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F1.1 · Compare exchange rates and convert currencies to and from Canadian dollars

Learn to compare exchange rates and convert currencies to and from canadian dollars through clear examples and targeted practice.

Ontario Grade 7 Mathematics

Financial Literacy

Ontario Grade 7 Mathematics · F1.1

Imagine a hypothetical exchange rate says that CAD 1 matches USD 0.72. CAD means Canadian dollars, and USD means US dollars. The rate says each Canadian dollar matches 0.72 US dollars. This value is made up for learning. It is not a current rate or a real exchange offer. In this lesson, you will read the direction of a rate, convert amounts, and compare rates fairly.

What you will learn

  • Explain what an exchange rate tells you.
  • Compare rates written for the same currencies and in the same direction.
  • Convert Canadian dollars to another currency and convert that currency to Canadian dollars.
  • Check a conversion using an estimate or a reverse conversion.

1. Read an exchange rate

A currency is a kind of money used in a country or place. An exchange rate tells how much of one currency matches an amount of another currency. Rates in this lesson are often written as the amount of another currency for CAD 1.
For example, CAD 1 = USD 0.72 means that each CAD 1 matches USD 0.72. If you have CAD 3 at this rate, you have three equal groups of USD 0.72. Thinking in equal groups gives a clear picture before you calculate.
Before comparing rates, check the currencies and the direction. USD 0.72 for CAD 1 can be compared directly with USD 0.75 for CAD 1. Both tell how many US dollars match one Canadian dollar. A rate that tells how many Canadian dollars match USD 1 goes in the opposite direction. Do not compare its number directly with the first two rates.
1 CAD=0.72 USD1\text{ CAD}=0.72\text{ USD}
  • An exchange rate relates amounts in two currencies.
  • Check which currency amount is given for CAD 1.
  • Compare rates directly only when they use the same currencies and direction.

2. Convert Canadian dollars to another currency

Suppose a rate gives the amount of another currency for each CAD 1. To change Canadian dollars to that currency, multiply by the rate. Multiplication is a short way to add equal groups. For example, CAD 10 makes ten groups of the amount given for CAD 1.
If each CAD 1 matches USD 0.72, then CAD 10 matches ten groups of USD 0.72. The rate tells the size of each group. The Canadian-dollar amount tells how many groups to use.
The currency units help you keep track of what the answer means. A Canadian-dollar amount multiplied by a rate in other currency per CAD 1 gives an amount in the other currency. Always write the currency beside the answer; a number by itself is not enough.
Estimate before calculating. If each CAD 1 matches less than USD 1, then CAD 10 should match less than USD 10 at that rate. If your answer does not fit the estimate, check the operation and arithmetic.
other-currency amount=CAD amount×(other-currency amountCAD 1)\text{other-currency amount}=\text{CAD amount}\times\left(\frac{\text{other-currency amount}}{\text{CAD }1}\right)
  • For a rate written as other currency for CAD 1, multiply to convert Canadian dollars to that currency.
  • Write the currency beside the answer.
  • An estimate can help you check whether the answer is reasonable.

3. Convert another currency to Canadian dollars

To convert back using the same rate, divide the amount in the other currency by the amount given for each CAD 1. Division tells how many equal groups fit into an amount.
For example, if each CAD 1 matches USD 0.72, then USD 7.20 contains ten groups of USD 0.72. Those ten groups match CAD 10. Dividing USD 7.20 by 0.72 finds the number of Canadian dollars.
Read the direction of the rate before choosing an operation. This division rule applies when the rate is written as the other-currency amount for CAD 1. If you convert an amount to another currency and then back using the same rate, you should return to the starting amount. This can help check your work.
CAD amount=other-currency amount÷(other-currency amountCAD 1)\text{CAD amount}=\text{other-currency amount}\div\left(\frac{\text{other-currency amount}}{\text{CAD }1}\right)
  • For a rate written as other currency for CAD 1, divide to convert that currency to Canadian dollars.
  • Division counts how many rate-sized groups fit in the amount.
  • A reverse conversion using the same rate can check your work.

4. Compare rates fairly

Suppose two hypothetical rates for the same currencies are CAD 1 = USD 0.72 and CAD 1 = USD 0.75. Both give US dollars for CAD 1, so their numbers can be compared directly. The second rate gives more US dollars for each Canadian dollar.
To compare what the rates give for a larger amount, use the same starting amount for both. For CAD 20, the first rate gives USD 14.40 and the second gives USD 15.00. The second gives USD 0.60 more. Using the same Canadian-dollar amount makes the comparison fair.
A larger number does not always mean a better rate. First check that both rates use the same currencies and direction. A larger number means more of the other currency for each CAD 1 only when both rates are written in that same direction. These examples use hypothetical rates, not live rates or exchange offers.
The rates differ by USD 0.03 for each CAD 1. For CAD 20, that difference is USD 0.60.
0.75>0.720.75>0.72
  • Compare the same currency pair in the same direction.
  • For rates written as other currency per CAD 1, the larger rate gives more of that currency for the same Canadian-dollar amount.
  • Use the same starting amount to compare what two rates give.

Choose an operation from the rate direction

Starting amountRate formOperationResult
Canadian dollarsOther currency for CAD 1MultiplyOther currency
Other currencyOther currency for CAD 1DivideCanadian dollars

Worked example

Convert Canadian dollars to US dollars

A hypothetical exchange rate is CAD 1 = USD 0.72. How many US dollars match CAD 35 at this rate?
Hypothetical rate and conversion
Hypothetical rate and conversionThe bars show the hypothetical rate and the converted amount from the example. They are measured in US dollars and do not show live rates.0.72 US dollarsPer CAD 125.2 US dollarsFor CAD 35

The bars show the hypothetical rate and the converted amount from the example. They are measured in US dollars and do not show live rates.

  1. Read the rate
    Each CAD 1 matches USD 0.72. The question starts with Canadian dollars, so multiply by the number of US dollars for each CAD 1.
    1 CAD=0.72 USD1\text{ CAD}=0.72\text{ USD}
  2. Multiply
    There are 35 groups of CAD 1. Each group matches USD 0.72, so multiply 35 by 0.72.
    35×0.72=25.2035\times0.72=25.20
  3. State the currency
    The product is in US dollars because the rate gives US dollars for each Canadian dollar.
    35 CAD=25.20 USD35\text{ CAD}=25.20\text{ USD}
Answer: CAD 35 matches USD 25.20 at the stated hypothetical rate.
Check: USD 0.72 is less than USD 1 for each CAD 1, so CAD 35 should match less than USD 35. USD 25.20 fits that estimate.

Worked example

Convert US dollars to Canadian dollars

Use the hypothetical rate CAD 1 = USD 0.72. How many Canadian dollars match USD 54?
Hypothetical rate and amount
Hypothetical rate and amountThe bars show the hypothetical rate and the US-dollar amount being converted. Both are measured in US dollars; the rate is not live.0.72 US dollarsPer CAD 154 US dollarsAmount given

The bars show the hypothetical rate and the US-dollar amount being converted. Both are measured in US dollars; the rate is not live.

  1. Identify the rate-sized group
    Each CAD 1 matches USD 0.72. The question gives US dollars and asks for Canadian dollars, so find how many groups of USD 0.72 fit into USD 54.
    54÷0.7254\div0.72
  2. Divide
    USD 0.72 fits into USD 54 exactly 75 times. Division counts the number of equal rate-sized groups.
    54÷0.72=7554\div0.72=75
  3. State the answer
    Those 75 groups each match CAD 1, so the amount is CAD 75.
    54 USD=75 CAD54\text{ USD}=75\text{ CAD}
Answer: USD 54 matches CAD 75 at the stated hypothetical rate.
Check: Multiply the answer by the rate: 75 times USD 0.72 is USD 54. The conversion returns to the amount given.

Worked example

Compare two hypothetical rates

Two hypothetical rates for exchanging Canadian dollars to US dollars are CAD 1 = USD 0.68 and CAD 1 = USD 0.71. Which rate gives more US dollars for CAD 24, and how much more?
Two hypothetical rates
Two hypothetical ratesThe bars compare two nonnegative hypothetical rates, measured in US dollars per CAD 1. They are not live rates.0.68 US dollars per CAD 1Rate A0.71 US dollars per CAD 1Rate B

The bars compare two nonnegative hypothetical rates, measured in US dollars per CAD 1. They are not live rates.

  1. Check the direction
    Both rates give US dollars for CAD 1, so compare the numbers directly. USD 0.71 is greater than USD 0.68, so it gives more US dollars for each Canadian dollar.
    0.71>0.680.71>0.68
  2. Convert the same amount
    Use CAD 24 for both calculations to compare fairly. Multiply 24 by each rate.
    24×0.68=16.32,24×0.71=17.0424\times0.68=16.32,\quad24\times0.71=17.04
  3. Find the difference
    Subtract the smaller US-dollar amount from the larger amount to find how much more the higher rate gives.
    17.04−16.32=0.7217.04-16.32=0.72
Answer: The rate CAD 1 = USD 0.71 gives more. For CAD 24, it gives USD 0.72 more than the rate CAD 1 = USD 0.68.
Check: The rates differ by USD 0.03 for each CAD 1. For CAD 24, that difference is USD 0.72, which matches the subtraction.

Common mistakes and how to avoid them

Dividing when converting Canadian dollars to another currency.
Correction: When the rate gives the other-currency amount for CAD 1, multiply the Canadian-dollar amount by that rate.
Multiplying when converting another currency back to Canadian dollars.
Correction: Divide the other-currency amount by the amount given for each CAD 1. This counts the number of rate-sized groups.
Comparing rates written in opposite directions.
Correction: First check that both rates describe the same currencies in the same direction, such as US dollars for CAD 1.
Leaving the currency off the answer.
Correction: Write CAD or the other currency with the final amount. The number alone does not show what was converted.

Lesson summary

  • An exchange rate tells how amounts in two currencies are related.
  • For a rate written as other currency for CAD 1, multiply to convert Canadian dollars to that currency.
  • For that same rate, divide to convert the other currency to Canadian dollars.
  • Compare rates only when the currencies and direction match.
  • Use the same starting amount to show what two rates give.

Check your understanding

Question 1

A hypothetical rate is CAD 1 = EUR 0.80. How many euros match CAD 15?
  1. EUR 12
  2. EUR 18.75
  3. CAD 18.75
  4. EUR 0.80
Show answer and explanation
EUR 12
Multiply 15 by 0.80. The result is EUR 12.

Question 2

At the hypothetical rate CAD 1 = GBP 0.50, how many Canadian dollars match GBP 18?
  1. CAD 9
  2. CAD 36
  3. GBP 36
  4. CAD 18.50
Show answer and explanation
CAD 36
Divide 18 by 0.50. The result is CAD 36.

Question 3

Which hypothetical rate gives more US dollars for CAD 10: CAD 1 = USD 0.66 or CAD 1 = USD 0.69?
  1. USD 0.66 per CAD 1
  2. USD 0.69 per CAD 1
  3. They give the same amount
  4. There is not enough information because both are rates
Show answer and explanation
USD 0.69 per CAD 1
The rates are written in the same direction. The higher rate gives more for each CAD 1, so it gives more for CAD 10.

Key terms

Currency
A kind of money used in a country or place.
Exchange rate
A relationship that tells how much of one currency matches an amount of another currency.
Hypothetical
Made up for an example, rather than stated as a live or real exchange rate.
Convert
Change an amount from one currency to an equal-value amount in another currency using an exchange rate.

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