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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.



Problem setup

How do the green-shaded portions of the figure above show that an operation with the fractions 2/3 and 1/4 has been completed?


Plans to Solve/Investigate the Problem

I will determine how the shaded portions of the figure is related to the non-shaded portions of the figure.



Investigation/Exploration of the Problem

The rectangle is cut into thirds horizontally.  The figure is also cut into fourths vertically.  The shaded portions represent only 2 of the 12 total portions of the figure. 

If one were allowed to color the figure in from the start, two thirds of the original horizontal rows would be shaded in, representing the 2/3 of the whole.


One fourth of the original vertical columns can be colored in to represent 1/4 of the whole.


The intersection of these two columns are the area of overlap between these two actions.


 It is the same area as pictured on the original problem.  It shows 2 of the 12 sections which have been 'colored in' twice, 2/12 of the whole. 

Since I have been repeatedly using the word 'of' in the explanation, I would assume that the figure in the original problem is the result of multiplication:  2/3 of 1/4 = 2/12.  

Extensions of the Problem

How could you show 2 1/2 x 1/4 using a model like that above?




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