IGCSE Maths Fractions, decimals, percentages topical questions

Convert between forms.

1. (a)Write 0.45 as a fraction in its simplest form.[1]
2. (b)Write 7/20 as a decimal.[1]
3. (c)Write 62.5% as a fraction in its simplest form.[2]

Work out 3¼ − 1⅚.

1. (a)Write each mixed number as an improper fraction.[1]
2. (b)Find the difference as a mixed number in its lowest terms.[2]

A train leaves at 09 40 and arrives at 13 05.

1. (a)How long does the journey take, in hours and minutes?[2]
2. (b)The timetable lists the same journey as 3.4166… hours on a calculator. Explain what the display means.[1]

A recipe uses 3/4 of a cup of flour for each batch of biscuits.

1. (a)Find the flour needed for 5 full batches, as a mixed number.[2]
2. (b)How many full batches can be made from 5 cups of flour?[2]
3. (c)Write your answer to part (a) as a decimal.[1]

Here are four values: 0.68, 13/20, 0.705, 27/40.

1. (a)Write the four values in ascending order.[3]
2. (b)State which of the four values is closest to 2/3.[1]

Fractions and order of operations.

1. (a)Work out 1¾ ÷ 1½, giving your answer as a mixed number.[3]
2. (b)Evaluate 2 + 3 × (7 − 4)².[2]

A shop sells a coat for 144 after a 25% reduction.

1. (a)Find the original price of the coat. (Extended)[2]
2. (b)During a later sale the original price is reduced by 30%, then a further 10%. Find the overall percentage reduction. (Extended)[3]

Money and currency.

1. (a)The exchange rate is £1 = €1.15. Convert 230 euros to pounds.[2]
2. (b)A wage of 8.40 per hour is paid for 7.5 hours. Calculate the pay, giving your answer in dollars and cents.[2]

A restaurant bill is 84 before service. A 10% service charge is added, and the total is shared equally between 4 friends.

1. (a)Find the total bill including service.[2]
2. (b)Find each friend’s share.[1]
3. (c)The friends pay with four 20 notes. Find the total change they receive.[2]

A water tank is 2/3 full. After 90 litres are drained, the tank is 1/2 full.

1. (a)Find the fraction of the tank that was drained.[2]
2. (b)The capacity is a whole number of litres. Show that the capacity is 540 litres.[2]
3. (c)Find the number of litres now in the tank.[1]

Two savings accounts both start with 2 400. Account A pays 6% simple interest per year; account B pays 6% compound interest per year.

1. (a)Find the value of account A after 4 years.[2]
2. (b)Find the value of account B after 4 years, correct to the nearest cent.[2]
3. (c)Find the difference between the two values after 4 years.[2]

A machine is bought for 64 000. Its value depreciates by 20% in the first year and by 12% of the new value in each following year. (Extended)

1. (a)Find its value after 1 year.[1]
2. (b)Find its value after 4 years, correct to 3 significant figures.[3]
3. (c)Find the overall percentage decrease over the 4 years.[3]

A club had 240 members in 2020. Membership rose by 25% in 2021, then fell by x% in 2022 to leave 225 members. (Extended)

1. (a)Find the number of members after the 2021 rise.[1]
2. (b)Find the value of x.[3]
3. (c)Find the overall percentage change from 2020 to 2022.[2]

Two shops sell the same coffee. Shop A sells a 750 g bag for 13.50. Shop B sells a 500 g bag for 8.95, with three bags for the price of two.

1. (a)Find the cost of Shop A’s coffee per 100 g.[2]
2. (b)Find the cost of Shop B’s coffee per 100 g when three bags are bought.[2]
3. (c)Which shop is better value, and by how much per 100 g? Give the difference correct to 2 decimal places.[2]