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Reducing Fractions

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Date: 5/30/96 at 15:44:39
From: Vivian McCraw
Subject: Reducing fractions

I was placed in ESE from Pre-k through grade 12 and they never had me
learn to reduce fractions. What is the easiest method of reducing
fractions to lowest terms that you know?

Greg
```

```
Date: 5/31/96 at 16:6:3
From: Doctor Byron
Subject: Re: Reducing fractions

Hi Greg,

In order to reduce a fraction, you need to find the biggest number
that divides into both the numerator (the top number) and the
denominator (the bottom number).  After some practice, you may find
that you can do this pretty quickly.  At first, though, it is often
helpful to list all the factors and simply look to see the biggest one
shared by both numbers.

Factors, by the way, are simply any number that divides into another
number evenly.  Let me give you an example:

Let's look at the fraction -

48
------
32

The factors of 48 are:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The factors of 32 are:
1, 2, 4, 8, 16, 32

If you look at both lists you'll see that 16 is the biggest number
that is on both lists.  So to reduce the fraction, we divide the top
and bottom by sixteen.

48/16        3
-------  =  -----
32/16        2

If you find that there are no numbers (other than one) which are
shared factors of both, the the fraction is as simple as it can get.

Also, you don't have to simply look for the biggest factor right away.
If you notice a shared factor quickly, you can go ahead and divide by
it right away.  You will have to make sure that there aren't any
factors left, though.  Let's look at the same example again:

You may have noticed that both 48 and 32 are even, so it's pretty
obvious that they both share two as a factor.  So you could start by
dividing both by two:

48/2       24
------  =  ----
32/2       16

Now you might notice that 24 and 16 are both divisible by four, so you
can go ahead and divide again:

24/4       6
------  =  ---
16/4       4

Finally, we see that these are even and can be divided by 2 again:

6/2       3
-----  =  ---
4/2       2

I hope this has been helpful.  I would suggest you find a math book
that has some problems with answers given so that you can practice
reducing fractions for a while, or maybe you could ask someone who
knows how to make some problems for you to practice.  Good luck!

-Doctor Byron,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
Elementary Fractions

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