We begin with adding 
by using a rectangle to represent the whole and divided into ten equal-sized pieces.
First, we shade 
of a whole rectangle.
Next, to show the addition, we shade 
more.
We now have 
of the whole rectangle shaded. So, we conclude that 
.
Notice that we added tenths to tenths and our answer was in tenths. It appears that the rule for adding fractions that have the same denominator is to add the numerators and keep the common denominator.
We can still simplify the answer 
as in the previous sessions by using the Fundamental Law of Fractions 
or by division by the greatest common factor 
. So, we have 
.
Similarly, we subtract 
by using a rectangle to represent the whole with 7 parts shaded.
This represents the 
of a whole from which we will take 
of the whole rectangle away. Next, we subtract of the whole rectangle by crossing out or unshading 3 of the parts.
We conclude that 
which can be simplified to 
.
Here are two more examples with models.
Example: Use fraction strips for 
.
Example: Use an area model for 
.
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Date last modified: June 1, 2010.
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By Kris Montis and Timothy Peil