On Thu, Jul 14, 2011 at 9:46 AM, David Corking <[email protected]> wrote:
> > > > In practice, nurses, pizza cooks, carpenters and so > > on don't "really" divide by fractions - they work with numerators and > > denominators separately. > > This may not be the case when dealing with decimal fractions or > percentages, when they might wish to crank a formula, or hit the > division key on a calculator. I agree completely, and I should have specified this case. People conceptualize decimals as "single numbers" for all operations, unlike fractions that are considered "pairs of numbers" for many purposes. > Therefore I think it is worthwhile to > give students a chance to develop a mental picture of division by a > fraction, even if they choose to forget it later, and rely on the > algorithm. > Do you teach division by decimals through division by fractions? Maybe some parts of it, e.g. why division by 0.01 is the same as multiplication by 100? > I see from your wiki page that you might not agree with me that > percentages and decimals are special cases of fractions. However, at > least in some curricula, fraction arithmetic is taught first, and the > others follow. > > A couple of examples: > (1) if a toy car completes a five foot track in three-quarters of a > second, what is its speed? > (2) if you want to take 20% sales tax, or value added tax, off an > invoice to find the pre-tax price, then you divide by 1.2 > (3) devise a formula to convert lap times measured in problem (1) into > speeds in miles per hour, or kilometres if you prefer. > > I think we will find numerous other examples in science, engineering > and finance. > Yes, grown-ups divide by decimals (as you said, usually using computers) all the time. Cheers, Maria Droujkova 919-388-1721 Make math your own, to make your own math.
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