How Egyptian Fractions Make Dividing a Cake a Piece of Cake


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?

Step 1:

Number of cakes -> 5

Number of family members -> 6

Fraction -> 5/6

Step 2:

5/6 = 1/2 + 1/3

That means each family member will receive half and one-third of a cake!

This lesson was featured in the Mad Maths section under the topic Fractions in Joyous Learning's P6 Mathematics curriculum.

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