Solve the following problem.
Pat used three-fourths of a bag of flour that was two-thirds full. How much of a full bag of flour did Pat use.
Here, we solve this problem by the use of an area model where we will use a rectangle to represent a bag of flour. We shade 
of the rectangle to show that we have two-thirds of a bag of flour.
Next, since Pat used 
of the bag of flour, we shade of the of the rectangle.
We now have 
of the rectangle that has been shaded twice; this is the region that represents the amount of flour used by Pat. Therefore, Pat used one-half of a full bag of flour.
Note that this problem is an example of 
. We could have also illustrated the problem with the following model which builds on the whole number area model for multiplication.
The diagram has 
shaded horizontally and shaded vertically. The solution is the amount of area shaded both horizontally and vertically.
Note that we have completed the multiplication problem: 
.
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Date last modified: June 7, 2010.
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By Kris Montis and Timothy Peil
