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Write-up


Let's operate on fractions!

Problem Statement
 

Using an area model for fractions, explain how the image below shows a particular operation is being performed on the given fractions, 2/3 and 1/4.

 

 

 

 

Plans to Solve/Investigate the Problem

Here, I must determine what operation the above illustration shows. 

Investigation/Exploration of the Problem

Breaking up the rectangle into thirds yields the following picture

 
 
 

 

Notice that there are 3 rows, hence the rectangle is divided into thirds.  I have shaded 2 of the 3 rows which equates to 2/3's of the rectangle.

 

Now if I want to find out what 1/4 looks like, I will need to divide my rows into four parts.

 

       
       
       

The shaded area is 1/4 of the entire rectangle.  Observe below what 2/3 of 1/4 looks like

 

       
       
       

So the operation that is taking place is multiplication  2/3*1/4 = 2/12 = 1/6.

Extensions of the Problem

Since students frequently miss the concept of multiplying fractions,  I would instruct my students to use this method to multiply various groups of fractions.

Author & Contact
mhouston@rockdale.k12.ga.us

 

Click here  to look at the problem in Geometers Sketchpad.  You may need to save the file and then open it in GSP.