Calculate prices, change and currency conversions
Interpret an exchange-rate direction · Include a specified fixed charge · Round final money amounts appropriately
Section Paper 2 · Historical Extended · non-calculator
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Decimals
- Unit rates
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Interpret an exchange-rate direction
- Include a specified fixed charge
- Round final money amounts appropriately
Read the rate's units
If 1 unit of currency A buys 1.25 units of B, multiply an A amount by 1.25 to get B, and divide a B amount by 1.25 to get A. Label the currencies to check the direction. Rates in these examples are fictional fixed problem data, not current exchange-rate advice.
Charges and rounding
Apply fees in the currency and order specified. A fixed charge of 3 A before conversion differs from a charge of 3 B after conversion. Retain sufficient precision through intermediate steps; round the final payment according to the stated smallest currency unit.
Sources for this lesson
Pause and explain
If 1 A = 1.25 B, how do you convert B back to A?
Worked example
At the fictional rate 1 A = 1.25 B, convert 80 A, then deduct a 2 B charge.
Show the worked solution
- 80×1.25 = 100 B.
- 100−2 = 98 B.
Answer 98 B after the charge.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →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.
At 1 A = 1.4 B, convert 50 A to B.
Give me a hint
Multiply by the quoted B per A rate.
Compare my reasoning
- 50×1.4 = 70.
- The result is in B.
70 B.
Look for these in your work
- State the currency
- Use the rate direction
At 1 A = 1.2 B, convert 90 B to A; then deduct a fee of 2 A.
Give me a hint
Reverse the rate before applying the A fee.
Compare my reasoning
- 90/1.2 = 75 A.
- 75−2 = 73 A.
73 A after the fee.
Look for these in your work
- Divide for the reverse direction
- Deduct the fee in its own currency
A shop converts 25 A at 1 A = 1.135 B, with no fee. If payments use hundredths of B and half-up rounding, find the payment.
Give me a hint
Keep the intermediate amount until the last step.
Compare my reasoning
- 25×1.135 = 28.375 B.
- Half-up rounding to two decimal places gives 28.38 B.
28.38 B under the stated rounding rule.
Look for these in your work
- Avoid early rate rounding
- Use the specified money convention
Common mistakes
- A number called an exchange rate still needs a direction.
- Do not deduct a fee in the wrong currency.
What can you explain now?
If 1 A = 1.25 B, how do you convert B back to A?
Compare with the explanation
Divide the B amount by 1.25.
This reverses the stated conversion multiplier.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
If 1 A = 1.25 B, how do you convert B back to A?
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.