In ancient Egypt, fractions were usually given in unit-fraction form. Unit fractions are fractions with one as the numerator. Examples of unit fractions are 1/2, 1/3, 1/12, 1/145. Conversely, 2/3, 5/2, 4/7, etc., are not unit fractions.
Hence, in ancient Egypt, 2/3 would have been expressed this way:
1/2 + 1/6
Go on! Try adding the above two unit fractions and see if they total up to 2/3. Today, Egyptian fractions are mainly used in recreational maths; doing maths for fun with no obvious practical use.
Sometimes, however, Egyptian fractions can be useful in our daily lives. Take 2/3 again as an example. If we had 2 cakes to be shared equally among 3 persons, each person would get 1/2 of a cake and 1/6 of a cake. See visual representation below:
A, B and C represent the 3 persons sharing the 2 cakes and the parts they each receive are marked accordingly. The next visual representation of the “cut-out” cakes makes this even clearer.
Here's a worked example:
Casey baked 5 cakes to feed her family of 6 (herself included). What's an easier way to slice up her cakes than trying to cut up each into 6 slices?
Number of cakes -> 5
Number of family members -> 6
Fraction -> 5/6
5/6 = 1/2 + 1/3