An exchange rate tells you how many units of a foreign currency you get for one pound. Knowing whether to multiply or divide is the single decision that determines whether every currency conversion answer is right or wrong. Get that right and the arithmetic is straightforward — it is just a multiplication or division.
What is an exchange rate?
An exchange rate is a ratio comparing the value of one currency to another. For example:
£1 = €1.18 (you get 1.18 euros for every pound you exchange)
Exchange rates change daily because they depend on international trade, inflation, and other economic factors. In exam questions you are always given the rate — you never need to know the real-world rate.
How do you convert pounds to a foreign currency?
To convert from pounds to a foreign currency, multiply the number of pounds by the exchange rate.
Worked example: Convert £250 to euros, using the rate £1 = €1.18.
- Multiply: 250 × 1.18 = €295.
Think of it this way: if £1 gives you €1.18, then £250 gives you 250 times as many euros: 250 × 1.18 = 295.
Second example: Convert £80 to US dollars, given £1 = $1.27.
- Multiply: 80 × 1.27 = $101.60.
How do you convert a foreign currency back to pounds?
To convert from a foreign currency back to pounds, divide by the exchange rate.
Worked example: Convert €354 to pounds, using £1 = €1.18.
- Divide: 354 ÷ 1.18 = £300.
The logic: if €1.18 buys you £1, then €354 buys you 354 ÷ 1.18 = 300 pounds.
Memory trick: Pounds → foreign: multiply (×). Foreign → pounds: divide (÷).
How do you compare prices in two different currencies?
When a question asks which is better value, convert both prices into the same currency and compare.
Worked example: A camera costs £85 in London and €98 in Paris. The exchange rate is £1 = €1.18. Which city offers the better price?
Method 1 — convert the Paris price to pounds: €98 ÷ 1.18 = £83.05
Since £83.05 < £85, the Paris price is cheaper.
Method 2 — convert the London price to euros: £85 × 1.18 = €100.30
Since €100.30 > €98, the Paris price is still cheaper. ✓
Both methods give the same conclusion. Choose whichever direction feels more natural for the question.
How do exchange rates appear as conversion graphs?
Some KS3 questions give an exchange-rate conversion graph rather than a numerical rate. The graph is a straight line through the origin with a positive gradient.
To use a conversion graph:
- Find the value you want to convert on one axis.
- Read across (or up) to the line.
- Read the equivalent value on the other axis.
Reading gradient as a rate: if the graph shows euros on the y-axis and pounds on the x-axis, the gradient = euros per pound = the exchange rate. For a line through (0, 0) and (100, 118), the gradient = 118/100 = 1.18, confirming £1 = €1.18.
What units and rounding should you use?
| Currency | Standard rounding | Example |
|---|---|---|
| Pounds (£) | Nearest penny (2 d.p.) | £83.05 |
| Euros (€) | Nearest cent (2 d.p.) | €98.00 |
| US dollars ($) | Nearest cent (2 d.p.) | $101.60 |
| Japanese yen (¥) | Nearest yen (0 d.p.) | ¥12 345 |
Always round at the end, not during the calculation. Write units in your final answer — a bare number without a currency symbol earns no marks.
Frequently asked questions
What if the exchange rate is given the other way round (e.g. €1 = £0.85)?
Flip the operation. If €1 = £0.85, then to convert euros to pounds you multiply by 0.85; to convert pounds to euros you divide by 0.85. Alternatively, find the equivalent rate for £1 first: £1 = 1 ÷ 0.85 = €1.176, then proceed as above. Always check your answer makes sense: you should get slightly more euros than pounds if the euro is the weaker currency.
How do bank charges affect exchange rate problems?
In exam questions, bank charges are sometimes given as a flat fee or a percentage. Subtract the fee after converting, or increase the amount you need to convert to account for the fee. For example, if a bank charges 2% commission: effective amount = converted total × (1 − 0.02) = converted total × 0.98.
What is the difference between an exchange rate and a conversion graph?
They show the same information in different forms. An exchange rate is a number (e.g. £1 = €1.18). A conversion graph is a visual representation of the same rate as a straight line through the origin. You can read approximate conversions from the graph quickly, but for exact answers, using the numerical rate and a calculator is more accurate.
Why is it always multiply to go abroad and divide to come home?
If you think of it in terms of one pound giving you more than one unit of a weaker foreign currency (like euros or dollars for a British traveller), then multiplying gives you the larger foreign number. Dividing brings you back to the smaller pound amount. This direction rule breaks down if sterling is the weaker currency, so it is safer to check: does your answer make logical sense? A holiday budget of £500 converted to euros should give you a number larger than 500.
For ratio and proportion practice with Professor Pi, visit aitutors.me.