GCSE Maths Fractions, decimals & percentages questions by topic

This question is about conversions.

1. (a)Write 0.7 as a fraction in its simplest form.[1]
2. (b)Write 9⁄40 as a decimal.[1]
3. (c)Write 0.185 as a percentage.[1]
4. (d)Write 3.5 as a mixed number.[1]

A shop applies a discount.

1. (a)A coat costs £80. Work out the price after a 25% discount.[2]
2. (b)A different shop sells the same coat for £72. Write £72 as a percentage of £80.[2]

Sarah spends her money in stages.

1. (a)Sarah has £90. She spends ⅖ of it on a rail ticket. How much does the ticket cost?[2]
2. (b)She spends 25% of the remainder on lunch. How much does lunch cost?[2]
3. (c)How much money does Sarah have left?[1]

A bakery compares two flours.

1. (a)A 1.5 kg bag of plain flour costs £1.80. A 2 kg bag of strong flour costs £2.60. Which is cheaper per kilogram?[3]
2. (b)The price of the strong flour bag rises by 5%. Work out the new price.[1]

A youth club has 120 members.

1. (a)5⁄8 of the members play football. Work out how many members play football.[2]
2. (b)15% of the members attend a drama workshop instead. Work out how many members attend the workshop.[2]

A fruit punch is mixed in jugs.

1. (a)One jug needs 2⁄5 litre of orange juice and 0.35 litre of mango juice. Work out the total volume of juice in one jug, in litres.[2]
2. (b)A bottle holds 6 litres of juice. Work out the greatest number of full jugs that can be made.[2]

Percentages of quantities and changes.

1. (a)Work out 34% of 450.[2]
2. (b)A value increases from 64 to 80. Find the percentage increase.[3]

Original values.

1. (a)After a 20% increase, a gym membership costs £564 per year. Work out the cost before the increase.[2]
2. (b)In a sale, a bicycle’s price falls by 18% to £494. Work out the price before the sale.[3]

A trainer’s price is changed twice.

1. (a)Trainers cost £72. The price rises by 25%. Work out the new price.[2]
2. (b)In a clearance the new price then falls by 25%. Work out the clearance price.[2]
3. (c)Explain why the clearance price is below £72.[1]

A quiz team’s scores are compared.

1. (a)In round one, Ama scores 17 of 20. Write this as a percentage.[2]
2. (b)In round two, Ben scores 33 of 40. Who performed better, by how many percentage points?[2]

A gym increased its monthly charge twice in one year.

1. (a)The charge was £30. It rose by 20% in January, and the new charge rose by 4% in July. Work out the charge after the July rise.[3]
2. (b)Write down the single multiplier for the two rises combined.[1]
3. (c)Use your multiplier to check your answer to part (a).[1]

Ben invests £2 000 in one of two banks for 3 years.

1. (a)Bank A pays 3% simple interest per year. Work out the total interest Ben would earn with Bank A.[2]
2. (b)Bank B pays 3% compound interest per year. Work out the final balance with Bank B, to the nearest penny.[2]
3. (c)Work out which bank gives Ben more interest, and by how much.[2]

Calculator not allowed for this question. (Higher)

1. (a)Using algebra, prove that 0.4̇5̇ can be written as 5⁄11.[3]
2. (b)Hence write 0.4̇5̇ + 3⁄11 as a single fraction in its simplest form.[3]

Compound interest and depreciation. (Higher)

1. (a)Elena invests £2500 at 2.4% compound interest per year. Work out her balance after 3 years, to the nearest penny.[3]
2. (b)A van worth £18 000 depreciates by 12% per year. Work out its value after 2 years.[2]
3. (c)Write down one assumption behind your answer to part (b).[1]

A shop’s pricing puzzle. (Higher)

1. (a)A fridge is priced at £340. In a sale its price falls by 15%. Work out the sale price.[2]
2. (b)At the till, a loyalty card takes a further 10% off the sale price. Work out the final price.[2]
3. (c)Show that the overall discount is 23.5%.[2]

Finding the rate. (Higher)

1. (a)A savings account pays compound interest at a fixed rate r% per year. £1000 grows to £1060.90 in 2 years. Show that (1 + r⁄100)² = 1.0609.[2]
2. (b)Find r.[2]
3. (c)Work out how much £1000 would be worth in this account after 5 years, to the nearest penny.[3]

This question is about recurring decimals.

1. (a)Using x = 0.4̇5̇ (that is, 0.454545…), show that 0.4̇5̇ = 5⁄11.[3]
2. (b)Hence convert 0.7̇2̇ (0.727272…) to a fraction in lowest terms.[2]

A craft shop sells picture frames.

1. (a)In a sale, a frame costs £96 after a 25% discount. Work out the original price.[3]
2. (b)A rival shop sells the same frame for £104 and promises a further 20% off next week. Work out whether next week's price beats £96, and by how much.[3]