You are here:

Word Problems/Comparing Fractions



Can you verify whether or not the following method that I used to compare fractions is a reliable method?

Which fraction is larger  5/9 or 3/14?

I determined which fraction is closer to the whole number 1.

5/9 is closer to 1 by adding only 4, 1/9.  With 3/14, 11, 1/14 are needed to equal 1.  So I reasoned that the fewer same denominator terms needed to get to 1 would indicate that that fraction is larger.  The more same denominator terms are needed would indicate that that fraction is smaller. 5/9 needs only 4, 1/9 and 3/14 needs 11, 1/4. So 5/9 is larger than 3/14.

Is this method always reliable in determining which fraction is larger or smaller?   It is much easier to compare fractions using this method than to convert to decimals or to change both fractions to the same denominator. Nevertheless, I have never seen this method explained in any textbooks.

I thank you for your reply.

A way that works every time is to multiply the top and bottom of each fraction by the denominator of the other fraction.  This gives (14/14)(5/9) and (3/14)(9/9).
Multiplying these out gives 60/126 and 27/126.

Since they both have the same denominator, it can be seen the 60 is greater than 70,
so its the first fraction that is bigger.

Another way to do it is to note that 5/9 = 0.5555... and 3/14 0.285714285714...

Doing this shows that the first fraction is greater than the second fraction.

Word Problems

All Answers

Answers by Expert:

Ask Experts


Scott A Wilson


I have answered every question that was a story problems that had any relation to math for which an answer existed. I have ever answered some questions which had a vague relation to math, but still related.


My experience is from when I started doing story problems in grade school. I have been assisting, helping, and bringing smiles to many others ever since. Are you the next one?

In over 850 questions answered to other users. Maybe you're the next one ...

I received a BA in Mathematical Sciences from OSU and a MS in Mathematics from OSU as well.

Awards and Honors
I earned Both my BS degree and MS degree with honors for having such a high grade point average.

Past/Present Clients
I have answered hundreds and hundreds of students at OSU in the 80's and over 8,500 questions right here, but only a little over 850 of them have been word problems.

©2017 All rights reserved.