Exchange Rates & Best BuysEdexcel IGCSE Maths: Revision notes

Section 1

How do you convert between currencies?

An exchange rate tells you how much of one currency you get for one unit of another. For example, if $1 = 3.67 AED$ , then to convert dollars to dirhams you multiply by 3.67, and to convert dirhams back to dollars you divide by 3.67.

Method:

Write the exchange rate as a ratio, e.g. $1 \text{ GBP} = 4.60 \text{ AED}$
To go from GBP to AED: multiply by 4.60
To go from AED to GBP: divide by 4.60

Convert	Operation
Base currency → other currency	Multiply by rate
Other currency → base currency	Divide by rate

Key termsexchange ratebase currency

Exam tip

Always check which currency the rate is 'per 1 unit of' before deciding whether to multiply or divide.

Example

If £1 = $1.25, convert £80 to dollars:$ 80 \times 1.25 = 100 $, so £80 =$ 100.

Section 2

How do you convert multi-step currency problems?

Some problems require converting through a third currency, or converting an amount, spending some, then converting back.

Steps for multi-step problems:

Convert the starting amount into the intermediate or target currency
Carry out any spending/subtraction in that currency
Convert the remaining amount back if needed

Keep at least 3 significant figures during working, and round only the final answer (usually to 2 decimal places for money).

Key termsintermediate currency

Common mistake

Rounding too early in a multi-step conversion causes the final answer to be wrong — only round at the very end.

Section 3

What is unit pricing and why does it matter?

Unit pricing means finding the cost (or amount) per single unit, e.g. per gram, per litre, per item. It lets you fairly compare products sold in different pack sizes.

Two equivalent methods:

Cost per unit: $\text{price} \div \text{quantity}$ — the smaller number is better value
Quantity per unit cost: $\text{quantity} \div \text{price}$ — the larger number is better value

$\text{unit price} = \dfrac{\text{total price}}{\text{total quantity}}$

Key termsunit priceunit pricing

Think of it like this

Think of unit pricing like converting everything to a common 'exchange rate' of pounds-per-gram, so you can compare products on equal footing.

Section 4

How do you decide which product is the 'best buy'?

To compare best buys, convert every pack to the same unit (e.g. price per gram) before comparing.

Method:

Convert all quantities to the same unit (e.g. all in grams or all in ml)
Divide price by quantity for each option to get cost per unit
The option with the lowest cost per unit is the best buy

Worked example:

Pack A: 500g for £2.00 → $2.00 \div 500 = £0.004$ per g
Pack B: 750g for £2.85 → $2.85 \div 750 = £0.0038$ per g
Pack B is better value (lower cost per gram)

Key termsbest buy

Common mistake

Comparing total prices without converting to the same unit quantity first — a bigger pack isn't automatically better value.

Section 5

How do ratios and proportion link to best buys?

Best buy problems are really direct proportion problems: cost is proportional to quantity (assuming no bulk discount changes the rate). You can also compare using ratios by scaling both packs to a common quantity.

Alternative method (scaling to a common amount):

Find a common quantity (e.g. scale both packs to 1000g or to the same number of items)
Compare the total price at that common quantity

This avoids decimals if the numbers scale neatly, e.g. comparing 400g and 600g packs by scaling both to 1200g (LCM).

Key termsdirect proportionlowest common multiple (LCM)

Must Know

To convert into the foreign currency, multiply by the exchange rate; to convert back, divide.
Only round your final answer in multi-step conversions — keep extra decimal places during working.
Unit price $= \dfrac{\text{price}}{\text{quantity}}$ — smaller unit price means better value.
Always convert all quantities to the same units before comparing prices.
The best buy has the lowest cost per unit (or the most quantity per £1).
Best buy questions are direct proportion problems — you can also compare by scaling packs to a common quantity.

That's the notes covered.

Carry on to the next subtopic.