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Reducing Fractions with Large Denominators
by Gail Englert

A response to the question:

How can I teach how to reduce fractions with large denominators in a clear way?

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I would like help in teaching how to reduce fractions with large denominators in a clear way. My son is having problems with this concept and my methods do not seem to be helping.

Wendy

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Dear Wendy,

One thing that works well for my students is for them to know ways to recognize if a number has a certain factor... for example, if I wanted to tell if a number had 2 as a factor (which means I can divide 2 evenly into the number), all I have to do is look to see if the number is even. If it is odd, then I know I won't be able to divide it by 2 evenly.

If the number ends with 0 or 5, then I know 5 is a factor. And if the number ends in 0, I know 10 is a factor.

If I can add all the digits, and the sum is evenly divisible by 3, then the whole number is divisible by 3... like this 1,234,560 1+2+3+4+5+6+0 = 21, and 3 divides into 21 evenly, so it will also divide 1,234,560 evenly.

So, what good is this? Well, one of the ways students can "reduce" or simplify fractions is to look for a factor that will divide evenly into both the numerator and the denominator... We call that a "common" factor.

Take 48 / 120 for example...

120 has 5 as a factor, but 48 doesn't, so I can't use 5 to make the fraction simpler.

120 has 3 as a factor, because 1+2+0 is 3.. And so does 48 because 4+8=12 so I could divide both by 3 and get a new simplified fraction: 16 / 40 16 and 40 both have a factor of 2 (because they are both even... )

Now my fraction is simplified to 8/20 and I can use the factor of 2 again... Now it is 4/10, and I can use the factor of 2 one more time to get 2/5.

Of course, I can use any factor that is common to both numbers, and the larger a factor I use, the less steps I have to take... I hope this helps.

-Gail, for the T2T service

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