To convert Australian dollars (AUD) to US dollars (USD), we need to use the exchange rate between the two currencies. We know that 1.2 AUD is equivalent to 1 USD. Our goal is to find how many USD are equivalent to 22 AUD.
### Step-by-Step Solution:
1. Understand the Conversion Rate:
- We know that 1.2 AUD = 1 USD
- This means that to convert AUD to USD, we need to find how much 1 AUD is worth in USD.
- To find 1 AUD in USD, we divide 1 USD by 1.2 AUD:
[tex]\[ \frac{1 \text{ USD}}{1.2 \text{ AUD}} \][/tex]
2. Set Up the Conversion Expression:
- We need to multiply the amount in AUD (22 AUD) by the conversion rate that expresses 1 AUD in terms of USD.
- The appropriate conversion rate is [tex]\(\frac{1 \text{ USD}}{1.2 \text{ AUD}}\)[/tex].
3. Select the Correct Conversion Expression:
- We have 22 AUD, so we should multiply this by the conversion rate:
[tex]\[ 22 \text{ AUD} \times \frac{1 \text{ USD}}{1.2 \text{ AUD}} \][/tex]
4. Calculate the Equivalent in USD:
- By using the above expression, we calculate:
[tex]\[ 22 \text{ AUD} \times \frac{1 \text{ USD}}{1.2 \text{ AUD}} \approx 18.33 \text{ USD} \][/tex]
Therefore, the expression that can be used to convert 22 Australian dollars to US dollars, given that 1.2 AUD equals 1 USD, is:
[tex]\[ 22 \text{ AUD} \times \frac{1 \text{ USD}}{1.2 \text{ AUD}} \][/tex]
Thus, the correct choice is:
[tex]\[ \$22 \text{ AUD} \times \frac{1 \text{ USD}}{1.2 \text{ AUD}} \][/tex]
And the resulting equivalent amount in US dollars is approximately [tex]\(\$18.33\)[/tex] (though rounding conventions may vary, here you would normally round to two decimal places if needed). The option number for this correct expression is:
[tex]\[ \boxed{2} \][/tex]
