Exchange rate: £1 = €1.20. How many euros is £10?
Multiply by 1.20.
£10 × 1.20 = €12.
Currency Conversion
Currency conversion involves changing values between different currencies using exchange rates. This is a real-life application of ratio and unit conversions, and requires careful multiplication or division depending on the context.
Overview
Currency conversion means changing an amount of money from one currency into another.
To do this, you use an exchange rate.
\( \text{new amount} = \text{old amount} \times \text{exchange rate} \)
In GCSE questions, you may need to convert from pounds to euros, dollars to pounds, or compare prices in different currencies.
What you should understand after this topic
- Understand what an exchange rate means
- Know when to multiply and when to divide
- Convert between different currencies
- Round money correctly
- Solve exam-style foreign money problems
Key Definitions
Currency
A type of money used in a country, such as pounds, euros or dollars.
Exchange Rate
The rate used to convert one currency into another.
Convert
Change from one unit or currency to another.
Foreign Currency
Money from another country.
Equivalent Value
The same amount of money expressed in a different currency.
Rounding Money
Usually to 2 decimal places because money is normally written to the nearest cent or penny.
Key Rules
Multiply if the rate is “for 1”
Example: £1 = €1.20, so pounds to euros means multiply by 1.20.
Divide to go backwards
If you want euros back to pounds, divide by 1.20.
Read the rate carefully
The direction of the exchange rate matters.
Round money sensibly
Usually to 2 decimal places unless told otherwise.
Quick Recognition
£1 = €1.20
Pounds to euros: multiply by 1.20
€ to £
Go back by dividing by 1.20
Same direction
Use the rate as given
Opposite direction
Use the inverse operation
How to Solve
What is currency conversion?
Currency conversion means changing money from one currency into another using an exchange rate.
Currency conversion is a real-life application of ratio introduction.
Main idea
Always read the exchange rate carefully before deciding whether to multiply or divide.
Understanding exchange rates
£1 = €1.20
This means every 1 pound is worth 1.20 euros.
To change pounds into euros, multiply by 1.20, making sure the units are consistent as in units and conversions.
To change euros back into pounds, divide by 1.20.
Exam tip: Write the exchange rate above your working so you use it the correct way round.
How to decide whether to multiply or divide
Why this matters: Most currency mistakes happen when the exchange rate is used the wrong way round.
Going with the rate
If the rate says £1 = €1.20, then pounds to euros uses multiplication.
Going back the other way
Euros to pounds uses division.
Check the units
Write what you start with and what you want to end with.
Estimate
Use rough mental maths to check whether your answer makes sense.
Rounding money
Money is usually given to 2 decimal places.
\( £23.456 \approx £23.46 \)
Rounding money uses the same skills as place value and rounding.
Example Questions
Edexcel
Exam-style questions inspired by Edexcel GCSE Mathematics, focusing on converting between currencies using given exchange rates.
Edexcel
The exchange rate is £1 = €1.20. Convert £50 into euros.
Edexcel
The exchange rate is £1 = $1.35. Convert £80 into US dollars.
Edexcel
The exchange rate is £1 = €1.25. Convert €100 into pounds.
Edexcel
A camera costs $540. The exchange rate is £1 = $1.50. Find the cost in pounds.
Edexcel
The exchange rate is £1 = €1.18. How many euros can be bought with £250?
AQA
Exam-style questions based on the AQA GCSE Mathematics specification, emphasising multi-step conversions and real-life contexts.
AQA
The exchange rate is £1 = €1.20. A hotel costs €360. Find the cost in pounds.
AQA
The exchange rate is £1 = $1.25. A tablet costs $375. Calculate the price in pounds.
AQA
£1 = €1.15. A traveller converts £400 into euros and spends €275. How many euros remain?
AQA
The exchange rate is £1 = €1.20. After returning from holiday, Maria converts €90 back into pounds. How much does she receive?
AQA
Explain why the amount received when converting money back is often less than the original amount.
OCR
Exam-style questions aligned with OCR GCSE Mathematics, focusing on reasoning, proportional thinking, and financial decision-making.
OCR
The exchange rate is £1 = $1.40. How many dollars will you receive for £65?
OCR
The exchange rate is £1 = €1.25. How many pounds are equivalent to €250?
OCR
A flight costs €480. The exchange rate is £1 = €1.20. Find the cost in pounds.
OCR
Two exchange bureaux offer the following rates: Bureau A: £1 = €1.18, Bureau B: £1 = €1.22. Which offers the better value for converting £500 into euros?
OCR
Describe the steps required to convert from one currency to another using an exchange rate.
Exam Checklist
Step 1
Read the exchange rate very carefully.
Step 2
Decide which currency you start with and which one you want.
Step 3
Multiply or divide correctly.
Step 4
Round your answer appropriately and include the currency symbol.
Most common exam mistakes
Direction mistake
Using the exchange rate the wrong way round.
Operation mistake
Multiplying when you should divide, or dividing when you should multiply.
Money mistake
Not rounding to sensible money values.
Symbol mistake
Forgetting whether the answer is in pounds, euros or dollars.
Common Mistakes
These are common mistakes students make when solving currency conversion problems in GCSE Maths.
Multiplying instead of dividing
Incorrect
A student multiplies by the exchange rate when they should divide.
Correct
Decide whether to multiply or divide based on the direction of conversion. If converting to a stronger currency, you usually divide; if converting to a weaker currency, you multiply.
Misreading the exchange rate
Incorrect
A student uses the exchange rate in the wrong direction.
Correct
Always read the exchange rate carefully. For example, if \(1\text{ GBP} = 1.2\text{ EUR}\), then converting GBP to EUR means multiplying, but converting EUR to GBP means dividing.
Forgetting currency symbols
Incorrect
A student writes the answer without a currency symbol.
Correct
Always include the correct currency symbol (e.g. £, €, $) in your final answer, as marks may be awarded for this.
Rounding too early
Incorrect
A student rounds intermediate values before completing the calculation.
Correct
Do not round until the final answer. Early rounding can lead to inaccurate results.
Using incorrect decimal places
Incorrect
A student gives an answer with too many decimal places.
Correct
Money should usually be given to 2 decimal places (e.g. £12.45). Always check the required level of accuracy.
Try It Yourself
Practise converting between currencies using exchange rates.
Foundation
Foundation Practice
Convert between currencies using basic exchange rates.
Exchange rate: £1 = €1.50. Convert £8 to euros.
Multiply pounds by the rate.
£8 × 1.50 = €12.
Exchange rate: £1 = €1.25. Convert €25 to pounds.
Divide by 1.25.
€25 ÷ 1.25 = £20.
Exchange rate: £1 = $2. Convert £7 to dollars.
Multiply by 2.
£7 × 2 = $14.
Exchange rate: £1 = €1.10. Convert €11 to pounds.
Divide euros by 1.10.
€11 ÷ 1.10 = £10.
Exchange rate: £1 = $1.50. Convert £20 to dollars.
Multiply by 1.5.
£20 × 1.5 = $30.
A student multiplies €30 by 1.20 to convert to pounds. What is wrong?
Think: reversing the exchange.
To go from euros to pounds, divide by the exchange rate.
Exchange rate: £1 = €1.40. Convert €28 to pounds.
Divide by 1.40.
€28 ÷ 1.40 = £20.
Exchange rate: £1 = $1.25. Convert £16 to dollars.
Multiply by 1.25.
£16 × 1.25 = $20.
Exchange rate: £1 = €2. Convert £6.50 to euros.
Multiply by 2.
£6.50 × 2 = €13.
Higher
Higher Practice
Solve multi-step currency conversion problems and reverse calculations.
Exchange rate: £1 = €1.25. A jacket costs €62.50. How much is this in pounds?
Divide by 1.25.
€62.50 ÷ 1.25 = £50.
Exchange rate: £1 = $1.20. A phone costs $240. Find the cost in pounds.
Divide by 1.20.
$240 ÷ 1.20 = £200.
Exchange rate: £1 = €1.50. A tourist exchanges £200. They pay a £5 fee. How many euros do they get?
Subtract fee first.
£200 − £5 = £195 → £195 × 1.50 = €292.50.
Exchange rate: £1 = €1.20. A person receives €96. How many pounds did they exchange?
Divide euros by rate.
€96 ÷ 1.20 = £80.
Exchange rate: £1 = $1.40. A hotel costs $350. How much is this in pounds?
Divide by 1.40.
$350 ÷ 1.40 = £250.
Exchange rate: £1 = €1.60. A person exchanges £75. How many euros do they get?
Multiply by 1.60.
£75 × 1.60 = €120.
A student converts €120 to pounds by multiplying by 1.20. What is wrong?
Reverse direction.
To convert euros to pounds, divide by the rate.
Exchange rate: £1 = $1.25. A person has $100. How many pounds is this?
Divide dollars by 1.25.
$100 ÷ 1.25 = £80.
Exchange rate: £1 = €1.10. Which calculation converts €55 to pounds?
Reverse conversion uses division.
To convert euros to pounds, divide by the exchange rate.
Exchange rate: £1 = €1.25. A person buys an item costing €75 and pays in pounds. How much do they pay?
Divide euros by 1.25.
€75 ÷ 1.25 = £60.
Games
Practise this topic with interactive games.
Games coming soon.