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This page sets out the method for exchange rates in the order you would use it, then walks through the full lesson explanation. For three complete worked examples with the slips that cost marks, see the Exchange rates topic page.
When you see '£1 = …', decide which way you are going before you touch the calculator.
When the same item has prices in two currencies, convert one so both are in the same currency.
£1 = €1.2 means each pound buys 1.2 euros.
Multiply pounds by 1.2 to get euros.
To change euros back into pounds, divide by the rate.
Multiplying both ways cannot be right.
Some exchanges charge a fee before or after the conversion.
Do the fee and the conversion as two steps, in the order the question says.
Work out how much of the foreign currency each offer gives for the same pounds.
The larger amount of foreign currency is the better deal when you are buying that currency.
Keep the currency symbol with the number.
A bare 12 is not an answer if the question asked for dollars.
If the rate is about 1, the two amounts should be similar.
If the rate is 3, the dollar amount should be about three times the pounds.
If you start with pounds, and the rate says what one pound buys, multiply. £36 at 1.25 euros per pound is 36 × 1.25 = 45 euros. The multiplication copies the “one pound” deal 36 times.
You can think of 1.25 as 1 + 0.25. Then 36 × 1 = 36 and 36 × 0.25 = 9, and 36 + 9 = 45. That split is a check, and it shows why the euro total sits above the pounds. Adding 1.25 once would only describe a single extra pound.
Method: 1. Start from the amount in pounds. 2. Multiply by how many foreign units one pound buys. 3. Keep the foreign currency as the unit of the answer. 4. Check that the foreign amount is on the correct side of the pounds.
If the price is already in the foreign currency, divide by the rate to find pounds. A jacket at 80 euros, with £1 = 1.25 euros, costs 80 ÷ 1.25 pounds. Division undoes the multiplication that built the euros.
A fraction makes the division exact. 1.25 = 5/4, and dividing by 5/4 means multiplying by 4/5. So 80 ÷ 5 = 16 and 16 × 4 = 64. The jacket costs £64. Multiplying 80 by 1.25 would price a different question.
Method: 1. Start from the foreign amount. 2. Divide by the rate that one pound buys. 3. Use an equivalent fraction if that makes the division exact. 4. Multiply the pound answer by the rate and check the foreign amount returns.
An exchange rate such as £1 = 1.18 euros is a ratio, written as one pound for every 1.18 euros. To go from pounds to euros you multiply by 1.18. To go from euros back to pounds you divide by 1.18. A rate is sometimes given the other way, such as 1 euro = £0.85, and then the same rule applies with the new rate: multiply to reach pounds, divide to reach euros.
Before you press any buttons, decide whether the answer should be larger or smaller. If one pound buys more than one euro, the number of euros is larger than the number of pounds. Foreign amounts in this lesson are usually larger than the pounds. If your answer goes in the wrong direction, you have multiplied when you should have divided, or the other way round.
Method: 1. Write the rate with the currency you have on the left and the one you want on the right. 2. Decide whether the answer should be bigger or smaller than the starting amount. 3. Multiply or divide by the rate to match. 4. Check the size of the answer against your prediction and write the currency.
Tip: Say it aloud: "I am turning pounds into euros, so there will be more of them." This avoids the usual direction error.
Money is rounded to the nearest penny or cent, which means two decimal places. If the calculator shows 18.6666dots, the answer is 18.67 because the next digit is 6, which rounds up. Do not cut the digits off. Keep the full calculator value in the working until the end, and round only the final answer.
Some questions are about notes or coins: "How many 50-euro notes can she get?" You can only receive a whole number of notes, so you work out the total, divide by the note size, and then round down, even if the decimal part is more than a half. "Is there enough money?" questions need the amounts in the same currency before you compare. Always say yes or no and quote both amounts.
Method: 1. Keep the full calculator display until the final line. 2. Round to two decimal places for money, unless the question says otherwise. 3. For notes, divide by the note size and round down to a whole number. 4. For "enough money", compare the two amounts in the same currency and give a clear yes or no.
To decide where something is cheaper, convert both prices into the same currency, usually pounds, since this is the one the student knows best. A price of 340 euros at £1 = 1.15 euros is 340 ÷ 1.15 = £295.65, which can be compared directly with a UK price. State which is cheaper and by how much, with the difference in pounds.
Other questions change money twice. A traveller changes pounds into dollars, spends some, and changes the rest back at a different rate. Each change is its own one-step calculation. Write down the rate each time, because the second rate is usually not the reverse of the first. A bureau may also charge commission, such as 3% of the pounds, which you take off before converting.
Method: 1. Convert every price into one currency. 2. Compare the amounts and say which is cheaper, and by how much. 3. For two changes of currency, work through them in order, writing each rate. 4. For commission, find the percentage of the starting amount and subtract it before converting.
Tip: When the leftover money is changed back at a different rate, always use the new rate, not the old one.
A conversion graph is a straight line through the origin showing pounds on one axis and the foreign currency on the other. To read it, find the amount on one axis, go across or up to the line, and read the other axis. The graph is only accurate to the width of one small square, so a calculated answer from the rate is better when the rate is given.
Some problems start with a foreign price that includes a tax, such as 21% sales tax. Remove the tax first using a reverse percentage: divide by 1.21. Then convert to pounds with the rate. Doing the steps in the wrong order gives the wrong answer, so write them as a short list and tick each one off as you go.
Method: 1. If a rate is given, use it to calculate rather than reading from a graph. 2. For a price with tax, divide by 1 + tax rate first. 3. Convert the result into pounds with the exchange rate. 4. Round to the nearest penny at the end.
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