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Re: least common multiple
Posted:
Feb 24, 2002 10:29 PM
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Although this thread has focused on algorithms for finding the lcm,
the original question was to compare four fractions with unequal
denominators. Although not commonly taught in middle school, consider
the following 2 options:
I. "Common numerators"
The lcm of 2,3,4, and 5 (the numerators of the fractions under
consideration) is 60. I often remind my students that there is nothing
sacred about common denominators! Thus
3/7 = 60/140; 2/5 = 60/150; 4/9 = 60/135; 5/11 = 60/132.
Since 60/132 has the smallest denominator, it is the largest fraction
and so on. This should engender fruitful discussion of fraction
concepts.
II. "Continued Fraction approach"
Rewrite each of these proper fractions a/b as 1/(b/a) and divide:
3/7 = 1/(7/3) = 1/(2 + 1/3)
Similarly, 2/5 = 1/(2 + 1/2),
4/9 = 1/(2 + 1/4),
5/11 = 1/(2 + 1/5)
Again, we have common numerators and the denominators are easy to
compare since they conveniently are of the form 2 + 1/k.
The efficiency of both of these methods of course depends on the
fractions involved, but they do employ some number sense, and, more
importantly, they may help to develop PUFF (sorry, I couldn't resist
this variation - I leave it to the reader to decode!).
Dave Marain
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