Comparing Fraction Size: Two Methods

Date: 10/24/2001 at 00:52:28
From: Megan
Subject: Fractions

What fraction is greatest?

   5/13     2/5     7/15

I can't find a common denominator for all three. Can you please help 
me? 

Thank you!

Date: 10/24/2001 at 12:06:32
From: Doctor Sarah
Subject: Re: Fractions

Hi Megan - thanks for writing to Dr. Math!

You can find a common denominator by multiplying together the 
denominators of your fractions. For example, try 13 * 15 = 195 (you 
don't need to use the 5 because anything divisible by 15 will also be 
divisible by 5).  

You know that 195 is divisible by 13 and 15 (because those are the two 
numbers you multiplied together to get it), and by 5 because 195 ends 
in a 5. Now convert the numerators so you have equivalent fractions:

5/13 = 75/195
 2/5 = 78/195
7/15 = 91/195

So 7/15 is the greatest.

But sometimes it's easier just to convert your fractions to decimals 
by dividing the numerators by the denominators:

5/13 = .38461538461538
 2/5 = .4
7/15 = .46666666666666 (repeating forever)

Here you can see that each fraction is larger than the one before it.

Does this help?

- Doctor Sarah, The Math Forum
  http://mathforum.org/dr.math/