If 1 AUD equals 0.65 USD, does 1 USD equal 0.65 AUD?

No. To find how many AUD you get for 1 USD, divide 1 by 0.65, which is about 1.54 AUD. The rates in each direction are reciprocals, not the same number.

If 1 AUD equals 0.65 USD, does 1 USD equal 0.65 AUD?

No. To find how many AUD you get for 1 USD, divide 1 by 0.65, which is about 1.54 AUD. The rates in each direction are reciprocals, not the same number.

Year 11 General Consumer Arithmetic: Personal Finance

Currency And Exchange Rates

Q: What is an exchange rate?

An exchange rate tells you how much of one currency you get for one unit of another. For example, 1 AUD equals 0.65 USD means you receive 65 US cents for every Australian dollar.

Q: How do you convert AUD to a foreign currency?

Multiply the AUD amount by the exchange rate. If 1 AUD equals 0.65 USD, then 300 AUD equals 300 times 0.65, which is 195 USD.

Q: How do you convert a foreign currency back to AUD?

Divide the foreign amount by the exchange rate. If 1 AUD equals 0.65 USD, then 195 USD equals 195 divided by 0.65, which is 300 AUD.

Q: How do you convert one foreign currency to another using AUD?

Convert the first currency to AUD by dividing by its rate, then convert AUD to the second currency by multiplying by its rate.

Q: How do bank fees affect currency conversion?

Banks usually charge a percentage commission. Apply the fee to the original amount first, then convert the reduced amount at the exchange rate. The order matters.

5 practice questions 2 video lessons Theory + worked examples

Theory

An exchange rate tells you how much of one currency you get for one unit of another. To convert AUD into a foreign currency, multiply by the rate; to convert back into AUD, divide by the rate. Bank fees and cross-currency conversions through AUD are common exam twists.

An exchange rate tells you how much of one currency you receive for one unit of another. Rates are usually quoted as $1$ AUD $= k$ of the other currency. For example, $1$ AUD $= 0.65$ USD means every Australian dollar buys $65$ US cents.

Each currency has a three-letter currency code: AUD for the Australian dollar, USD for the US dollar, EUR for the Euro, GBP for the British pound, JPY for the Japanese yen, and NZD for the New Zealand dollar.

A commission or fee is what the bank charges to exchange currency. It is usually a small percentage of the amount being exchanged and is applied before the conversion.

Round-trip rates are not equal. Converting AUD to USD and back to AUD using a bank's quoted rates leaves you with less than you started — the gap is how exchange providers make money.

Multiply AUD by the rate to get the other currency

Multiply going out, divide coming back

Given an exchange rate of $1$ AUD $= k$ other currency:

foreign amount = AUD amount \times k

foreign = AUD \times k

AUD amount = \frac{foreign amount}{k}

AUD = \frac{foreign}{k}

Reverse-rate (how many AUD for one unit of the other currency):

1 other = \frac{1}{k} AUD

1 other = \frac{1}{k} AUD

Cross-currency via AUD: to convert (say) USD to EUR, first divide by the AUD/USD rate to get AUD, then multiply by the AUD/EUR rate to get EUR.

Common currency codes:

Code	Currency
AUD	Australian dollar
USD	US dollar
EUR	Euro
GBP	British pound
JPY	Japanese yen
NZD	New Zealand dollar

How to convert between currencies

Identify the rate in the form " $1$ AUD $= k$ other currency".
Multiply or divide: AUD to other, multiply by $k$ ; other to AUD, divide by $k$ .
Apply any fee to the original amount first (if quoted as a percentage of the AUD), then convert.

For cross-currency, route through AUD in two steps: first to AUD, then to the target currency.

Example 1 — AUD to JPY

The rate is

1

AUD

= 92.50

JPY. How much JPY does Lia get for

$ 800

AUD?

Solution

Going from AUD to a foreign currency — multiply by the rate.

$JPY$	$=$	$800 \times 92.50$
$JPY$	$=$	$74,000$

JPY = 74000

Lia gets $74{,}000$ JPY.

Example 2 — USD to AUD

A US online store charges

$ 120

USD. The rate is

1

AUD

= 0.64

USD. What is the cost in AUD?

Solution

Going back to AUD — divide by the rate.

$AUD$	$=$	$\frac{120}{0.64}$
$AUD$	$=$	$$ 187.50$

AUD = 187.50

The cost is $$187.50$ AUD.

Example 3 — Cross via AUD

1

AUD

= 0.65

USD and

1

AUD

= 0.60

EUR. How many EUR for

$ 200

USD?

Solution

Step 1: USD to AUD (divide).

$AUD$	$=$	$\frac{200}{0.65}$
$AUD$	$\approx$	$307.69$

Step 2: AUD to EUR (multiply).

$EUR$	$=$	$307.69 \times 0.60$
$EUR$	$\approx$	$184.62$

EUR \approx 184.62

About $184.62$ EUR.

Example 4 — Conversion with a fee

Sam exchanges

$ 1,000

AUD for USD. The rate is

1

AUD

= 0.66

USD, and the bank charges a

2 %

fee on the AUD before conversion. How much USD does he receive?

Solution

Apply the $2 %$ fee first, then convert.

$after fee$	$=$	$1,000 \times 0.98$
$after fee$	$=$	$980 AUD$
$USD$	$=$	$980 \times 0.66$
$USD$	$=$	$$ 646.80$

USD = 646.80

Sam receives $$646.80$ USD.

Common pitfalls

Reversing the rate incorrectly. "

1

AUD

= 0.65

USD" does not mean "

1

USD

= 0.65

AUD". For the reverse rate, take the reciprocal:

1 / 0.65 \approx 1.54

AUD per USD.

Multiplying instead of dividing (or vice versa). When converting AUD to a foreign currency, multiply. When converting foreign currency to AUD, divide. Mixing these flips the answer in the wrong direction.

Applying fees in the wrong order. Read carefully: is the fee taken from the original AUD before conversion, or from the converted amount afterwards? It changes the final figure.

Forgetting cross-currency needs two steps. If only AUD-based rates are given, route through AUD: foreign currency → AUD → other foreign currency.

Frequently asked questions

What is an exchange rate?

An exchange rate is the price of one currency in terms of another. " $1$ AUD $= 0.65$ USD" means each Australian dollar buys $65$ US cents.

How do you convert AUD to a foreign currency?

Multiply the AUD amount by the rate. For $$ 300$ AUD at $1$ AUD $= 0.65$ USD, the result is $300 \times 0.65 = $ 195$ USD.

How do you convert a foreign currency back to AUD?

Divide the foreign amount by the rate. For $$ 195$ USD at $1$ AUD $= 0.65$ USD, the result is $195 \div 0.65 = $ 300$ AUD.

If 1 AUD = 0.65 USD, does 1 USD = 0.65 AUD?

No. To find how many AUD per USD, take the reciprocal: $1 / 0.65 \approx 1.54$ AUD per USD.

How do you convert one foreign currency to another using AUD?

Two steps. First convert the source currency to AUD (divide by its rate), then convert AUD to the target currency (multiply by its rate).

How do bank fees affect currency conversion?

If the fee is a percentage of the AUD amount, subtract it from the AUD first, then convert the reduced amount at the exchange rate.

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