Examples of Fraction Multiplication and Division

Date: 05/14/98 at 20:24:10
From: Allison
Subject: Fractions

I know how to add and subtract fractions, but I always get confused on 
how to multiply and divide them. I know how to reduce, so you don't 
need to teach me that part. But I have a big test soon and am in dire 
need. This test is for a job, so I would appreciate an answer as soon 
as possible.

Thank you,
Allison

Date: 05/16/98 at 16:47:38
From: Doctor Santu
Subject: Re: Fractions

Multiplying and dividing fractions can actually be easier than adding 
and subtracting them because multiplying and dividing do not require 
finding common denominators.

To multiply: write the fractions side-by-side, multiply the tops to 
get the new top ("numerator"), multiply the two bottoms to get the new 
bottom ("denominator"). Then simplify.

Example: multiply (12/25) and (40/81)

   12   40    480    96    32
   -- * -- = ---- = --- = ---
   25   81   2025   405   135

You can make it a bit easier by reducing first. Just like reducing a 
fraction by cancelling common factors of the top and the bottom, you 
are allowed, just before multiplying the tops together and the bottoms 
together, to cancel common factors of the top of one fraction and the 
bottom of the OTHER fraction. You can reduce the usual way, too. 
Remember: always cancel top against bottom.  

For the same problem as before:

   12   40 
   -- * --
   25   81

      4   40
   = -- * --   I cancelled a 3 from the 12 (top) and the 81 (bottom)
     25   27

      4    8
   = -- * --   I cancelled a 5 from 40 (top) against 25 (bottom)
      5   27

       32
   =  ---
      135

The answer has to be the same. The only reason for doing it this way 
is to avoid huge numbers. Smaller numbers usually make for more 
accurate mental arithmetic!

To divide, simply multiply by the reciprocal. For instance:

   (2/3) divided by (5/6)
   
is the same as
   
   (2/3) MULTIPLIED by (6/5)

You flip the number that's DOING THE DIVIDING, not the one that's 
being divided.

In this case, the answer will be:

   (2/3) / (5/6)
   
   = (2/3)*(6/5)  
   
   = (2/1)*(2/5)  I cancelled a 3 from 3 (top) and 6 (bottom)
   
   = (4/5)

Hope this helps, and hope you feel more comfortable with math as you
go along. :-)

-Doctor Santu, The Math Forum
Check out our web site! http://mathforum.org/dr.math/