An exchange rate such as £1 = €1.18 tells you how much foreign currency each pound buys. Multiply by the rate to convert pounds into the foreign currency, and divide by the rate to convert back into pounds. To find the best value, compare prices for the same amount, such as the price per 100 g; the lowest unit price is the best buy.
Exchange rates and best value
- Pounds to foreign currency: × exchange rate
- Foreign currency to pounds: ÷ exchange rate
- Unit price = price ÷ amount
- Best value: the lowest price per unit (or the most per £1)
Converting pounds into another currency
An exchange rate of £1 = €1.18 means each pound is worth €1.18, so multiply the number of pounds by 1.18. £250 converts to 250 × 1.18 = €295. Check the answer makes sense: if the rate is more than 1, you get more euros than pounds.
Converting back into pounds
To convert from a foreign currency to pounds, divide by the exchange rate. With £1 = €1.15, €92 is 92 ÷ 1.15 = £80. Dividing gives a smaller number of pounds than euros, which matches a rate above 1.
Comparing prices in different countries
Convert both prices into the same currency before comparing. A pair of shoes costing €96 abroad, with £1 = €1.20, costs 96 ÷ 1.2 = £80 in pounds. If the same shoes cost £75 in the UK, the UK price is £5 cheaper.
Finding the best buy
To compare different pack sizes, work out the price per unit, such as the price per 100 g, per litre or per item. A 500 g pack for £2.40 is 48p per 100 g, and a 750 g pack for £3.45 is 46p per 100 g, so the larger pack is better value. You can also compare how much you get for £1.
Showing your working
Best-buy questions usually say “you must show your working”. Write the unit price for every option, using the same units, then state clearly which is the best value and why.
Worked examples
Example 1. The exchange rate is £1 = €1.18. Convert £250 into euros.
- Pounds to euros: multiply by 1.18.
- 250 × 1.18.
Answer: €295.
Example 2. The exchange rate is £1 = €1.15. Convert €92 into pounds.
- Euros to pounds: divide by 1.15.
- 92 ÷ 1.15.
Answer: £80.
Example 3. Shoes cost €96 in Spain and £75 in the UK. The exchange rate is £1 = €1.20. Where are they cheaper, and by how much?
- Spain: €96 ÷ 1.2 = £80.
- UK: £75.
Answer: Cheaper in the UK, by £5.
Example 4. Rice is sold in a 500 g bag for £2.40 and a 750 g bag for £3.45. Which is better value?
- 500 g: £2.40 ÷ 5 = 48p per 100 g.
- 750 g: £3.45 ÷ 7.5 = 46p per 100 g.
Answer: The 750 g bag, at 46p per 100 g.
Example 5. A shop sells one bottle for £1.80, or three for £4.50. Work out the saving per bottle with the three-pack.
- Three-pack: £4.50 ÷ 3 = £1.50 per bottle.
- £1.80 − £1.50.
Answer: 30p per bottle.
Common mistakes
- Multiplying when converting back to pounds. Foreign currency to pounds means divide by the rate.
- Comparing prices in different currencies. Convert both into the same currency first.
- Comparing total prices of different sizes. Compare the price per unit, not the total price.
- Using different units for unit prices. Compare per 100 g with per 100 g, not with per kg.
- Not stating the conclusion. Say clearly which option is the best value.
How exchange rates and best value are examined
Exchange rates and best buys are Foundation tier problem-solving topics in the 1MA1 and 4MA1 specifications, and they often include an instruction to show working. Questions ask you to:
- convert between pounds and another currency in either direction
- compare prices from two countries
- decide which pack size is the best value
- solve a multi-step money problem with a conversion
Questions of both kinds, with answers, are on the exchange rates worksheet. The proportion revision engine generates more.
Currency conversion is an example of direct proportion, and best buys use rates.
Frequently asked questions
How do you convert pounds to euros?
Multiply by the exchange rate.
How do you convert euros back to pounds?
Divide by the exchange rate.
How do you work out the best value?
Find the price per unit for each option and choose the lowest.