F. Financial Literacy · Money and Finances: Exchange Rates, Budgets, Financial Decisions and Interest

Converting Canadian Dollars to Other Currencies

F1.1 A1About 40 minutes

Learning goals

I can convert Canadian dollars to a foreign currency by dividing.
I can decide whether to multiply or divide when converting.
I can explain buy and sell rates and how fees change what I get.
I can compare places to exchange money to find the best deal.

Words to know

buy rate
The rate a bank or exchange booth uses when it buys foreign money from you (you get Canadian dollars back).

sell rate
The rate a bank or exchange booth uses when it sells foreign money to you (you pay Canadian dollars).

spread
The difference between the sell rate and the buy rate. It's one way exchange businesses earn money.

foreign transaction fee
An extra charge some cards add when you pay in another currency, often a percent of the purchase.

commission
A fee charged for a service, like exchanging money.

Getting ready for a trip

Owen's hockey team is going to a tournament in Lake Placid, New York. His grandparents gave him $70 CAD in spending money. He wants to change it to US dollars before he goes. How many US dollars will he get?

Last lesson you went from a foreign currency to Canadian dollars. Now Owen needs to go the other way.

Converting Canadian dollars to a foreign currency

The rate 1 USD = 1.40 CAD tells you that each US dollar costs $1.40 Canadian. So the question is: how many groups of $1.40 are in $70? That's division!

Amount in CAD ÷ (CAD per unit) = amount in the foreign currency

Owen: 70 ÷ 1.40 = 50 USD.

Check by going back: 50 × 1.40 = 70 ✓

You have...	You want...	Do this	Example (1 USD = 1.40 CAD)
Foreign money	Canadian dollars	Multiply by the rate	20 USD × 1.40 = 28 CAD
Canadian dollars	Foreign money	Divide by the rate	28 CAD ÷ 1.40 = 20 USD

Multiply and divide undo each other, so you can always check your answer by going back.

Buy rates and sell rates

Banks and exchange booths need to earn money too. So they use two rates:

The sell rate is used when they sell you foreign money. It's a little higher, so you pay a bit more CAD for each unit.
The buy rate is used when they buy back foreign money from you. It's a little lower, so you get a bit less CAD for each unit.

The difference is called the spread. Some places also charge a fee or commission for each exchange. And some credit cards add a foreign transaction fee (often a few percent) when you pay in another currency.

All rates and fees in this lesson are examples. Real ones are different at each place and change often.

The bank sells US dollars to you at the higher rate and buys them back at the lower rate. The gap between them, the spread, is how the bank earns money. (Example rates.)

Worked example

Example 1: Owen's spending money

Owen has $70 CAD. The rate is 1 USD = 1.40 CAD. How many US dollars will he get?

CAD to foreign money, so divide by the rate: 70 ÷ 1.40.
Make it easier: multiply both numbers by 10. 700 ÷ 14 = 50.
Check: 50 × 1.40 = 70 ✓. And it makes sense that the USD number (50) is smaller than 70, because each US dollar costs more than $1 CAD.

Owen gets 50 USD.

Worked example

Example 2: Buying and selling back

A bank sells US dollars at 1 USD = 1.44 CAD and buys them back at 1 USD = 1.36 CAD. Sofia buys 100 USD for a trip. Then the trip is cancelled, and she sells all 100 USD back. How much money does she lose?

Buying 100 USD at the sell rate: 100 × 1.44 = 144.00 CAD.
Selling 100 USD back at the buy rate: 100 × 1.36 = 136.00 CAD.
Loss: 144.00 − 136.00 = 8.00 CAD.

Sofia loses $8.00 CAD because of the spread. Changing money back and forth costs money, so only exchange what you need.

Changing money and then changing it straight back costs money. Sofia ends with $8.00 less than she started with, even though she never spent any of it.

Worked example

Example 3: Compare two places

Jun needs US dollars and has $300 CAD. Which choice gives more US dollars?

Bank: 1 USD = 1.44 CAD, no fee.
Airport booth: 1 USD = 1.50 CAD, and a $5 fee taken first.

Bank: 300 ÷ 1.44 = 208.333... ≈ 208.33 USD.
Booth: take off the fee first: 300 − 5 = 295. Then 295 ÷ 1.50 = 196.666... ≈ 196.67 USD.
Compare: 208.33 − 196.67 = 11.66 USD more at the bank.

The bank gives Jun about 11.66 USD more. A lower sell rate and no fee both help.

Worked example

Example 4: Paying by card in another currency

Mira's mom buys a 40 USD souvenir with a credit card. The card uses 1 USD = 1.40 CAD and adds a 2.5% foreign transaction fee (an example fee). What is the total in CAD?

Convert: 40 × 1.40 = 56.00 CAD.
Fee: 2.5% of 56.00. 1% of 56.00 is 0.56, so 2.5% is 2.5 × 0.56 = 1.40 CAD.
Total: 56.00 + 1.40 = 57.40 CAD.

The souvenir really costs $57.40 CAD. Fees are part of the real cost, just like HST.

Multiply or divide?

Ask yourself: "Is one unit of the foreign money worth more or less than $1 CAD?"

USD, EUR and GBP are each worth more than $1 CAD (with our example rates). So the foreign amount will be a smaller number than your CAD amount.
MXN is worth less than $1 CAD. So you get lots of pesos: $20 CAD ÷ 0.08 = 250 MXN.

Always check by going back the other way.

Think it through, out loud

Money problems with rates and fees have several steps. Say each step out loud or write it down: "First I take off the fee, then I divide by the rate." Explaining your thinking to someone else helps you catch mistakes, and that's what mathematicians do.

Just for fun

Why do the loonie and the US dollar never stay mad at each other?

They always know how to make an exchange!

Hands-on activity

Plan a pretend trip

You need: paper, a pencil and a calculator. Optional, with a grown-up: a website with today's exchange rates.

Choose a pretend trip to the United States, Mexico, the United Kingdom or a European country that uses the euro.
Your pretend spending money is $250 CAD.
Convert it to that country's currency using this lesson's example rate (or today's real rate).
Make a list of three things you'd buy there, with prices in the foreign currency. Keep the total under what you have.
Convert each price back to CAD to check the total.
Now pretend a booth charges a $6 fee first. How much foreign money would you get instead? How much less is that?

What to look for: dividing to go from CAD to foreign money, multiplying to go back, and taking the fee off before converting.

Your turn

Convert $70 CAD to US dollars. (1 USD = 1.40 CAD)

Convert $150 CAD to euros. (1 EUR = 1.50 CAD)

Convert $90 CAD to British pounds. (1 GBP = 1.80 CAD)

Convert $20 CAD to Mexican pesos. (1 MXN = 0.08 CAD)

Ava has $420 CAD for a school band trip to the US. How many US dollars is that?

A bank sells euros at 1 EUR = 1.55 CAD. How many euros can you buy with $310 CAD?

To change $75 CAD into US dollars, do you multiply or divide by 1.40? What is the answer?

More practice: warm-up

$14 CAD = ___ USD (1 USD = 1.40 CAD)

$30 CAD = ___ EUR (1 EUR = 1.50 CAD)

$8 CAD = ___ MXN (1 MXN = 0.08 CAD)

$1.80 CAD = ___ GBP (1 GBP = 1.80 CAD)

$140 CAD = ___ USD (1 USD = 1.40 CAD)

More practice: on your own

A bank sells US dollars at 1.45 CAD and buys them back at 1.35 CAD. Kai exchanges $290 CAD, spends 150 USD, and sells the rest back. How many Canadian dollars does he get back?

Zoe has $200 CAD. A concert ticket costs 120 USD. Is that enough? How much CAD is left? (1 USD = 1.40 CAD)

Convert $45 CAD to Mexican pesos.

You want euros with $500 CAD. Bank: 1 EUR = 1.55 CAD, no fee. Kiosk: 1 EUR = 1.52 CAD with a $10 fee taken first. Which gives more euros?

A card adds a 2.5% fee on a 60 USD purchase. With 1 USD = 1.40 CAD, what is the total in CAD?

Challenge

A booth sells US dollars at 1.45 CAD and buys at 1.35 CAD. You change $1000 CAD to US dollars, then change it all straight back. About how much do you lose?

A family's trip to Florida needs 2 nights of hotel at 150 USD each and 200 USD for food. They have $750 CAD. Is it enough at 1 USD = 1.40 CAD? How many extra US dollars would they have?

Change 150 EUR into US dollars by going through Canadian dollars. (1 EUR = 1.50 CAD, 1 USD = 1.40 CAD)

Check your understanding

Quiz

To convert Canadian dollars to US dollars with 1 USD = 1.40 CAD, you...

How many euros is $60 CAD? (1 EUR = 1.50 CAD)

How many pesos is $4 CAD? (1 MXN = 0.08 CAD)

A bank sells USD at 1.44 CAD and buys USD at 1.36 CAD. Which rate is used when you get US dollars from the bank?

A booth takes a $5 fee before exchanging $145 CAD at 1 USD = 1.40 CAD. How many US dollars do you get?

Why do you usually lose money if you exchange money and then change it straight back?

For parents and teachers

Big idea: This lesson completes F1.1 by converting Canadian dollars to foreign currencies (dividing), and comparing real-world exchange choices with buy and sell rates and fees.

Common difficulties:

Choosing the operation. Have your child predict whether the answer should be bigger or smaller, then check by converting back.
Dividing by decimals, like 70 ÷ 1.40. Show that multiplying both numbers by 10 (700 ÷ 14) gives the same answer. A calculator is fine once the setup is right.
Forgetting fees, or adding the fee after converting instead of taking it off first.
Mixing up buy and sell: the words are from the bank's point of view.

How to help: If you travel or shop online in another currency, let your child estimate the Canadian price before checking the statement. All rates and fees here are examples. This lesson also builds A1 skills: explaining multi-step thinking and checking work by reversing an operation.