Dividing Fractions

  The other day I was looking for new ways to present the concept of dividing fractions so students understand why they end up multiplying by the reciprocal.  I know as a teacher I have trouble teaching this because it is one of those processes we teach as the way its done.  I found a way but it is not as clear as this method.

I will start out by thinking Fawn Nguyen and her blog Finding Ways for this method.  It is cool and makes a lot of sense.  Look at the division problem 3/4 divided by 2/3.

Fawn uses rectangles as a way of creating the base for the problem so for 3/4 she recommends a 3 by 4 rectangle and the same 3 by 4 rectangle for 2/3.  3/4th of the squares are colored in to represent 3/4th of 1 while 2/3rds of the other rectangle is colored in to represent 2/3rds of 1.

3/4 and 2/3 are colored in.

 Now you count the number of shaded in squares for 2/3 and you discover 8 squares are colored in.  This is the number of squares that make 1 so you count the number of squares in the 3/4ths and find there are 9 squares colored in so you know you have 8 squares or 1 plus 1/8th left over or 1 1/8

 If you do the math you find it is correct because 3/4/2/3 is 3/4 * 3/2 or 9/8 = 1 1/8

This is one of the cooler ways I've seen to illustrate the concept for division.  Most of the sites simply tell people to invert and multiply but they do not provide a conceptual drawing to help explain.  I like this method and I'm going to play around with it to see if it works in a certain form.  I'll report back in a while on it.  Enjoy playing with this idea.