Q&A #7499

Curious about fractions

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From: Pat Ballew (for Teacher2Teacher Service)
Date: Dec 12, 2001 at 01:49:43
Subject: Re: Curious about fractions

Cooper, I'm not sure it has an "official" name, but I call it the "three arrow method". When I do it I draw an arrow upward from the right denominator to the left numerator (this way \) and another from the left denominator to the right numerator (this way/) and one across through the two denominators (this way --). It also works for subtraction by the way... 15 8 3 2 15-8 7 -- - ---- = ---- = ---- 4 5 20 20 The earliest record I can find of this (with the three arrows as straight lines drawn between the values to be multiplied) is by Nicholas Chuquet in the fifteenth century. It was used quite regularly in the early arithmetics such as that by Recorde. WHY it works??? If the two denominators are relatively prime, then their product is the least common denominator and the "other denominator" is the multiplier to make an equivalent fraction. [20/4 = 5 and 20/5 = 4 ] If they are not, you just have to reduce as a final step. In the U.S. we often emphasize finding the Least Common Multiple to be the common denominator, but ANY common multiple will work, it just forces you to simplify the final answer to get it in simplest terms. The easy way to find a common multiple of two numbers is to multiply them against each other, thus making each the co-factor of the others numerator to express the fractions in a common denominant unit. The nice thing for students is that it also works when you get to algebra and beyond and have to add stuff like 2 + 3x ----- ----- = (x-1) (x+1) Hope that helps... good luck -Pat Ballew, for the T2T service

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