MATH 110A: Mathematics for Elementary Teachers

Using pattern blocks to model division of fractions

We are answering the question: how many groups of 1/3 are there in 5/12?

1. The whole = 2 hexagons, therefore 5/12 is 5 triangles.
    

2. What is 1/3?  2 rhombi = 4 triangles.
    

3. How many  "2 rhombi" fit into 5/12, i.e. into 5 triangles?

                     One "2 rhombi" fits into 5/12 and we have a triangle left over.

  4.  How much does the one left-over triangle represent?

                    2 rhombi = 4 triangles. Thus 1 triangle is ¼ of "2 rhombi."

 Therefore, we have a total of 1 ¼ one-thirds in 5 /12.

The answer to our question is:    There are  1 ¼  groups of 1/3 in 5/12.