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### Using Common Denominators to Compare Fractions

```
Date: 03/17/98 at 20:37:56
From: Tasha Thompson
Subject: pre-algebra

Here are the directions: write <, >, or = for each blank. Use
equivalent fractions to decide.

Here's an example: 3/8 ___ 4/9

I can't figure out how to do it. Can you tell me the answer and show
me how you got it?
```

```
Date: 03/18/98 at 11:23:17
From: Doctor Johnny
Subject: Re: pre-algebra

Tasha,

Hello there. My name is Dr. Johnny, and I am going to try to help you
compare fractions.

There are several ways that you can compare fractions, but since you
have expressed an interest in using equivalent fractions, that is what
I will try to explain.

Before we discuss how to compare fractions, we must answer the
question: "What is an equivalent fraction?" Equivalent fractions are
fractions that, although they have different numbers, they have
exactly the same value.

The first thing that you must do is consider a common denominator
(what will both denominators go into?). If you cannot see what both
denominators will go into, a common way to find a common denominator
is to multiply the two denominators together. NOTE: This may not be
the least common denominator, but it is a common denominator that will
serve the same purpose.

3     4
-     -  A common denominator is 72, which is 8 times 9.
8     9

Now that you have a common denominator, you must concentrate on
renaming the fraction. To do this, you must use division and
multiplication.

3    27
- = ---- Divide 8 into 72. Multiply the answer by 3. This renames
8    72  the fraction.

4    32
- = ---- Divide 9 into 72. Multiply the answer by 4. This renames
9    72  the fraction.

Now that you have the fractions with the same denominator, all you
have to do is compare the numerators 27 and 32. Since 27 < 32, the
fractions can be compared in the following manner:

27     32
--  <  --
72     72

So you can say that

3     4
-  <  -
8     9

I hope that this explanation will help you better understand how to
compare fractions by using equivalent fractions.

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

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