Multiplying Fractions and Mixed Numbers

Date: 03/12/97 at 19:41:52
From: Gloria Richardson
Subject: Multiplying Mixed Numbers

Dr. Math,

We have started multiplying fractions, and are now multiplying 
fractions by whole numbers.  I am really confused - can you help? 
Here's the kind of problem we're doing:

     1 1/3 X 1/4 = ?  

   2/3  X  1 1/3 = ?

We have to show our work and reduce our answers to lowest terms.

Thank you,
Justin

Date: 03/16/97 at 16:23:05
From: Doctor Reno
Subject: Re: Multiplying Mixed Numbers

Hi, Justin,

Fractions can be confusing because of all the times that we have to 
change them back and forth between mixed numbers and improper 
fractions. Once you understand why we use mixed numbers for some 
things and improper fractions for other things, I think you will have 
fewer problems with fractions.

A fraction like 2 2/3 is much easier to understand than an improper 
fraction like 8/3. When we see "2 2/3" we can immediately see in our 
head what we are talking about - whether it be candy bars, pies, or 
whatever. We can see two whole cakes and two-thirds of a third one. 
But if I tell you that I have 8/3 cakes, then you can't easily tell 
how many cakes I'm talking about, can you?

That's why when we talk about objects, we usually use mixed numbers.  
However, when we do math, fractions are MUCH easier to deal with! 

1 1/3 x 1/4  will be easier for us to multiply if we change the mixed 
number to a fraction:

4/3 x 1/4......then we simply multiply across, and we find that the 
product is 4/12.

And of course we teachers always want our students to "reduce" a 
fraction like 4/12 - the answer would be 1/3.

I think that you will have an easier time now.  Just remember to use 
improper fractions for your math and mixed numbers for talking about 
objects, and math will be easier. If you still have a problem, be sure 
to write back to Dr. Math!

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