To convert 22 Australian dollars (AUD) to US dollars (USD) given that 1.2 AUD equals 1 USD, we need to use the appropriate conversion factor. Let's consider each expression provided:
1. [tex]\(\$ 22\)[/tex] AUD [tex]\(\times \frac{1.2 \text{ USD }}{1 \text{ AUD }}\)[/tex]
This expression suggests that 1 AUD = 1.2 USD, which is incorrect according to the given conversion rate. Therefore, this expression should not be used.
2. [tex]\(\$ 22\)[/tex] AUD [tex]\(\times \frac{1 \text{ USD }}{1.2 \text{ AUD }}\)[/tex]
This expression correctly represents the conversion rate given: 1 USD = 1.2 AUD. It converts AUD to USD by multiplying the amount in AUD by the units of USD per AUD. This is the correct expression to use.
3. [tex]\(\$ 1.20\)[/tex] AUD [tex]\(\times \frac{1 \text{ USD }}{1.2 \text{ AUD }}\)[/tex]
This expression only converts 1.20 AUD to USD, rather than the total amount of 22 AUD. Therefore, this expression is not suitable for converting the full amount.
4. [tex]\(\$ 1.20\)[/tex] AUD [tex]\(\times \frac{1.2 \text{ USD }}{1 \text{ AUD }}\)[/tex]
This expression wrongly assumes 1 AUD = 1.2 USD and only converts 1.20 AUD to USD, so it should not be used.
Given the above analysis, the correct expression to convert 22 AUD to USD is:
[tex]\[
\$ 22 \text{ AUD} \times \frac{1 \text{ USD }}{1.2 \text{ AUD }}
\][/tex]
To verify the correctness of this expression, performing the conversion:
[tex]\[
\$ 22 \text{ AUD} \times \frac{1 \text{ USD }}{1.2 \text{ AUD}} = \$ 18.333333333333336 \text{ USD}
\][/tex]
Thus, the correct expression is:
[tex]\[
\$ 22 \text{ AUD} \times \frac{1 \text{ USD }}{1.2 \text{ AUD}}
\][/tex]
