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/