Two resources from the UK for Egyptian fractions

This user-friendly resource from the University of Surrey offers detailed information about Egyptian

Excerpt from the Rhind Mathematical Papyrus

fractions (and lots of other teaching ideas around fractions) from professor Ron Knott.

It's a good starting point for understanding Egyptian fractions and how and why to calculate them in a variety of ways -- including Fibonacci's Greedy Algorithm as a last resort.

N-Rich maths from the UK has a related user-friendly page on Egyptian fractions