Multiplying Fractions

Date: 1/28/96 at 22:0:41
From: Anonymous
Subject: Fractions

I don't know where to begin.  I need help with problems such 
as this one:

        3 1/4 x 3/4 = 

I'm trying to get my G.E.D. and I'm stuck on fractions so 
if you have anything on fractions that could help me do 
them easier I would really appreciate hearing about them 

Thank you very much,
Dennis Humphrey

Date: 1/29/96 at 11:25:50
From: Doctor Syd
Subject: Re: Fractions

Hello, Dennis!

We're glad you wrote.  Fractions can be very tricky, indeed.  
My 23-year-old sister still grumbles about having to learn fractions, 
in fact!  But if you can learn a few strategies, things will go 
much more smoothly.  

I will write fractions in the form p/q, with the slanted bar in 
this message, but when you do it, it will be easier to see if you 
can write the fractions with a horizontal bar... 

Okay...In problems where you are asked to multiply two fractions 
together, the best strategy is to get both fractions into the form 
p/q.  How do we write 3 1/4?  Well, 3 1/4 means we have 3 + 1/4 of 
whatever we have, right?  And, 3 = 3/1 So, how do we add these two 
fractions?  We find a common denominator!  

The least common denominator of two numbers is the smallest number 
such that both numbers divide it.  So, in our case, the smallest 
number such that 1 and 4 divide that number is just 4, right?  So, 
we want both of the fractions we are adding up to have a 4 in the 
denominator.  

To get a 4 in the denominator of the 3/1 fraction, we multiply 
by 4/4 which is just 1, so this should not change the number.  
So, 3 = 3/1 * 4/4.  To multiply two fractions together, you just 
multiply the numbers in the numerators (the numbers above the 
division line) and the numbers in the denominators (the numbers 
below the division line).  So, in this case we get that 3 = 3/1 * 
4/4 = 12/4

Now we are ready to figure out this:

3 + 1/4 = ?

We can now rewrite this as:

12/4 + 1/4 = ?

To add two fractions with the same denominator, you just add the 
numbers in the numerator and keep the denominator the same.

So, 12/4 + 1/4 = 13/4. 

Thus our answer is 13/4. 

So, back to the original problem (stick with me, here!  I know 
the explanation may seem long, but after you practice these 
methods on some problems it will be much better, I guarantee!)

To find out what 3 1/4 * 3/4 is, we rewrite the problem as:

13/4 * 3/4

Now, we've already practiced mulitplying two fractions of this 
form, sofollow that procedure, and you should get your answer!  

Write back if you need any more help!  

-Doctor Syd,  The Math Forum