You have investigated how the Egyptians expressed fractions as the sum of different unit fractions. A famous mathematician, Fibonacci, found a strategy for generating Egyptian fractions called the Greedy Algorithm.
At every stage of the algorithm, find the largest possible unit fraction that is smaller than the fraction you’re working on. Consider the fraction 11⁄12. The largest unit fraction that is smaller than 11⁄12 is 1⁄2 , and 11⁄12 – 1⁄2 = 5⁄12:.
11⁄12 = 1⁄2 + 5⁄12
The largest unit fraction that is smaller than 5⁄12 is 1⁄3, and 5⁄12 – 1⁄3 = 1⁄12:
11⁄12 = 1⁄2 + 1⁄3 + 1⁄12
Since 11⁄12 is now expressed as the sum of unit fractions, we are done!
Use the Greedy Algorithm for the following fractions: