Money.
Calculate amounts accurately and follow exchange rates in the right direction.
Calculate costs and change · convert currencies · account for fees and compare offers
Keep the amount and the currency together
Money problems combine ordinary arithmetic with careful interpretation. A total cost adds purchases; change subtracts the total from the payment. Prices written with one decimal place still need the correct cents when presented.
Begin by listing the amounts that are paid, received or deducted. Keep the currency consistent throughout. If several identical items are bought, multiply the unit price by the quantity before combining it with other costs, discounts or payments.
Align decimal places for addition and subtraction, use consistent units, and express final money answers to the required precision.
Buy 3 notebooks at $2.75 and 2 pens at $1.40. Find change from $20.
Change = 20 − 11.05 = $8.95
Write $8.95 rather than 895 unless you explicitly state cents.
Pause and explainWhat does a calculator answer of 6.4 mean for a dollar price?
$6.40. It means six dollars and forty cents, not six dollars and four cents.
Use the direction of the exchange rate
An exchange rate tells you how much of one currency corresponds to a stated amount of another. Treat the rate as a matching pair, such as $1 matching 3 units of another currency.
To choose multiplication or division, first find the amount corresponding to one unit of the starting currency. Converting in the opposite direction reverses that operation. Writing the currencies beside the numbers is more reliable than memorising “always multiply”.
Exchange rates below are illustrative rates supplied for the examples. Read “1 unit of which currency equals how many of the other?”
Given 1 USD = 1.25 EUR, convert 240 USD to EUR and 175 EUR to USD.
240 USD × 1.25 = 300 EUR.
175 EUR ÷ 1.25 = 140 USD.
The currency labels help verify the direction: each USD buys more than one EUR at this stated rate.
Pause and explainIf $1 buys 3 units of a currency, how many dollars correspond to 12 units?
$4. Divide 12 by 3 to reverse the conversion from dollars.
Fees and comparing exchange offers
An advertised rate is not always the full deal. A transaction can include a fixed fee, a percentage fee or different buying and selling rates. Those conditions change the amount the customer actually receives.
Follow the order described by the offer. A fee charged before conversion reduces the starting currency; one charged afterward reduces the converted amount. Compare offers using the same starting money and the final amount received, rather than the headline rate alone.
Convert 500 USD at 1 USD = 1.25 EUR, with a 4 EUR fee deducted after conversion.
If the fee were 4 USD deducted before conversion, the result would instead be (500 − 4) × 1.25 = 620 EUR. Follow the stated currency and order.
For 200 USD, compare Offer A: 1.24 EUR per USD, no fee; Offer B: 1.27 EUR per USD, a 5 EUR fee.
A gives 200 × 1.24 = 248 EUR.
B gives 200 × 1.27 − 5 = 249 EUR.
Offer B gives 1 EUR more for this amount. Compare the final amount received after all stated fees.
Pause and explainWhy might a better exchange rate still give less money?
A larger fee can outweigh the rate advantage. Compare the final amount after all stated charges.
Your turn. Label each currency.
Write the starting currency, target currency and rate relationship before calculating. Track every fee in the currency in which it is charged.
Check the direction of conversion by estimating a simple amount first. Round the final money as requested, and distinguish the amount converted from the amount actually received after charges.
You buy 4 items at $3.65 each. Find the change from $20.
Reveal worked answer
Given 1 GBP = 1.6 USD, convert 75 GBP to USD and 248 USD to GBP.
Reveal worked answer
At 1 USD = 2.5 units of B, convert 360 USD after a 10 USD fee is deducted before conversion.
Reveal worked answer
A 500-unit foreign-currency purchase is converted at 1 home unit = 4 foreign units. A 2-home-unit fee is added. Find the total home-currency charge.