A unit fraction is a fraction with a numerator of $1$, like $\frac{1}{3}$ or $\frac{1}{7}$or $\frac{1}{224}$.
An Egyptian Fraction is written as the sum of different unit fractions.
We can write $\frac{2}{3}$ and $\frac{3}{7}$ as Egyptian Fractions:
$\frac{2}{3}=\frac{1}{2} + \frac{1}{6}$
$\frac{3}{7} = \frac{1}{3} + \frac{1}{11} + \frac{1}{231}$.
I wonder whether all fractions can be written as Egyptian Fractions...
A good place to start investigating Egyptian Fractions is to explore whether all unit fractions can be written as the sum of two different unit fractions.
Here are two examples:
$\frac{1}{2} = \frac{1}{3} + \frac{1}{6}$.
$\frac{1}{6} = \frac{1}{7} + \frac{1}{42}$
Can you write other unit fractions as the sum of two unit fractions?
Can you write all unit fractions as the sum of two unit fractions?
Share your thoughts and discoveries