Learning Objectives
- interpret an exchange rate;
- convert between currencies;
- decide when to multiply or divide;
- use buying and selling rates;
- solve multi-step currency problems.
Introduction
This lesson develops Exchange Rates from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.
Key Notes
Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.
Visual Exploration
Use the diagrams, tables or examples in this lesson to identify what changes, what stays fixed and which relationship connects the values.
🌍 Where Will You Use This?
Exchange rates are used in travel, international shopping, imports, online subscriptions and business transactions.
Understanding a Rate
This means one US dollar is equivalent to 18.50 South African rand.
Multiply or Divide?
Convert US$240 to rand at US$1 = R18.50.
240×18.50 = R4,440.
Convert R2,775 to US dollars.
2775÷18.50 = US$150.
Buying and Selling Rates
A bank buys foreign currency from you at its buying rate and sells foreign currency to you at its selling rate.
| Situation | Rate to use |
|---|---|
| You give foreign currency to the bank | Bank buying rate |
| You obtain foreign currency from the bank | Bank selling rate |
Worked Example: Two Rates
A bank buys pounds at US$1.24 per £1 and sells pounds at US$1.29 per £1.
To buy £300, pay 300×1.29 = US$387.
To sell £300 to the bank, receive 300×1.24 = US$372.
Cross-Currency Conversion
US$1 = R18 and US$1 = €0.92. Convert R3,600 to euros.
Rand to dollars: 3600÷18 = US$200.
Dollars to euros: 200×0.92 = €184.
💼 Money Smart Tip
Exchange providers may also charge fees, so the advertised rate may not be the complete cost.
🧠 Let’s Think Together
Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.
Practice Questions
Foundation- At US$1=R19.20, convert US$85 to rand.
- Convert R5,760 to US dollars at the same rate.
- At £1=US$1.28, convert £250 to US dollars.
- A bank sells euros at US$1.10 per euro. How many euros can US$660 buy?
- A bank buys pounds at US$1.22 and sells at US$1.27. Find the difference between buying and selling £500.
- US$1=R18.40 and US$1=€0.91. Convert R9,200 to euros.
- A traveller changes US$800 into rand at US$1=R18.75. She spends R9,000 and changes the remainder back at US$1=R19.20. How many US dollars does she receive?
✅ Check Your Work
Show practice answers
- R1,632.
- US$300.
- US$320.
- 660÷1.10 = €600.
-
Buying value=500×1.22=US$610.
Selling cost=500×1.27=US$635.
Difference=US$25. - 9200÷18.40=US$500; 500×0.91=€455.
-
Initial rand=800×18.75=R15,000.
Remainder=R6,000.
Dollars received=6000÷19.20=US$312.50.
Common Mistakes
- Choosing a rule before identifying what the question describes.
- Skipping working or changing notation part-way through a solution.
- Accepting an answer without checking its size, sign or units.
Exam Focus
Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.
Summary
- Read the direction of the rate carefully.
- Multiply when moving to the quoted currency.
- Divide when reversing the quoted rate.
- Use selling rate when buying currency from a bank.