is another example of the limits of the PEMDAS mnemonic as pointed out by @LSLGuy Yeah, I don’t mean to say “I’m right and you’re wrong”; I’m showing there are clear problems with expectations among different people who are both educated about the supposed rules. Which is why, again, ALWAYS use parentheses. ---
**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:** [October 30, 2020, 10:48pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/50 "2020-10-30T22:48:02Z")
> [@glowacks](#): > > Ok, what does 2/3a mean? (2/3)a or 2/(3a)? If the latter, why should 2/3\*4 be different, when the \* is simply implied by juxtaposition? Even if you say the former, I hope you’ll agree that it’s less clear cut. Or at least trust that this person who did a lot of mathematics would never even consider the former what was meant. A person who “would never even consider the former what was meant” is likely to run into trouble sooner or later. If you put Y=2/3X into a TI graphing calculator, for example, it will interpret it as Y=(2/3)\*X. ---
**Author:** ![glowacks](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/glowacks/32/5548_2.png) [@glowacks](https://boards.straightdope.com/u/glowacks)\ **Post date:** [October 30, 2020, 10:54pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/51 "2020-10-30T22:54:00Z")
> [@Thudlow\_Boink](#): > > A person who “would never even consider the former what was meant” is likely to run into trouble sooner or later. If you put Y=2/3X into a TI graphing calculator, for example, it will interpret it as Y=(2/3)\*X. Yes, which is why I mentioned it, because I was very annoyed with how Excel interprets it, even if it makes more sense in terms of “the rules”, simply because it doesn’t conform with my notions of how things are tied together automatically. This is part of the reason why I brought up my anecdote about subtraction - I basically thought the same thing there, and while it’s clearly wrong there, it just goes to show how thorny of an issue this is, because I’m clearly not an idiot when it comes to math, and I have different notions than the rest of the world. I used a TI-82(?) in high school (though I lost it somewhere along the way), and I don’t remember my experiences with it in this issue. I probably learned that I needed the parentheses then and totally forgot about it until I was regularly using Excel formulae in the same matter over a decade later. ---
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [October 31, 2020, 1:55am UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/52 "2020-10-31T01:55:27Z")
> [@Summerday](#): > > After you completed the second step, I don’t think that the parentheses should’ve been moved to include the 16. That was my fault. I was merely trying to indicate where I thought the next operation should take place for those not using PEMBAS. In hindsight I shouldn’t have since it looks like they popped out of nowhere. ---
**Author:** ![Kron](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kron/32/12444_2.png) [@Kron](https://boards.straightdope.com/u/Kron)\ **Post date:** [October 31, 2020, 2:16am UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/53 "2020-10-31T02:16:34Z")
> [@Shoeless](#): > > 8 + (4)^2 ÷ (7/2 - 2) 8 + 16 ÷ (1/2) 8 + 32 1. ---
**Author:** ![Babale](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/babale/32/15666_2.png) [@Babale](https://boards.straightdope.com/u/Babale)\ **Post date:** [October 31, 2020, 2:29am UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/54 "2020-10-31T02:29:36Z")
7/2 is 3.5, not 2.5 ---
**Author:** ![Kron](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kron/32/12444_2.png) [@Kron](https://boards.straightdope.com/u/Kron)\ **Post date:** [October 31, 2020, 2:43am UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/55 "2020-10-31T02:43:14Z")
Ha! I plead exhaustion. So yes, 8 + 10 2/3 = 18 2/3 ---
**Author:** ![elfkin477](https://avatars.discourse-cdn.com/v4/letter/e/a9a28c/32.png) [@elfkin477](https://boards.straightdope.com/u/elfkin477)\ **Post date:** [October 31, 2020, 4:41am UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/56 "2020-10-31T04:41:25Z")
Is ^ meaning squared a recent thing? Until I read some of your answers I had no idea what it was supposed to represent… ---
**Author:** ![Kron](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kron/32/12444_2.png) [@Kron](https://boards.straightdope.com/u/Kron)\ **Post date:** [October 31, 2020, 4:44am UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/57 "2020-10-31T04:44:00Z")
It’s an exponent marker. ^2 is squared, ^3 cubed, etc. Been that way for at least a few decades from my personal knowledge… ---
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [October 31, 2020, 4:44am UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/58 "2020-10-31T04:44:19Z")
> [@elfkin477](#): > > Is ^ meaning squared a recent thing? Until I read some of your answers I had no idea what it was supposed to represent… ^ means “to the power of”. So, 4^6 means 4 to the power of 6. (can we do superscripts on the new board?) ---
**Author:** ![Kron](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kron/32/12444_2.png) [@Kron](https://boards.straightdope.com/u/Kron)\ **Post date:** [October 31, 2020, 4:46am UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/59 "2020-10-31T04:46:35Z")
Testingcubed ``` Testingcubed ``` ---
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [October 31, 2020, 4:46am UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/60 "2020-10-31T04:46:55Z")
Cool! How did you do that? (I see the edit…thanks) [Previous page](https://boards.straightdope.com/t/math-homework-sanity-check/924310.md?page=2) [Next page](https://boards.straightdope.com/t/math-homework-sanity-check/924310.md?page=4)