Putting Fractions in Order

Date: 01/24/2001 at 22:32:09
From: Mat
Subject: Ordering fractions

Dear Dr. Math,

I am trying to order fractions from least to greatest, but am having 
no luck. Could you please give me a hand?

Your friend,
Mat

Date: 01/25/2001 at 08:29:35
From: Doctor Rick
Subject: Re: Ordering fractions

Hi, Mat.

Which is greater, two quarters or four dimes? You solve this by 
converting each to cents: two quarters are 50 cents, and four dimes 
are 40 cents, so two quarters are greater.

You compare fractions the same way: convert each fraction to a common 
denominator. The thing that makes it a little harder than comparing 
money is that, with money, you always know you can choose a common 
denominator (or denomination) of 1 cent (1/100 dollar). With 
fractions, you first need to decide what denominator you can use.

Which is greater, 4/5 or 3/4? You can choose a common denominator of 
20, the product of the two denominators (5*4). This will always work, 
though it may not be the LEAST common denominator, so you may have 
bigger numbers to work with than necessary.

Convert 4/5 to 20ths: the denominator 20 is four times the denominator 
5, so you multiply the numerator 4 by 4, as well:

  4/5 = (4*4)/(5*4) = 16/20

Convert 3/4 to 20ths: the denominator 20 is 5 times the denominator 4, 
so you multiply the numerator 3 by 5, as well:

  3/4 = (3*5)/(4*5) = 15/20

Now, which is greater: 16/20 or 15/20? You just have to compare 
numerators, since the denominators are the same. Since 16 > 15, you 
know that 16/20 > 15/20, so 4/5 > 2/3. (In case you haven't seen it 
before, > means "is greater than.")

If you need to order three or more fractions, you can either put them 
all over a common denominator, or compare two at a time. If you choose 
the first approach, you will probably want to work with LEAST common 
denominators, because otherwise you could end up with some really big 
numbers.

If you have a particular problem you'd like us to walk through with 
you, we'd be happy to do so.

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