To convert 22 Australian dollars (AUD) to US dollars (USD), we need to use the appropriate conversion factor. We know that 1 US dollar is equivalent to 1.2 Australian dollars.
The correct conversion factor should allow us to cancel out the AUD unit and obtain the amount in USD. Here is the step-by-step breakdown:
1. First, we recognize the given conversion rate: [tex]\( 1 \text{ USD} = 1.2 \text{ AUD} \)[/tex].
2. To convert from AUD to USD, each 1 AUD should be divided by the conversion rate (since it takes 1.2 AUD to make 1 USD). Therefore, we use the fraction [tex]\(\frac{1 \text{ USD}}{1.2 \text{ AUD}}\)[/tex].
3. Multiply 22 AUD by the conversion factor:
[tex]\[ 22 \text{ AUD} \times \frac{1 \text{ USD}}{1.2 \text{ AUD}} \][/tex]
In this expression, the 'AUD' units cancel out (since they appear in both the numerator and denominator), leaving us with:
[tex]\[ 22 \times \frac{1}{1.2} \text{ USD} \][/tex]
4. When calculating this, we get the value:
[tex]\[ \frac{22}{1.2} = 18.333333333333336 \text{ USD} \][/tex]
Thus, the correct expression to convert 22 AUD to USD is:
[tex]\[ 22 \text{ AUD} \times \frac{1 \text{ USD}}{1.2 \text{ AUD}} \][/tex]
This matches the second option in your list:
[tex]\[ \$ 22 A U D \times \frac{1 \text{ USD }}{1.2 \text{ AUD }} \][/tex]
