## Egyptian Fractions

I discovered Egyptian Fractions while studying number theory at PROMYS. It was one of the long term projects that teachers could research, but didn’t really interest me at the time. When I saw a group of teachers present their research at the end of the summer I saw the implications for teaching fraction operations.

Egyptians used only unit fractions. To represent $\frac{3}{8}$ the Egyptians would have used the fraction $\frac{1}{4}$ and $\frac{1}{8}$. Together these fractions are equivalent to the original total, but use only unit fractions to express the sum. Once students have some knowledge of fraction addition they can begin to attack these problems. My students had also covered multiplication of fractions which made the process easier. Here is the activity they did:

Before introducing this activity in class students watched a five minute video about Egyptian Fractions. If you have access to United Streaming from Discovery Education, this video was a great way to start students thinking about how the Egyptians work. Our students study Ancient Egypt this time of year in history as well so this is a great activity.

One process introduced in the video is the “loaf of bread method.” Many of my students understood this method and stuck with it through the activity. If an Egyptian wants to share 5 loaves of bread with eight people he will start by splitting 4 loaves into halves. Then the leftover loaf will get split into eighths. Each person will then get half a loaf and an eighth of a loaf.  $\frac{5}{8}=\frac{1}{2}+\frac{1}{8}$

In this activity students were forced to work together to discuss methods. One single method will not work for all of the fractions.  This is one of those problems that students cannot divide and conquer.