Let's analyze the student's approach step by step to identify the conversion ratio that was skipped.
1. The student starts with 720 seconds and aims to convert this into hours. They directly use the conversion factor between hours and minutes:
[tex]\[ 720 \, \text{seconds} \times \left( \frac{1 \text { hour }}{60 \text { minutes }} \right) = 12 \, \text{hours} \][/tex]
This result is incorrect. Let's identify why by understanding the correct conversion process.
2. First, the student should convert seconds to minutes. The conversion factor is:
[tex]\[ \frac{1 \text { minute }}{60 \text { seconds }} \][/tex]
Using this ratio, we convert 720 seconds to minutes:
[tex]\[ 720 \, \text{seconds} \times \left( \frac{1 \text { minute }}{60 \text { seconds }} \right) = 12 \, \text{minutes} \][/tex]
3. Next, we need to convert minutes to hours. The correct conversion factor for this step is:
[tex]\[ \frac{1 \text { hour }}{60 \text { minutes }} \][/tex]
Using this ratio, we convert 12 minutes to hours:
[tex]\[ 12 \, \text{minutes} \times \left( \frac{1 \text { hour }}{60 \text { minutes }} \right) = 0.2 \, \text{hours} \][/tex]
4. By combining the steps, we can clearly see that the student missed the initial conversion from seconds to minutes. The skipped step is:
[tex]\[ \frac{1 \text { minute }}{60 \text { seconds }} \][/tex]
So, the correct answer is:
A. [tex]\(\frac{1 \text { minute }}{60 \text { seconds }}\)[/tex]
