Adding Fractions

Date: 08/13/97 at 09:56:20
From: Maria Angelica P. Bocade
Subject: fractions

          1                              3 
Sally ate - of a cake and her sister ate - of it.
          8                              8
What fraction did they eat altogether?

I've tried so hard to solve this question!

Thanks,
Angel                          

Date: 08/13/97 at 11:23:04
From: Doctor Mike
Subject: Re: Fractions

Hello Angel,   
   
It's nice you are starting to learn about fractions. Usually
fractions are introduced by talking about dividing something up
into a certain number of equal sized pieces, and then focusing
on just a PART of the whole, consisting of some of those pieces.
   
I want to draw a picture to help you understand. Most cakes are
round, and that's hard to draw well with a keyboard, so I'll draw
a long thin cake here, and show it divided up into 8 equal parts: 
       _________________________________________________
       |     |     |     |     |     |     |     |     |
       |  1  |  2  |  3  |  4  |  5  |  6  |  7  |  8  |
       |_____|_____|_____|_____|_____|_____|_____|_____|
   
One eighth of the cake is 1 of those 8 equal parts. Three eighths
of the cake is 3 of those 8 equal parts. Let's re-draw the cake 
to show what Sally and her sister ate : 
       _________________________________________________
       |     |                 |     |     |     |     |
       |Sally|  Sally's sister |  5  |  6  |  7  |  8  |
       |_____|_________________|_____|_____|_____|_____|
     
As you can see, exactly 4 of the 8 pieces have been eaten by the two
sisters. This is half of the cake. When the cake is divided up into 
8 pieces, half of the cake corresponds to 4/8 of the cake.  
  
Let's explore some other ways to divide up the cake.  If you make
only 2 pieces by cutting it right down the center you get : 
       _________________________________________________
       |                       |                       |
       |           1           |           2           |
       |_______________________|_______________________|
    
In this cake, a half of it would be just one of the 2 big pieces.
So, 1 of the 2 big pieces is the same part of the cake as 4 of the
smaller pieces.  Writing this with fractions it looks like : 
    
                1         4   
              -----  =  -----
                2         8   
    
and we often write that as  1/2 = 4/8  to save space.  If you divide 
the cake into 52 pieces, then half of the cake would be 26 pieces :
    
                1         26   
              -----  =  ------
                2         52   
  
So, finally, the answer to your question is that the sisters ate
4/8 of the cake, which is the same as 1/2 of the cake.  And as we
saw there are many other equivalent ways to write that fraction.
   
I hope this helps.   Enjoy fractions!    

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