# 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:** 17\ **Page:** 6
**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:** [November 1, 2020, 2:56pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/101 "2020-11-01T14:56:29Z")
> [@Chronos](#): > > Suppose that I have an expression that, when fully typeset, looks like > 2 > — a > 3 > And I want to write that all on one line. Surely, the proper way to do that would be 2/3a, no? My immediate thought is definitely “no”… Your follow-up is exactly how I would do that, 2a/3, but perhaps that doesn’t exactly teach a concept to a learning-age child? Otherwise I would use parentheses, (2/3)a. But I admit to programming bias, there. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [November 1, 2020, 3:06pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/102 "2020-11-01T15:06:08Z")
`(2/3)a` is acceptable, I believe? Hard to misread it that way. Or just write it ‘fully typeset’, only smaller so it fits in line. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [November 1, 2020, 3:19pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/103 "2020-11-01T15:19:23Z")
According to the link above, out of 60 students (in Harvard, 2014) asked to compute “2x/3y-1 with x=9 and y=2 ,” 58 got 2, and two got 18/5. That is the reality you must deal with. ---
**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:** [November 1, 2020, 4:40pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/104 "2020-11-01T16:40:37Z")
You’re not wrong. But I still prefer to at least attempt to teach the students what they need to know, even if our culture encourages them to immediately forget it. And teaching right now is hard enough, with high schoolers. Anyone who manages to get meaningful education to kindergartners under these conditions deserves a Nobel Prize. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [November 1, 2020, 7:27pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/105 "2020-11-01T19:27:49Z")
> [@Chronos](#): > > Everyone nowadays uses computers (of some form) to do calculations, and nearly all modern computer system will interpret 2/3a as meaning “two thirds of a”. I don’t use any computer math systems so I can’t speak to those, but that would be a syntax error in all programming languages that I’m familiar with. All of them require the explicit multiplication, so 2/3\*a. That looks different to my eyes than the implicit version. Of course, in many languages, that expression is exactly equivalent to “a”. Evaluating left-to-right, the 2/3 is performed first _in integer math_, resulting in 1, which gets multiplied with a. a\*2/3 is more likely to give the result you want. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [November 1, 2020, 7:54pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/106 "2020-11-01T19:54:34Z")
Huh–turns out that some (once popular) calculators [treat 2/3a as 2/(3a)](https://www.themathdoctors.org/order-of-operations-implicit-multiplication/): > Solution 11773: Implied Multiplication Versus Explicit Multiplication on TI Graphing Calculators. > > Does implied multiplication and explicit multiplication have the same precedence on TI graphing calculators? > > Implied multiplication has a higher priority than explicit multiplication to allow users to enter expressions, in the same manner as they would be written. For example, the TI-80, TI-81, TI-82, and TI-85 evaluate 1/2X as 1/(2_X), while other products may evaluate the same expression as 1/2_X from left to right. Without this feature, it would be necessary to group 2X in parentheses, something that is typically not done when writing the expression on paper. > > This order of precedence was changed for the TI-83 family, TI-84 Plus family, TI-89 family, TI-92 Plus, Voyage™ 200 and the TI-Nspire™ Handheld in TI-84 Plus Mode. Implied and explicit multiplication are given the same priority. That said, I’m not sure TI did students any favors when their own products can’t be trusted to behave consistently across the lineup. ---
**Author:** ![Ficer67](https://avatars.discourse-cdn.com/v4/letter/f/c57346/32.png) [@Ficer67](https://boards.straightdope.com/u/Ficer67)\ **Post date:** [November 1, 2020, 9:13pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/107 "2020-11-01T21:13:28Z")
Doing my best… (7/2 - 2) = (7/2 - 4/2) = 3/2, so the equation is now 8 +4^2 ÷ 3/2 4^2 = 16, 16+8 = 24, so the equation is now 24 ÷ 3/2 24 ÷ 3/2 = 24 x 2/3 = 48/3 = 16 My answer is 16. I followed the convention of doing everything in parentheses first. I considered the 16+8 to be the numerator of a fraction and the 2/3 to be the denominator. Right or wrong, if I were being tested, I would answer 16. I hope I have helped you ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [November 1, 2020, 9:45pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/108 "2020-11-01T21:45:37Z")
> [@Dr.Strangelove](#): > > Evaluating left-to-right, the 2/3 is performed first _in integer math_ , resulting in 1 Uh, I can’t math today. 2/3 gets rounded _down_ to zero in most languages. Still not the result you probably want, though 🙂. ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [November 2, 2020, 12:35am UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/109 "2020-11-02T00:35:41Z")
> [@Chronos](#): > > Suppose that I have an expression that, when fully typeset, looks like > 2 > — a > 3 > And I want to write that all on one line. Surely, the proper way to do that would be 2/3a, no? This just illustrates what I wrote a few posts up: The / is used instead of the horizontal bar in order to write a fraction on one line, BUT the problem is that / doesn’t really have the same semantics as the horizontal-line format of a fraction. When I learned algebra, starting in 9th grade in 1965, we learned the symbols of grouping: ( ), (that’s supposed to be left and right square brackets), and { } AND also, that a horizontal bar above or below part of an expression is also a symbol of grouping. The book had many sample problems to work that made use of that, in ways that you would NEVER EVER see elsewhere. But the point (that the textbook never explicitly mentioned) was the use of the horizontal bar in fractions, and also the horizontal bar in writing radicals with the entire radicand under the bar. In those uses, the horizontal bar does serve double-duty as a symbol of grouping, while the slash / does not. ---
**Author:** ![MandaJo](https://avatars.discourse-cdn.com/v4/letter/m/ac91a4/32.png) [@MandaJo](https://boards.straightdope.com/u/MandaJo)\ **Post date:** [November 2, 2020, 1:04am UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/110 "2020-11-02T01:04:06Z")
The issue is always opportunity cost. Complex abstract concepts can be taught, but they take time. So what do you cut out of Alg 1 to make a couple weeks to really dig into notation? ---
**Author:** ![MandaJo](https://avatars.discourse-cdn.com/v4/letter/m/ac91a4/32.png) [@MandaJo](https://boards.straightdope.com/u/MandaJo)\ **Post date:** [November 2, 2020, 1:17am UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/111 "2020-11-02T01:17:33Z")
To the wider point: Google Classroom and Google Forms have basically no formating options. You can’t bullet, bold, anything. You can attach a Google doc, but then you have to grade by hand (which this teacher may well be doing for other assignments). Of she’s using Google as her main platform (and I think most of us are), it really sucks for math. ---
**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:** [November 2, 2020, 2:02am UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/112 "2020-11-02T02:02:39Z")
> [@MandaJo](#): > > The issue is always opportunity cost. Complex abstract concepts can be taught, but they take time. So what do you cut out of Alg 1 to make a couple weeks to really dig into notation? Agreed. I don’t expect them to be able to teach this to all kids at the primary school level. I think if you can, and if your child takes to it, its a fantastic form of additional enrichment you can take-- deep dive into this kind of stuff. ---
**Author:** ![Ficer67](https://avatars.discourse-cdn.com/v4/letter/f/c57346/32.png) [@Ficer67](https://boards.straightdope.com/u/Ficer67)\ **Post date:** [November 2, 2020, 2:08am UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/113 "2020-11-02T02:08:04Z")
Does this help the OP in any way? ---
**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:** [November 2, 2020, 3:48am UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/114 "2020-11-02T03:48:19Z")
The OP’s question was answered a long time ago and the discussion moved past that already. Who shat in your cornflakes? ---
**Author:** ![Dead\_Cat](https://avatars.discourse-cdn.com/v4/letter/d/9fc29f/32.png) [@Dead\_Cat](https://boards.straightdope.com/u/Dead_Cat)\ **Post date:** [November 2, 2020, 10:18am UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/115 "2020-11-02T10:18:00Z")
Sorry, I don’t follow what point you’re making here - it seems to me the vast majority are getting the ‘correct’ answer on that basis, and the 2 that didn’t have interpreted the calculation in a way that isn’t entirely unreasonable. Either way there is no reason not to add some parentheses to make things unambiguous. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [November 2, 2020, 10:33am UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/116 "2020-11-02T10:33:54Z")
The point is that none of the 60 humans got the computerised answer, even though ‘everyone nowadays uses computers.’ Secondarily, that not everyone got the same answer. Therefore, absolutely, some parentheses or some reformatting may be necessary. ---
**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:** [November 2, 2020, 9:43pm UTC](https://boards.straightdope.com/t/math-homework-sanity-check/924310/117 "2020-11-02T21:43:24Z")
Oh, sure, a few extra sets of parentheses never hurt anyone. When in doubt, make things less ambiguous. [Previous page](https://boards.straightdope.com/t/math-homework-sanity-check/924310.md?page=5)