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I want help phrasing the instructions in a math question. The issue is the correct way to express mixed units.

For example, if an answer is “25 inches,” I don’t want to accept “25 inches” or “1 foot 13 inches,” but only “2 feet 1 inch.”

I guess you might say that I want the total number of units to be small as possible. But I don’t think anyone would understand what I meant by that. Similarly, I don't think it would do to say that I want the answer "simplified."

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  • $\begingroup$ Is this about giving the final answer to a problem in a particular way, such as "find the perimeter of the circle, giving your answer in terms of feet and inches", or is the question itself about just rewriting a dimensioned object, such as "rewrite 215 inches in terms of feet and inches"? $\endgroup$ – Nick C Mar 27 '19 at 21:28
  • $\begingroup$ @Nick C The former. One problem gives the base and height of a triangle, each in feet and inches, and asks for the area in square feet and square inches. $\endgroup$ – Chaim Mar 27 '19 at 21:50
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    $\begingroup$ Aahh the joy of non-SI-units. I agree that 1 foot 13 inches is bad, but I 'd be fine with both alternatives. $\endgroup$ – Jasper Mar 27 '19 at 22:17
  • $\begingroup$ In SI 25 cm would be simply 2.5*10^-1 m, because meters is the base unit for length. Chaim, why won't you switch to SI instead? $\endgroup$ – Rusty Core Mar 27 '19 at 23:44
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    $\begingroup$ Maybe something like "use larger units if values larger than 1 are possible"? Still sounds kludgy without an example. By the way, 2640 ft is 880 yd or 0.5 mi ? According to your pattern it should be 880 yd, but I think 0.5 mi is much clearer to everyone. $\endgroup$ – Rusty Core Mar 28 '19 at 16:05
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The best way to teach this concept would be using money. For example if you were in the US, you can say that you want the least coins and bills for $5.80 cents. Only a five dollar bill, 3 quarters, and a nickel would satisfy that criteria. Once the class understands the idea of the "least coins and bills", ask them how you would apply a similar concept to feet and inches. They can then help you give a name to the idea, maybe least feet and inches?

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    $\begingroup$ "Fewest coins and bills" might be more correct. (Implicitly, this is avoiding improper fractions. "1 foot 13 inches" is like "(1 + (13/12)) feet" and [in this scheme] should be simplified to "(2 + (1/12)) feet" or "2 feet 1 inch".) $\endgroup$ – robphy Apr 4 '19 at 21:38
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There's no conventional phrase that clearly expresses that. The only way to convey that is to give an example.

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Assuming this is about some kind of exam: If there's still time in class to clear this up, use it. Explain why one might consider 1 foot 13 inches as bad and why 2 foot 1 inch might be better than 25 inches.

If there's no time, the most simple and precise way is to use an example to show the students which answer you like and which you don't.

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