How do I know whether to multiply or divide by an exchange rate?

Follow the direction of the rate. If $£1 = €1.20$, multiply pounds by $1.20$ to obtain euros and divide euros by $1.20$ to obtain pounds. Checking whether the result has a sensible size can help identify an incorrect operation.

Can exchange rate questions appear on a non-calculator paper?

Yes. Exchange rate and proportional reasoning questions may appear in calculator or non-calculator assessments. On a non-calculator paper, the numbers will normally be chosen so that an appropriate written or mental method can be used.

Does the highest exchange rate always give the best deal?

Not always. When changing the same number of pounds into a foreign currency, a higher rate gives more foreign currency if there are no other charges. Commission, fixed fees or minimum transaction amounts can change which deal is best.

What unit should I use for a best buy calculation?

Use a unit that allows every option to be compared directly. Suitable choices include price per item, per $100$ g, per kilogram, per $100$ ml or per litre. The same comparison unit must be used for every option.

Should money answers always have two decimal places?

Amounts involving pounds, euros or dollars should normally be given to the nearest penny or cent, using two decimal places when needed. Exact whole-currency amounts, such as $£340$, do not need to be written as $£340.00$ unless a particular format is requested.

How can I earn full marks on a best buy exam question?

Show the comparison calculation for every option, keep the units consistent and state a clear conclusion. A correct choice without supporting calculations may not earn all available method marks.

Exchange Rates and Best Buys GCSE Maths Revision

Exchange rates and best buys GCSE Maths questions test the same central skill: comparing quantities fairly using multiplication, division and proportional reasoning. For exchange rates, you convert an amount from one currency into another. For best buys, you convert prices to a common unit or common quantity before deciding which option offers better value.

This Foundation-tier guide explains both methods step by step. It includes worked examples, common mistakes, exam-style questions with answers and links to relevant MathsGenie revision resources.

What are exchange rates and best buys?

An exchange rate states how much one currency is worth in another currency. For example,

£ 1 = €1.18

means that every pound can be exchanged for $1.18$ euros.

A best buy question asks you to compare two or more products, packs or offers and identify which gives the best value for money. The prices cannot always be compared directly because the quantities may be different.

Both topics are applications of ratio and proportion. They appear across the main GCSE Maths exam boards, although the wording and contexts vary. You can use the GCSE Maths topics by exam board and tier guide to check how topics are organised for your course.

How to calculate exchange rates

The safest method is to read the rate carefully and identify the currency represented by one unit.

For a rate written as

£ 1 = €1.18,

use these rules:

To change pounds into euros, multiply by $1.18$ .
To change euros into pounds, divide by $1.18$ .

This works because each pound produces $1.18$ euros. Reversing the conversion requires the inverse operation.

Conversion	Operation when $£ 1 = € r$
Pounds to euros	Multiply by $r$
Euros to pounds	Divide by $r$

Do not memorise a rule such as “always multiply when going abroad”. The rate might instead be written as $€1 = £ 0.85$ , which changes the operation you need. Follow the units shown in the rate.

Worked example 1: pounds to euros

Mia changes $£ 240$ into euros. The exchange rate is

£ 1 = €1.17.

Since the amount is changing from pounds into euros, multiply by $1.17$ :

240 \times 1.17 = 280.80.

Mia receives $€280.80$ .

A useful estimate confirms that this is sensible. Since one pound is worth more than one euro at this rate, the number of euros should be greater than $240$ .

Worked example 2: euros to pounds

A traveller has $€351$ . The exchange rate is

£ 1 = €1.17.

This time the conversion goes against the direction of the stated rate, so divide:

351 \div 1.17 = 300.

The traveller receives $£ 300$ .

You can check by reversing the calculation:

300 \times 1.17 = 351.

For more guided teaching, use the MathsGenie Exchange Rates revision lesson and Exchange Rates revision guide.

Comparing currency exchange offers

Some questions give exchange rates from two banks or travel money companies. If both companies convert pounds into the same foreign currency and there are no fees, the higher exchange rate gives more foreign currency for each pound.

You should still calculate the actual amounts unless the question only asks which rate is better. Charges and commission can change the answer.

Worked example 3: comparing exchange rates

Amir wants to change $£ 450$ into dollars. Two companies offer these rates:

Company A: ${\char36}1.24$
Company B: ${\char36}1.27$

For Company A:

450 \times 1.24 = 558.

For Company B:

450 \times 1.27 = 571.50.

Company B is the better option because Amir receives $$571.50{\char36}571.50$ , which is $$13.50{\char36}13.50$ more than Company A.

If a company charges a fixed fee, subtract that fee from the money being exchanged before applying the rate, provided the question says that the fee is taken from the original amount. Always follow the wording because fees can be applied in different ways.

How to solve best buy questions

A fair comparison requires both options to be expressed using the same quantity. There are two main methods.

Method 1: calculate a unit price

Divide each price by its quantity. This could produce:

cost per item
cost per gram or kilogram
cost per millilitre or litre
cost per $100$ g
cost per metre

The option with the lower unit price is normally the best value.

Method 2: compare a common quantity

Scale both options up to the same number of items, mass or volume. This is particularly useful when the quantities have a simple common multiple.

For example, packs of $6$ and $10$ can both be scaled to $30$ items. You can then compare the cost of $30$ from each pack.

Neither method is always better. Choose the one that makes the arithmetic clear and efficient.

Exchange rates and best buys worked examples

Worked example 4: comparing prices per item

Shop A sells $6$ notebooks for $£ 2.70$ . Shop B sells $10$ notebooks for $£ 4.30$ .

Calculate the price of one notebook from Shop A:

£2.70 \div 6 = £0.45.

Calculate the price of one notebook from Shop B:

£4.30 \div 10 = £0.43.

Shop B is the best buy because each notebook costs $43$ p rather than $45$ p.

You could also compare $30$ notebooks:

\times £2.70 = £13.50

\times £4.30 = £12.90

Both valid methods give the same conclusion.

Worked example 5: converting units before comparing

A $750$ g packet of cereal costs $£ 3.30$ . A $1.2$ kg packet costs $£ 4.92$ .

The units must match. Convert $1.2$ kg to grams:

1.2\text{ kg} = 1200\text{ g}.

Compare the cost per $100$ g.

For the $750$ g packet:

£3.30 \div 7.5 = £0.44.

For the $1200$ g packet:

£4.92 \div 12 = £0.41.

The $1.2$ kg packet is the best buy because it costs $41$ p per $100$ g, compared with $44$ p per $100$ g.

Worked example 6: a special offer

A $500$ ml bottle costs $£ 1.60$ , with an offer of buy two and get one free. A separate $1.5$ litre bottle costs $£ 4.50$ .

Three small bottles contain:

\times 500 = 1500\text{ ml} = 1.5\text{ litres}.

Under the offer, only two bottles are paid for:

\times £1.60 = £3.20.

The special offer costs $£ 3.20$ for $1.5$ litres, so it is better value than the $£ 4.50$ bottle. It saves:

£ 4.50 - £ 3.20 = £ 1.30.

The Best Buy Questions revision guide provides further explanation of this comparison process.

Best value does not always mean the lowest total cost

A smaller packet may cost less at the till but still have a higher cost per item. For example, a $4$ -pack costing $£ 2$ is cheaper to buy than a $10$ -pack costing $£ 4$ , but the unit prices are $50$ p and $40$ p respectively. The larger pack gives better value.

However, the best mathematical value is not automatically the most sensible real-life purchase. A person may not need the larger quantity, or some of it may be wasted. In an exam, answer the precise question asked:

“Which is the best value?” Compare unit prices.
“Which costs less?” Compare the actual amounts paid.
“How much is saved?” Subtract the smaller relevant cost from the larger one.

Common mistakes to avoid

Multiplying or dividing in the wrong direction

Write the currency units beside your calculation. If $£ 1 = €1.20$ , then $£ 100$ should produce more than $100$ euros, so multiplying is reasonable.

Comparing pack prices without comparing quantities

A $£ 3$ packet is not necessarily better value than a $£ 4$ packet. The quantities must be equalised or converted to unit prices first.

Mixing grams and kilograms

Convert quantities to the same unit before dividing. Remember:

1\text{ kg} = 1000\text{ g}

and

1\text{ litre} = 1000\text{ ml}.

Rounding too early

Keep the full calculator display during intermediate steps. Round money to the nearest penny only when giving the final answer, unless the question specifies otherwise.

Giving numbers without a conclusion

A comparison question requires a written decision. State which company, shop or product is better and support it with the calculated values.

Ignoring whether the required quantity is available

If someone needs exactly $18$ cans and cans are sold in packs of $8$ , they must buy three packs, not $18$ separate cans. Best-buy questions may test the number of whole packs required as well as the unit price.

Exchange rates and best buys exam questions

Try these Foundation-tier questions before checking the answers.

Question 1

The exchange rate is ${\char36}1.28$ . Work out how many dollars Rosa receives for $£ 460$ .

Question 2

The exchange rate is $£ 1 = €1.25$ . Ben changes $€425$ into pounds. Work out how many pounds he receives.

Question 3

A box of $80$ tea bags costs $£ 2.56$ . A box of $120$ tea bags costs $£ 3.72$ . Determine which box is the best buy.

Question 4

Detergent is sold in these bottles:

Bottle A: $1.5$ litres for $£ 5.40$
Bottle B: $2$ litres for $£ 6.80$

Work out which bottle gives the lower price per litre.

Answers to the exam-style questions

Answer 1

460 \times 1.28 = 588.80

Rosa receives $$588.80{\char36}588.80$ .

Answer 2

425 \div 1.25 = 340

Ben receives $£ 340$ .

Answer 3

For the box of $80$ :

£2.56 \div 80 = £0.032

This is $3.2$ p per tea bag.

For the box of $120$ :

£3.72 \div 120 = £0.031

This is $3.1$ p per tea bag, so the box of $120$ is the best buy.

Answer 4

For Bottle A:

£5.40 \div 1.5 = £3.60

For Bottle B:

£6.80 \div 2 = £3.40

Bottle B gives the lower price per litre.

Embedded exam-style question

Sofia has $£ 250$ to exchange into euros.

Company A offers $£ 1 = €1.14$ with no fee.
Company B offers $£ 1 = €1.11$ and deducts a $£ 3$ fee from the $£ 250$ before exchanging the remaining money.

Work out which company gives Sofia more euros and calculate the difference.

For Company A:

250 \times 1.14 = 285.

For Company B, first subtract the fee:

250 - 3 = 247.

Then apply the exchange rate:

247 \times 1.11 = 274.17.

The difference is:

285 - 274.17 = 10.83.

Company A gives Sofia $€10.83$ more.

Try 4 more exchange rate exam questions, then continue with the Best Buy Questions practice bank. A printable Exchange Rates exam booklet is also useful for showing complete working on paper.

Conclusion

For exchange rates, identify the direction of the stated rate and decide whether multiplication or division follows the units. For best buys, compare like with like by calculating unit prices or scaling each option to a common quantity.

Show every stage, keep units consistent, avoid early rounding and finish comparison questions with a clear conclusion. Use the MathsGenie revision lesson first if the method is unfamiliar, then consolidate it with practice questions and the printable exam booklet.

Sources and referenced URLs

This Foundation-tier guide explains both methods step by step. It includes worked examples, common mistakes, exam-style questions with answers and links to relevant MathsGenie revision resources.

What are exchange rates and best buys?

An exchange rate states how much one currency is worth in another currency. For example,

£ 1 = €1.18

means that every pound can be exchanged for $1.18$ euros.