Question

(grade 9 academic math) last night your sister made cake for dessert. she cut the cake into 15 equal slices but only 13 slices were eaten. the next day, you ate 1/5 of the remaining cake for a snack. what fraction of the cake was left?

Answer 1

`(8)/(75)`

Explanation:

If the cake was initially cut into 15 equal slices and 13 of those were eaten:

`(15)/(15)-(13)/(15)=(2)/(15)`

`(2)/(15)` slices would be left

`(1)/(5)of(2)/(15)=(1)/(5)*(2)/(15)=(2)/(75)`

Since you only had 2/15 left and ate 2/75, we can subtract these amounts to find the remaining amount of cake. However, fractions can only be subtracted if they have the same denominator:

`(2)/(15)=(10)/(75)`

`(10)/(75)-(2)/(75)=(8)/(75)`