Question

Jared has iced 3/4 of a cake when he walks away to answer the phone. Kylie sneaks into the kitchen to steal a piece of cake. The stolen piece is 1/6 of the whole cake, and is 2/3 covered in icing. What fraction of the original cake remains not iced?

Answer 1

If Jared iced 3/4 of the cake, then 1/4 of the cake remains not iced. The stolen piece is 1/6 of the whole cake, so 1/6 of the remaining uniced cake is stolen, which is 1/6 * 1/4 = 1/24 of the whole cake. The stolen piece is 2/3 covered in icing, so 1/3 of the stolen piece is not iced. The uniced portion of the stolen piece is therefore 1/3 * 1/6 = 1/18 of the whole cake. If we subtract the uniced portion of the stolen piece from the uniced portion of the original cake, we get 1/24 - 1/18 = 1/72 of the cake remaining uniced. To express this as a fraction of the original cake, we need to divide by the total number of pieces the original cake was divided into, which is 24. This means that 1/72 of the original cake is uniced, which is equivalent to 1/3 * 1/72 = 1/216 of the original cake.