Money calculations and currency conversions
Build a total from prices, change and fees, and use the direction of a stated exchange rate correctly.
Core and Extended.
Before you begin
- Multiply and divide decimals.
- Use percentages and recognise the direction of a rate.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
At 1 USD = 1.25 CAD, how many CAD are received for 40 USD before any fees?
What you will learn
- Calculate costs, balances, change and earnings.
- Convert currencies using a stated rate.
- Apply stated fees in the correct order and report monetary precision.
Separate each part of the transaction
A total cost is quantity multiplied by unit price, with any stated fixed charges added afterwards. Three notebooks at $2.40 and a $1.10 delivery fee cost 3 × 2.40 + 1.10 = $8.30. Change from $10 is $1.70. Keep units and labels so a price, fee and balance are not confused.
For earnings, apply each pay rate to the matching number of hours. If five hours are paid at $12 per hour and two at $18 per hour, total pay is $60 + $36 = $96. A deduction may be fixed or percentage based; calculate it from the stated base and subtract it after finding gross pay.
Read which currency the rate produces
Suppose a fictional exchange rate is 1 USD = 1.25 CAD. Converting USD to CAD multiplies by 1.25, because every US dollar becomes 1.25 Canadian dollars. Converting CAD to USD divides by 1.25. Write the equality and try a one-unit conversion before applying it to a larger amount.
The reverse rate is the reciprocal: 1 CAD = 0.8 USD in this simplified model. These example rates are invented for calculation practice, not live quotations. In a problem with two different buy/sell rates, use the one explicitly applying to the transaction; a real exchange need not be exactly reversible.
Fees can change the order
If a $4 fee is removed from $200 before exchange at 1 USD = 1.25 CAD, exchange $196 to get 245 CAD. If the stated fee is 4 CAD after conversion, first convert to 250 CAD and then subtract to get 246 CAD. The same written digit does not imply the same currency or processing order.
A percentage fee also needs its base stated. In a simplified transaction, a 2% fee on the original $200 is $4. A 2% fee on a different post-exchange amount must be calculated in that currency. Draw a short sequence of labelled amounts to avoid subtracting incompatible units.
Round at the point specified
A money answer such as 9.5 dollars is normally written $9.50. Keep extra precision during the calculation and round the final monetary amount to the nearest cent unless the problem specifies something different. If a fee is explicitly rounded before exchange, follow that rule rather than silently moving all rounding to the end.
To compare two offers, calculate what the customer receives after every stated fee. A better headline exchange rate can produce less currency once charges are included. State the mathematical comparison and its assumptions; costs outside the question are not part of this simplified calculation.
Pause and explain
A fee of 3 EUR is charged after converting 100 USD at 0.9 EUR per USD. What is received?
Worked example
In a fictional exchange, $240 is converted at 1 USD = 0.92 EUR after a $5 fee is removed. Find the euros received.
Show the worked solution
- The amount exchanged is 240 − 5 = 235 USD.
- Multiply by 0.92 EUR per USD: 235 × 0.92 = 216.2 EUR.
- Report the money as €216.20; the fee was deducted before conversion.
Answer €216.20
From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Four tickets cost $7.50 each, with one booking fee of $2.80. Find the total and change from $40.
Give me a hint
The booking fee is added once, not once per ticket.
Compare my reasoning
- Tickets total 4 × 7.50 = $30.
- Add the booking fee: total $32.80.
- Change = 40 − 32.80 = $7.20.
Total $32.80; change $7.20.
Look for these in your work
- Applied the fixed fee once.
- Checked total and change add to the payment.
At the fictional rate 1 USD = 1.25 CAD, convert 360 CAD to USD, then remove a 2% fee based on that USD amount.
Give me a hint
Divide to reverse the rate; the fee base is the converted USD amount.
Compare my reasoning
- 360/1.25 = 288 USD.
- The fee is 0.02 × 288 = $5.76.
- Received amount = 288 − 5.76 = $282.24.
$282.24
Look for these in your work
- Used the reciprocal direction for the exchange.
- Calculated the fee from the explicitly stated currency amount.
A fictional customer exchanges $200. Offer A gives 0.90 EUR per USD after a $4 fee. Offer B gives 0.89 EUR per USD with no fee. Which yields more euros, and by how much?
Give me a hint
Compare final amounts rather than the displayed rates alone.
Compare my reasoning
- Offer A exchanges $196, producing 196 × 0.90 = €176.40.
- Offer B produces 200 × 0.89 = €178.00.
- B yields €1.60 more despite its smaller headline rate.
Offer B by €1.60
Look for these in your work
- Included the stated fee before conversion.
- Compared final amounts in the same currency.
Common mistakes
- Multiplying when converting in the reverse direction.
- Subtracting a fee in a different currency without conversion.
- Comparing headline rates instead of final amounts.
What can you explain now?
At an invented rate 1 USD = 0.8 EUR, convert 64 EUR to USD before fees.
Compare with the explanation
$80.00
Divide 64 by 0.8; checking 80 × 0.8 returns €64.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Invent an exchange rate, convert an amount and reverse the conversion. Explain how a fixed fee breaks that exact reversal.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.
Original StudyForA teaching content · AI-assisted checks · Human teacher review pending.
Number contains 19 sequenced lessons; Algebra and graphs contains 21; Coordinate geometry contains 10 teaching lessons and a mixed checkpoint. Nine earlier overviews support selected topics across the syllabus. The other six syllabus areas, full cumulative assessment and human teacher review are not yet complete. Written lesson practice is self-checked, not automatically graded. The checkpoint samples skills and does not save an exam grade or certify mastery.
Check the official syllabus 2025–2027 Open related practice and resources