To solve this problem, we need to use the correct conversion factor to change Australian dollars (AUD) to US dollars (USD). Here’s a detailed, step-by-step solution.
1. Understand the given exchange rate:
- We are given that 1.2 AUD is equivalent to 1 USD.
2. Identify the correct conversion factor:
- To convert AUD to USD, we should multiply the amount in AUD by the ratio [tex]\(\frac{1 \text { USD }}{1.2 \text { AUD }}\)[/tex], since each 1.2 AUD is equal to 1 USD.
3. Set up the conversion:
- The amount we want to convert is 22 AUD.
- Our conversion expression becomes: [tex]\(22 \text{ AUD} \times \frac{1 \text{ USD}}{1.2 \text{ AUD}}\)[/tex].
4. Evaluate the conversion expression:
- By multiplying 22 AUD by the conversion factor [tex]\(\frac{1 \text{ USD}}{1.2 \text{ AUD}}\)[/tex], the AUD units cancel out, leaving us with USD.
Thus, the expression that correctly converts 22 AUD to USD with the given exchange rate of 1.2 AUD per 1 USD is:
[tex]\[
\$ 22 \text{ AUD} \times \frac{1 \text{ USD}}{1.2 \text{ AUD}}.
\][/tex]
After evaluating the expression, the result of the conversion is approximately 18.33 USD. Therefore, the correct expression among the given choices is:
[tex]\[
\$ 22 \text{ AUD} \times \frac{1 \text{ USD}}{1.2 \text{ AUD}}.
\][/tex]
