
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 7th, 2007, 07:19 AM  #1 
Senior Member Joined: Jan 2007 From: India Posts: 161 Thanks: 0  Any method to compare fractions??
Hi friends, A long time since I posted here. My query is * Is there any method/shortcut other than reducing them to decimals to compare 2 fractions say, 25/27 and 65/68 and say which is greater. It is clear that (a+x)/(b+x) is greater than a/b. Using tis in our example, we can say that 25/27 is smaller than (25+40)/(27+40) or 65/67. But it seems nothin can b said abt 25/27 and 65/68..... Can someone help.. 
October 7th, 2007, 08:55 AM  #2  
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  Quote:
Quote:
i. a/b>c/d ii. a/b=c/d iii. a/b<c/d Multiply by bd on both sides, and we get i. ad>bc ii. ad=bc iii. ad<bc Do some multiplication arithmetic for those, and you can determine if it's equal, or greater, or less of between those two fraction values without doing arithmetic decimal values. For example, 1/2 and 2/3 Multiply (2)(3) on both fractions (1)(3) and (2)(2) 3 and 4 Therefore, 2/3 is greater than 1/2.  
October 7th, 2007, 08:58 AM  #3 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
Other way to solve is to find the LCM of the two denominators of a/b and c/d, and let lcm(b, d)=m, and therefore, p/m and q/m (p and q are the new numerator values, so you will need to find p and q), and p/m=a/b and q/m=c/d, so therefore you will need to determine whether i. p>q ii. p=q iii. p<q to find which fraction is greater, less, or equal. 
October 7th, 2007, 10:27 AM  #4 
Senior Member Joined: Dec 2006 Posts: 1,111 Thanks: 0 
Hey, it's good to see you again, 'arun'! It's easy to tell if two fractions are equal, because all you have to do is flip one of the them and then multiply it by the other. It the result is 1, then they are equal. I'm tempted to say this also works, but I have no proof for it: Flip the second of your two fractions and multiply it by the first. If the result is larger than one, then the second fraction is less than the first. Else if the result is less that one, then the second fraction is greater than the first. Can anyone prove this? 
October 8th, 2007, 02:12 AM  #5  
Senior Member Joined: Jan 2007 From: India Posts: 161 Thanks: 0  Quote:
Quote:
Now wen the second fraction is flipped, it is 1/Y . Multiply wit X to get X/Y. If this is greater than 1, it implies X> Y else Y>X... While flippin and multiplyin, wat we indirectly do is multiply the fractions wit the LCM of the denominators(b,d) and compare them ie., (a/b) * bd and (c/d)*bd which is ad and bc ( comparing this "ad" and "bc" is nothing but flippin the second fraction Y and multiplyin with the first fraction X.....) { Remember this emoticon infinity }  

Tags 
compare, fractions, method 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
compare s and t  Albert.Teng  Algebra  8  August 24th, 2013 10:21 AM 
How to compare two objects?  Natalia  Abstract Algebra  1  July 6th, 2013 03:27 PM 
How can I compare these two variables? Statistics  Socialgain  Probability and Statistics  0  April 19th, 2013 12:10 PM 
Integral  compare solution  debad  Calculus  9  July 1st, 2012 02:18 AM 
Compare  math4u  Calculus  0  December 22nd, 2009 12:54 AM 