Title
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 greenshaded 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 nonshaded 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?
Author & Contact
rrogers@rockdale.k12.ga.us
