To convert 22 Australian dollars (AUD) to US dollars (USD) given the conversion rate of 1.2 AUD = 1 USD, we need to find the correct expression that corresponds to this conversion.
Let’s analyze each of the given expressions:
1. \(\$22 \, \text{AUD} \times \frac{1.2 \, \text{USD}}{1 \, \text{AUD}}\)
- This expression suggests multiplying 22 AUD by a factor that converts AUD to USD. The factor used is \( \frac{1.2 \, \text{USD}}{1 \, \text{AUD}} \), implying that 1 AUD equals 1.2 USD. This is incorrect because 1 AUD does not equal 1.2 USD. Hence, this expression is incorrect.
2. \(\$22 \, \text{AUD} \times \frac{1 \, \text{USD}}{1.2 \, \text{AUD}}\)
- This expression suggests converting 22 AUD to USD by multiplying with a factor that correctly represents the conversion rate. The factor used is \( \frac{1 \, \text{USD}}{1.2 \, \text{AUD}} \), meaning 1 USD equals 1.2 AUD, which is our given conversion rate. This configuration is correct because it uses the conversion rate appropriately.
3. \(\$1.20 \, \text{AUD} \times \frac{1 \, \text{USD}}{1.2 \, \text{AUD}}\)
- This expression is incorrect because it starts with 1.20 AUD, which is not the amount we are converting (22 AUD).
4. \(\$1.20 \, \text{AUD} \times \frac{1.2 \, \text{USD}}{1 \, \text{AUD}}\)
- This expression is also incorrect for the same reason as the previous one. It begins with 1.20 AUD instead of 22 AUD.
Given these analyses, the correct expression to use for converting 22 AUD to USD with the given rate of 1.2 AUD = 1 USD is:
[tex]\[
\$ 22 \, \text{AUD} \times \frac{1 \, \text{USD}}{1.2 \, \text{AUD}}
\][/tex]
Using this conversion factor, we get:
[tex]\[
\[tex]$22 \, \text{AUD} \times \frac{1 \, \text{USD}}{1.2 \, \text{AUD}} = \$[/tex]18.333333333333336 \, \text{USD}
\][/tex]
Thus, 22 AUD is approximately equal to 18.333333333333336 USD.
