Today we moved into the 2nd chapter of the book and looked at fractions. I’d actually heard the term “Egyptian fractions” before, but never really knew what it meant. The book gives a great explanation as well as several examples. With just two examples from me the boys were able to work through a couple of problems on their own.

I started with a quick introduction to the ideas behind Egyptian fractions:

With the introduction out of the way, I had the boys pick two numbers to form a fraction. They picked 8/13 which is quite a bit more complicated than the example in the first video, but also instructive. We work out that 8/13 = 1/2 + 1/10 + 1/70 + 1/910. There are also other ways to write 8/13 as a sum of reciprocals of integers. For example, 8/13 = 1/2 + 1/9 + 1/234. I wanted to stay with the “bread sharing” methods that the book used, though, and didn’t want to discuss multiple solutions just yet.

Now it was time for the kids to work through a problem on their own. My older son went first and worked through the fraction 7/10. He found it was equal to 1/2 + 1/6 + 1/30. Here I almost decided to show him how you could think of this as 1/2 + 1/5, but, again, I didn’t want to get into the multiple solutions today.

Finally my younger son gave it a shot and picked a big challenge – the fraction 11/17. He got a little confused by which number represented the loaves of bread and what number represented the people, but once we clarified that point he was able to work through to the end. He found that 11/17 = 1/2 + 1/8 + 1/48 + 1/816. Wow!

This was a fun project. It is definitely a neat historical lesson about fractions, but also provides a great way to review the way we think about fractions. Excited to try out more from this book with the boys next week.

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