# Can you solve a semi-complex math problem with just pencil and paper? **URL:** \ **Category:** In My Humble Opinion\ **Created:** [September 16, 2011, 9:25pm UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557 "2011-09-16T21:25:16Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![VOW](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/vow/32/3043_2.png) [@VOW](https://boards.straightdope.com/u/VOW)\ **Post date:** [September 17, 2011, 3:40am UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557/21 "2011-09-17T03:40:02Z")
Gahhhhh… Calculators weren’t INVENTED when I was in high school! (Class of 71) We used slide rules in college chemistry. I really wouldn’t remember how to use a slide rule today. I know I wouldn’t be able to do logarithms today, or worse yet natural logarithms (base e, right?) I could do trig if you gave me a table book and the formulae. My head is too cluttered with all the zip codes I’ve lived at over the past 30-plus years. _eyeroll_ I find I can still do algebra. Before I retired, I ended up tutoring several coworkers who had gone back to school and really hit the brick wall with algebra. I loved the tutoring. Your question cracks me up, because when you are talking about algebra, trig, chemistry, or physics, just the final answer won’t do it. You have to SHOW YOUR WORK. ~VOW ---
**Author:** ![Skald\_the\_Rhymer](https://avatars.discourse-cdn.com/v4/letter/s/ecccb3/32.png) [@Skald\_the\_Rhymer](https://boards.straightdope.com/u/Skald_the_Rhymer)\ **Post date:** [September 17, 2011, 2:30pm UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557/22 "2011-09-17T14:30:06Z")
> [@TriPolar](#): > > I’m approximately 11/8ths your age. We weren’t allowed to use calculators in high school math class because of all the noise they would make. But you could learn how to use one in the advanced typing class. So you’re in your mid-fifties or therabouts, I say without bothering to pick up pen or paper. By my high school years calculators were about the size they are now, solar-powered, and quite quiet, but we still weren’t allowed to use them before trig. And I’m not sure they were allowed even then. ---
**Author:** ![Khadaji](https://avatars.discourse-cdn.com/v4/letter/k/9e8a1a/32.png) [@Khadaji](https://boards.straightdope.com/u/Khadaji)\ **Post date:** [September 17, 2011, 3:04pm UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557/23 "2011-09-17T15:04:05Z")
Yes, I still can, but likely not as quickly, and I would likely write out more steps than I used to. I’ll be 50 in December. ---
**Author:** ![astro](https://avatars.discourse-cdn.com/v4/letter/a/9dc877/32.png) [@astro](https://boards.straightdope.com/u/astro)\ **Post date:** [September 17, 2011, 5:26pm UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557/24 "2011-09-17T17:26:53Z")
> [@rostfrei](#): > > I’d definitely be screwed without a calculator. I was thinking today, I’m 45 and I have completely forgotten how to add/multiply/divide fractions. I can do simple ones, but 1 and 1/7 multiplied by 2 and 3/16…forget it.. I remember it being taught in Junior/Senior math class, I vividly remember it…I just can’t remember how to do it. > > I can’t say that I’ve ever needed to know the answer to above question, but I’d at least like to re-teach myself how to do it. > > Anyone else incapable of doing any sort of math that does not involve a checkbook? I’m 53 and I could do the fraction problem, however, I’m in commercial real estate and do all sorts of business math calculations, but short of cutting up a pizza or baking a cake I can’t recall a single time over the years where there was a real world math problem that inherently needed to be expressed and dealt with as a fraction vs being expressed as a decimalized percentage. ---
**Author:** ![Skald\_the\_Rhymer](https://avatars.discourse-cdn.com/v4/letter/s/ecccb3/32.png) [@Skald\_the\_Rhymer](https://boards.straightdope.com/u/Skald_the_Rhymer)\ **Post date:** [September 17, 2011, 5:54pm UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557/25 "2011-09-17T17:54:55Z")
> [@astro](#): > > I’m 53 and I could do the fraction problem, however, I’m in commercial real estate and do all sorts of business math calculations, but short of cutting up a pizza or baking a cake I can’t recall a single time over the years where there was a real world math problem that inherently needed to be expressed and dealt with as a fraction vs being expressed as a decimalized percentage. Decimals and percentages _are_ fractions. They’re just instances in which everyone has agreed to use a common denominator for ease of calculation. ---
**Author:** ![Joey\_P](https://avatars.discourse-cdn.com/v4/letter/j/919ad9/32.png) [@Joey\_P](https://boards.straightdope.com/u/Joey_P)\ **Post date:** [September 17, 2011, 6:06pm UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557/26 "2011-09-17T18:06:06Z")
> [@rostfrei](#): > > I’d definitely be screwed without a calculator. I was thinking today, I’m 45 and I have completely forgotten how to add/multiply/divide fractions. I can do simple ones, but 1 and 1/7 multiplied by 2 and 3/16…forget it.. I remember it being taught in Junior/Senior math class, I vividly remember it…I just can’t remember how to do it. I guess it depends on what you mean by “complex.” When I read the question my brain went to things like differential equations, differentiating multivariable functions, statistics etc. As a math major, no, I can’t do that off the top of my head any more. But high school level arithmetic (multiplying fractions, basic trig, solving for an unknown) really doesn’t present a problem. They aren’t what I consider 'complex." For me, complex doesn’t happen until you are at least past first year calc. Well, technically, complex doesn’t happen until you want the square root of a negative number, but I don’t think that’s where this was going. ---
**Author:** ![panache45](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/panache45/32/64_2.png) [@panache45](https://boards.straightdope.com/u/panache45)\ **Post date:** [September 17, 2011, 6:15pm UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557/27 "2011-09-17T18:15:08Z")
When I was a kid, I could do fairly complicated math entirely in my head. I was always “teacher’s pet” in every math class, because I ALWAYS knew the answer to every question, often entirely in my head. And yes, I did get an SAT 1600, back when 1600 really meant something. Of course, that was before calculators, and before the constant decline in my brain cells. ---
**Author:** ![Gary\_Robson](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/gary_robson/32/3448_2.png) [@Gary\_Robson](https://boards.straightdope.com/u/Gary_Robson)\ **Post date:** [September 17, 2011, 6:42pm UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557/28 "2011-09-17T18:42:40Z")
> [@VOW](#): > > Gahhhhh… > > Calculators weren’t INVENTED when I was in high school! (Class of 71) Sure they were. They just weren’t cheap little pocket-sized calculators. ---
**Author:** ![Jaledin](https://avatars.discourse-cdn.com/v4/letter/j/f9ae1b/32.png) [@Jaledin](https://boards.straightdope.com/u/Jaledin)\ **Post date:** [September 17, 2011, 6:52pm UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557/29 "2011-09-17T18:52:05Z")
> [@Joey\_P](#): > > Well, technically, complex doesn’t happen until you want the square root of a negative number, but I don’t think that’s where this was going. I see what you did there, Torless! ---
**Author:** ![astro](https://avatars.discourse-cdn.com/v4/letter/a/9dc877/32.png) [@astro](https://boards.straightdope.com/u/astro)\ **Post date:** [September 17, 2011, 7:30pm UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557/30 "2011-09-17T19:30:14Z")
> [@Skald\_the\_Rhymer](#): > > Decimals and percentages _are_ fractions. They’re just instances in which everyone has agreed to use a common denominator for ease of calculation. That was kind of my point. Relatively few real world operations are actually dealt with in a numerator-denominator fractions format where multiplying or dividing fractions expressed as x over y is the preferred mode of calculation. ---
**Author:** ![Skald\_the\_Rhymer](https://avatars.discourse-cdn.com/v4/letter/s/ecccb3/32.png) [@Skald\_the\_Rhymer](https://boards.straightdope.com/u/Skald_the_Rhymer)\ **Post date:** [September 17, 2011, 7:47pm UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557/31 "2011-09-17T19:47:44Z")
> [@astro](#): > > That was kind of my point. Relatively few real world operations are actually dealt with in a numerator-denominator fractions format where multiplying or dividing fractions expressed as x over y is the preferred mode of calculation. Sure they are. They’re just simplified before they get to you. ---
**Author:** ![VOW](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/vow/32/3043_2.png) [@VOW](https://boards.straightdope.com/u/VOW)\ **Post date:** [September 17, 2011, 7:49pm UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557/32 "2011-09-17T19:49:32Z")
To the Wombat: You know what I mean! ~VOW ---
**Author:** ![astro](https://avatars.discourse-cdn.com/v4/letter/a/9dc877/32.png) [@astro](https://boards.straightdope.com/u/astro)\ **Post date:** [September 17, 2011, 7:53pm UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557/33 "2011-09-17T19:53:14Z")
> [@Skald\_the\_Rhymer](#): > > Sure they are. They’re just simplified before they get to you. Possibly I’m missing your point. Other than cooking give me a cite for a real world scenario where the preferred or necessary mode of calculation would be to express something as fractions. ---
**Author:** ![VOW](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/vow/32/3043_2.png) [@VOW](https://boards.straightdope.com/u/VOW)\ **Post date:** [September 17, 2011, 8:09pm UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557/34 "2011-09-17T20:09:31Z")
To Astro: SEWING. Fabric is measured in yards, and fractions of a yard. ~VOW ---
**Author:** ![Skald\_the\_Rhymer](https://avatars.discourse-cdn.com/v4/letter/s/ecccb3/32.png) [@Skald\_the\_Rhymer](https://boards.straightdope.com/u/Skald_the_Rhymer)\ **Post date:** [September 17, 2011, 8:10pm UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557/35 "2011-09-17T20:10:45Z")
> [@astro](#): > > Possibly I’m missing your point. Other than cooking give me a cite for a real world scenario where the preferred or necessary mode of calculation would be to express something as fractions. My wife just supplied with sewing as an example, but I see that VOW beat me to it. But may I ask why you disqualify cooking? ---
**Author:** ![antonio107](https://avatars.discourse-cdn.com/v4/letter/a/7ea924/32.png) [@antonio107](https://boards.straightdope.com/u/antonio107)\ **Post date:** [September 17, 2011, 8:21pm UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557/36 "2011-09-17T20:21:33Z")
I suck at math. I can do the question in the OP in my head if I tried, or with pen and paper. Simple algebra as well. I’m not sure if this is an indictment of my highschool education (I’m 25), but we NEVER learned Trigonometry with the SIN, COS, and TAN buttons on our calculators. I literally DO NOT know what those buttons represent, what they stand for, and if I didn’t have a calculator handy I would be at a loss to solve any problem that required them. That having been said, I don’t remember any problems that would require them. See my first sentence! 😛 ---
**Author:** ![astro](https://avatars.discourse-cdn.com/v4/letter/a/9dc877/32.png) [@astro](https://boards.straightdope.com/u/astro)\ **Post date:** [September 17, 2011, 8:46pm UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557/37 "2011-09-17T20:46:55Z")
> [@VOW](#): > > To Astro: > > SEWING. > > Fabric is measured in yards, and fractions of a yard. > ~VOW Is this the best way to do it? Do Europeans using the metric system measure fabric by a fractions based system? I understand in cooking it may be necessary to use fractional calculations to adjust recipes etc. I suppose what I’m asking is if there is any kind of everyday math people use in real life (other than cooking) that would not be better expressed and more easily calculated as decimalized percentages vs manipulating these ratios as numerator/denominator based fractions. I understand that N/D fractions and ratios are the same thing. Is there an advantage to using fractions where you can also use more easily manipulated decimalized ratios? ---
**Author:** ![Chefguy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chefguy/32/138_2.png) [@Chefguy](https://boards.straightdope.com/u/Chefguy)\ **Post date:** [September 17, 2011, 8:50pm UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557/38 "2011-09-17T20:50:37Z")
I solve algebraic, fractional and ratio/proportion problems on paper all the time. For most trig problems you need tables, but with those available, I could do those on paper also. On the other hand, I never understood calculus when it was fresh in my mind, so would be totally lost now. ---
**Author:** ![Malacandra](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Malacandra](https://boards.straightdope.com/u/Malacandra)\ **Post date:** [September 17, 2011, 8:54pm UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557/39 "2011-09-17T20:54:32Z")
> [@antonio107](#): > > I suck at math. > > I can do the question in the OP in my head if I tried, or with pen and paper. Simple algebra as well. > > I’m not sure if this is an indictment of my highschool education (I’m 25), but we NEVER learned Trigonometry with the SIN, COS, and TAN buttons on our calculators. I literally DO NOT know what those buttons represent, what they stand for, and if I didn’t have a calculator handy I would be at a loss to solve any problem that required them. > > That having been said, I don’t remember any problems that would require them. See my first sentence! 😛 Sin, cos and tan refer to the ratio of sides and angles in a right-angled triangle. Mark one of the non-right angles, and the sine (SIN) of that angle is the length of the side opposite the angle divided by the length of the hypotenuse (the longest side). For any given angle, this ratio is fixed no matter whether the triangle is a tiny one or a huge one. The other buttons refer to ratios between other pairs of sides. The applications include map-making and engineering, for a start - with a little working-out you can fill in the blanks for any triangle where you know at least two sides and the angle between them, or one side and the angle at each end, which is darn handy if you want to survey the height of a hill or work out your position at sea relative to a lighthouse on the shore. Sin and so on also turn up in equations of rotary motion or the movement of a heavy thing on a spring (such as your car suspension). Then there’s tide calculations, the amount of sunlight falling on a solar panel by day of the year and time of day, and so on, and so on… I can do quite complicated math with just a pencil and paper, including extracting square roots using the binomial theorem, but then I’m just finishing off a math B Sc so I’m a bit of a statistical outlier. 😛 ---
**Author:** ![Malacandra](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Malacandra](https://boards.straightdope.com/u/Malacandra)\ **Post date:** [September 17, 2011, 8:56pm UTC](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557/40 "2011-09-17T20:56:30Z")
> [@astro](#): > > Is this the best way to do it? Do Europeans using the metric system measure fabric by a fractions based system? I understand in cooking it may be necessary to use fractional calculations to adjust recipes etc. > > I suppose what I’m asking is if there is any kind of everyday math people use in real life (other than cooking) that would not be better expressed and more easily calculated as decimalized percentages vs manipulating these ratios as numerator/denominator based fractions. > > I understand that N/D fractions and ratios are the same thing. Is there an advantage to using fractions where you can also use more easily manipulated decimalized ratios? There can be. What’s 67% x 37.5%? What’s 2/3 of 3/8? The latter takes a moment to answer if you understand about cancelling fractions… [Previous page](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557.md?page=1) [Next page](https://boards.straightdope.com/t/can-you-solve-a-semi-complex-math-problem-with-just-pencil-and-paper/596557.md?page=3)