Understanding Egyptian Fractions

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📚 Part 1: Brief Lesson & Quick Check

An Egyptian fraction represents a positive rational number as a sum of distinct unit fractions (fractions with numerator 1), for example 2/3 = 1/2 + 1/6. A common method to find such a representation is the greedy algorithm: repeatedly subtract the largest possible unit fraction until you reach zero.

1. Which statement best describes an Egyptian fraction?

A sum of distinct unit fractions (numerator 1)

Any fraction written with denominator 1

A decimal representation with repeating 1s

A product of unit fractions

2. Which of these is an Egyptian fraction representation of 3/4?

1/2 + 1/4

1/4 + 1/4 + 1/4

1/3 + 1/6

1/5 + 1/20

3. True or False: Every positive rational number can be written as a sum of distinct unit fractions.

True

False

4. Which methods can help find Egyptian fractions? (Check all that apply)

Greedy algorithm (take largest unit fraction ≤ remaining)

Rewriting using common denominators and splitting fractions

Dividing into equal integer parts only

Using continued-fraction expansions or algebraic identities

✏️ Part 2: Practice Problems

5. Use the greedy algorithm to write 5/6 as an Egyptian fraction. Show your steps.

6. Find an Egyptian fraction representation for 4/13. Show work.

7. Write 7/10 as a sum of distinct unit fractions. Explain one check you use to confirm your result.

8. Match each fraction (left) with an equivalent Egyptian fraction (right). Draw lines between columns.

1. 1/2

2. 2/3

3. 3/5

A. 1/2 + 1/10

B. 1/2

C. 1/2 + 1/6

9. In one sentence, describe the greedy algorithm for finding Egyptian fractions.

Understanding Egyptian Fractions

Understanding Egyptian Fractions

📚 Part 1: Brief Lesson & Quick Check

✏️ Part 2: Practice Problems

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