operate on fractions!
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
Here, I must determine what operation
the above illustration shows.
Investigation/Exploration of the
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
to look at the problem in Geometers Sketchpad. You may need to save the
file and then open it in GSP.