# Definition:Egyptian Fraction

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## Contents

## Definition

An **Egyptian fraction** is a fraction either:

- whose numerator is $1$

or

- which is $\dfrac 2 3$

All other fractional quantities are expressed as sums of different **Egyptian fractions**.

## Examples

### Egyptian Fraction $\frac 7 {10}$

- $\dfrac 7 {10} = \dfrac 2 3 + \dfrac 1 {30}$

## Examples of Double Unit Fractions

### Egyptian Fraction $\frac 2 7$

- $\dfrac 2 7 = \dfrac 1 4 + \dfrac 1 {28}$

### Egyptian Fraction $\frac 2 {11}$

- $\dfrac 2 {11} = \dfrac 1 6 + \dfrac 1 {66}$

### Egyptian Fraction $\frac 2 {97}$

- $\dfrac 2 {97} = \dfrac 1 {56} + \dfrac 1 {679} + \dfrac 1 {776}$

## Also see

## Historical Note

**Egyptian fractions** are so called because they were the only means of representations of fractional values in the mathematics of ancient Egypt.

David Wells, in his $1986$ book *Curious and Interesting Numbers*, refers to $2 / 3$ as "uniquely unrepresentative".

## Sources

- 1992: David Wells:
*Curious and Interesting Puzzles*... (previous) ... (next): Egyptian Fractions - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): Glossary - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $1$: Tokens, Tallies and Tablets: The Ancient Egyptians