Egyptian Fractions
Writing a fraction as a sum of distinct unit fractions.
Key idea
Writing a fraction as a sum of distinct unit fractions.
In depth
The Egyptians wrote fractions as sums of distinct unit fractions (numerator 1). Any positive fraction can be written this way using a greedy method: subtract the largest unit fraction that fits.
Worked example
3/4 = 1/2 + 1/4. And 2/7 = 1/4 + 1/28.
Formula
Real-world uses
- Historical problem-solving such as splitting loaves into unit fractions
- Puzzles in number theory
Common mistake
Repeating the same unit fraction; the terms must be distinct.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Egyptian Fractions?
Writing a fraction as a sum of distinct unit fractions. It is a topic at the expert level in Arithmetic & Number Sense.
What is the formula for Egyptian Fractions?
The key formula is 3/4 = 1/2 + 1/4.
Where is Egyptian Fractions used in real life?
Real-world examples: Historical problem-solving such as splitting loaves into unit fractions; Puzzles in number theory.
What should I learn before Egyptian Fractions?
Make sure you are comfortable with Ancient Number Systems, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Egyptian Fractions?
Repeating the same unit fraction; the terms must be distinct.
How can I practise Egyptian Fractions?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Egyptian Fractions?
Move on to Continued Fractions Intro next.
Related expert topics in Arithmetic & Number Sense
- Continued Fractions Intro – Nested fractions that give best rational approximations of reals.