# Pencil-and-paper arithmetic: are kids still supposed to be able to do it? **URL:** \ **Category:** In My Humble Opinion\ **Created:** [March 22, 2026, 6:16pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688 "2026-03-22T18:16:47Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\ **Post date:** [March 22, 2026, 10:02pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/21 "2026-03-22T22:02:01Z")
> [@DPRK](#): > > An HP-35 was about $395 in 1970s’ dollars so not many high-schoolers were buying them. I got my first calculator in jr. high in the early-’70s. It had four functions: Addition, Subtraction, Multiplication, and Division. It had an 8-digit nixie tube display, used (IIRC) eight AA cells, and cost $99. I recall it got rather warm, and burned through AA cells pretty quickly. ---
**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:** [March 22, 2026, 10:04pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/22 "2026-03-22T22:04:10Z")
> [@Timz](#): > > Are US high-school graduates still supposed to know their times tables? What do you mean by “know their times tables”? And is that a question about “pencil-and-paper arithmetic” or about “mental math” or about remembering basic facts? > [@Timz](#): > > If you gave 100 teenagers pencil and paper and asked them whether 29/67 was more or less than 16/37, how many of them could answer in 2-3 minutes like us older folks? How many could answer at all, assuming no cheating? I think that it’s more important to be able to see that both fractions are a bit less than 1/2 and that they are fairly close to each other in value, and to know how to tell which is larger _with_ a calculator available. ---
**Author:** ![Si\_Amigo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/si_amigo/32/2877_2.png) [@Si\_Amigo](https://boards.straightdope.com/u/Si_Amigo)\ **Post date:** [March 22, 2026, 10:04pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/23 "2026-03-22T22:04:43Z")
> [@beowulff](#): > > The problem with doing this is: you have turned a trivial calculation ($5.40 - $5.31 = .1¢) into something that requires much more concentration. Please concentrate more on the trivial calculations. 🙂 The answer is 9¢, not .1¢. ---
**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:** [March 22, 2026, 10:05pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/24 "2026-03-22T22:05:51Z")
Good catch. It is indeed nine cents, not one tenth of a cent! ---
**Author:** ![BigT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bigt/32/12044_2.png) [@BigT](https://boards.straightdope.com/u/BigT)\ **Post date:** [March 22, 2026, 10:09pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/25 "2026-03-22T22:09:59Z")
The math that the cashier would need to do is still taught. I would not even assume she couldn’t do that math ordinarily. She easily could have had trouble thinking of it due to the script being flipped on her. She’s not used to having to think about the transaction, as the machine tells her what to give you back, and she’d now have to think about “how do I handle changing the amount he gave me?” I suspect in other words it could be less practical knowledge of need to use it, and just the rut of working a job, possibly on low sleep. And not that she couldn’t handle it in a math classroom. ---
**Author:** ![DrDeth](https://avatars.discourse-cdn.com/v4/letter/d/b487fb/32.png) [@DrDeth](https://boards.straightdope.com/u/DrDeth)\ **Post date:** [March 22, 2026, 10:28pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/26 "2026-03-22T22:28:51Z")
> [@doreen](#): > > Never - now, if the question is whether 3/4 is more or less than 1/2, that might be useful. Good point. > [@DPRK](#): > > How many digits do you _need_, is a question the student needs to ask themselves. “sig figs” as my college prof put it. ---
**Author:** ![beowulff](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/beowulff/32/542_2.png) [@beowulff](https://boards.straightdope.com/u/beowulff)\ **Post date:** [March 22, 2026, 11:37pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/27 "2026-03-22T23:37:28Z")
The two errors cancel out, don’t they? ---
**Author:** ![Timz](https://avatars.discourse-cdn.com/v4/letter/t/6a8cbe/32.png) [@Timz](https://boards.straightdope.com/u/Timz)\ **Post date:** [March 23, 2026, 12:00am UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/28 "2026-03-23T00:00:49Z")
> [@Thudlow\_Boink](#): > > What do you mean by “know their times tables”? Know the product of any pair of single digits, instantly – no thought involved. Pencil-and-paper long division takes five? ten? times as long, if you have to figure out each multiplication involved. By the way – my question isn’t about what kids should know. All I’m asking is: what do they know, nowadays? ---
**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:** [March 23, 2026, 12:21am UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/29 "2026-03-23T00:21:46Z")
When I’m teaching Algebra II and Precalculus students about polynomials, and specifically division of polynomials, I always start by asking them, first, how many of them learned long division of numbers (almost all hands go up), and second, how many of them actually remember it (maybe a third of the hands go up). And of that second group, it’s probably a smaller number yet that actually remember it. Anyway, I re-teach it anyway, because most students definitely don’t remember it (the technique for dividing polynomials is almost identical to long division of numbers). ---
**Author:** ![TokyoBayer](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tokyobayer/32/13989_2.png) [@TokyoBayer](https://boards.straightdope.com/u/TokyoBayer)\ **Post date:** [March 23, 2026, 1:24am UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/30 "2026-03-23T01:24:30Z")
> [@Timz](#): > > how many of them could answer in 2-3 minutes like us older folks? I’ve got a math minor and a EE degree, but even back then we were using calculators for most of our long division problems. I still can do long division, but it’s not something I’m super fast with. ---
**Author:** ![SCAdian](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/scadian/32/3292_2.png) [@SCAdian](https://boards.straightdope.com/u/SCAdian)\ **Post date:** [March 23, 2026, 1:52am UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/31 "2026-03-23T01:52:45Z")
> [@Bear\_Nenno](#): > > What? “[New Math](https://www.youtube.com/watch?v=W6OaYPVueW4)”, by Tom Lehrer ---
**Author:** ![China\_Guy](https://avatars.discourse-cdn.com/v4/letter/c/779978/32.png) [@China\_Guy](https://boards.straightdope.com/u/China_Guy)\ **Post date:** [March 23, 2026, 4:17am UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/32 "2026-03-23T04:17:05Z")
Don’t judge math skills by a cashier. Fast food places all switched in the 1980’s to cash registers with item icons, automatically calculated totals and maybe even change (?). It was a marked change from the 70’s style where one had to punch in each individual item price. Abacus skills seem to generally no longer taught to school kids throughout Asia these days. Japan still seems to teach: “Soroban remains part of the national curriculum in many elementary schools.” (Copilot) ---
**Author:** ![chappachula](https://avatars.discourse-cdn.com/v4/letter/c/d2c977/32.png) [@chappachula](https://boards.straightdope.com/u/chappachula)\ **Post date:** [March 23, 2026, 6:01am UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/33 "2026-03-23T06:01:34Z")
> [@doreen](#): > > now, if the question is whether 3/4 is more or less than 1/2, that might be useful. There’s a famous proof that most adults cannot understand fractions. A hamburger chain tried to beat McDonalds by selling a 1/3 pounder at the same price as McD’s quarter pounder. People refused to buy it, because they thought 1/3 was less than 1/4. [https://medium.com/better-marketing/the-a-w-third-pounder-failed-because-people-didnt-understand-fractions-a86b966a973a](https://medium.com/better-marketing/the-a-w-third-pounder-failed-because-people-didnt-understand-fractions-a86b966a973a) ---
**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:** [March 23, 2026, 11:05am UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/34 "2026-03-23T11:05:09Z")
[![](https://img.youtube.com/vi/EMNqJQaf08E/maxresdefault.jpg "The A&W 3/9 lb. Burger | A&W Restaurants") ](https://www.youtube.com/watch?v=EMNqJQaf08E) ---
**Author:** ![Steven\_Maven](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/steven_maven/32/3272_2.png) [@Steven\_Maven](https://boards.straightdope.com/u/Steven_Maven)\ **Post date:** [March 23, 2026, 10:26pm UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/35 "2026-03-23T22:26:12Z")
> [@Johnny\_L.A](#): > > We had to calculate square roots by hand when I was in jr. high. I must have missed the method, so I just used trial-and-error until I came up with the answer. (ISTR it looked something like long division.) Trial & Error is not far from the “official” method. Make a guess. Divide the number by the guess. Average the 2 numbers. Repeat until the 2 numbers are “close enough.” ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [March 24, 2026, 12:58am UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/36 "2026-03-24T00:58:13Z")
> [@Chronos](#): > > You’re also assuming that pencil and paper is needed for that problem. It isn’t. Okay, show me. Here’s how I did it. Each line is equivalent to the line above. 16/37 \< 29/67 iff 37/16 \> 67/29 iff (subtract 2 from each side) 5/16 \> 9/29 iff 16/5 \< 29/9 iff (sub 3) 1/5 \< 2/9 iff 5 \> 9/2 which is obviously true. But I don’t think I could carry this out in my head. ---
**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:** [March 24, 2026, 1:23am UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/37 "2026-03-24T01:23:08Z")
I cross-multiplied (see [post 11](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/11)). But I like the continued fraction method, too. ---
**Author:** ![AnalogSignal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/analogsignal/32/1085_2.png) [@AnalogSignal](https://boards.straightdope.com/u/AnalogSignal)\ **Post date:** [March 24, 2026, 2:43am UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/38 "2026-03-24T02:43:36Z")
I did the same basic thing as Chronos without the fancy square roots and mental arithmetic. It may be worth spelling it out for anyone getting lost. ```plaintext 29/67 ? 16/37 (29*37)/(67*37) ? (16*67)/(37*67) make the denominators the same 29*37 ? 16*67 ignore the denominators now that they match 1073 > 1072 do the two multiplications (on paper) ``` ---
**Author:** ![GuanoLad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/guanolad/32/42_2.png) [@GuanoLad](https://boards.straightdope.com/u/GuanoLad)\ **Post date:** [March 24, 2026, 3:37am UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/39 "2026-03-24T03:37:33Z")
I don’t recall ever learning this at school, so the whole discussion of that equation has had me mystified from the beginning. And I think of myself as reasonably academically smart. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [March 24, 2026, 5:13am UTC](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688/40 "2026-03-24T05:13:22Z")
> [@Steven\_Maven](#): > > > [@Johnny\_L.A](#): > > > > We had to calculate square roots by hand when I was in jr. high. I must have missed the method, so I just used trial-and-error until I came up with the answer. (ISTR it looked something like long division.) > > Trial & Error is not far from the “official” method. “Long division” means long division: ``` 11.09053 ---------- 123.00 1 --- 023 21 --- 200 0 --- 20000 19881 ----- 11900 0 ----- 1190000 1109025 ------- 8097500 6654309 ``` If you look at the [Harvard admissions exam from 1869](https://graphics8.nytimes.com/packages/pdf/education/harvardexam.pdf), page 6, or the one from [MIT](https://web.archive.org/web/20190404065753im_/https://libraries.mit.edu/archives/exhibits/exam-entrance1876/img/arithmetic-test.jpg), you can see that finding square roots and cube roots to a few places of decimals was on the test, though the method is not specified: it just asks to show your work. [Previous page](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688.md?page=1) [Next page](https://boards.straightdope.com/t/pencil-and-paper-arithmetic-are-kids-still-supposed-to-be-able-to-do-it/1028688.md?page=3)