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
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.
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.
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.
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.
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.
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.
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!
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?
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.
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.
