Math CentralQuandaries & Queries


Question from Nikheel, a student:

Amar baked a cake. john ate 1/6 of the cake. susan ate 1/5 of what was left. chan ate 1/4 of what was left. cindy ate 1/3 of what was left. luigi ate 1/2 of what was left.

how much of the original cake was left.

Hi Nikheel.

Start with a whole cake (mine is round).

1. John ate 1/6 of it. So divide it into 6 pieces and take one away.

This leaves (5/6 of the cake).

2. Susan ate 1/5 of what was left. So divide what is left into 5 pieces and take one away.

This leaves 4/5 of 5/6 of the cake = 4/5 x 5/6 = 4/6 of the cake.

3. Continue this process until you find out how much is left. The key is to multiply the fractions, simplifying (cancelling) as you go.

Stephen La Rocque.

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