## Compounded Fractions and Percentages

Some fractions and percentage questions need to be read and well understood. Typical of these are questions that require you to find fractions or percentages of things and then fractions or percentages of the remainder.

Example: If I start with £50, spend 20% of this on sweets and 30% of the remainder on a train fare, how much is left?

20% of £50 is so after I have bought the sweets I have £50-£10 =£40 left.

30% of this remainder is spent on a train fare so I need to find 30% of £40. After having paid the train fare I have £40-£12=£28 left.

Notice that in the question it states 30% of the remainder' so I need to find 30% of the money I have left after having bought the sweets.

Example: If I start with £40, spend a quarter of this on chocolate and half on a birthday present, how much is left?

A quarter of £40 is so after I have bought the chocolate I have £40-£10 =£30 left.

I also spend half the money on a birthday present so I need to find half of £40.

Half of £40 is I had £30 left after having bought the chocolate. Now I have £30-£20=£10 left.

Notice that the question says I spent a quarter of the money on chocolate and half of the money on a birthday. Both fractions (a quarter and a half) refer to fractions of the money I started with and not on any amount left after I bought the chocolate.

Example: If I start with £450, spend a third on a garage bill and a quarter of the remainder on books, how much is left?

A third of £450 is so after having paid the garage bill, £450-£150=£300 is left.

I spend a quarter of the remainder on books so I need to find a quarter of £300 and subtract it.

A quarter of £300 is so after having bought the books £300-£75=£225 is left. 