To determine how much medicine O. Andrea must administer, we follow these steps:
1. Convert the mixed number to a decimal:
The medicine bottle contains [tex]\(3 \frac{4}{10}\)[/tex] fluid ounces. Convert this mixed number to a decimal:
[tex]\[
3 \frac{4}{10} = 3 + \frac{4}{10} = 3 + 0.4 = 3.4
\][/tex]
Hence, the medicine bottle contains 3.4 fluid ounces.
2. Find the fraction of the bottle to be administered:
O. Andrea needs to administer [tex]\(\frac{1}{12}\)[/tex] of the total medicine.
3. Calculate the amount of medicine to be administered:
Multiply the total amount of medicine by the fraction to find the amount to be administered:
[tex]\[
\text{Amount to be administered} = 3.4 \times \frac{1}{12}
\][/tex]
Simplifying this calculation step-by-step,
[tex]\[
3.4 \times \frac{1}{12} = \frac{3.4}{12}
\][/tex]
4. Convert decimal result to a fraction (optional but for better understanding):
To refine the decimal into an exact fraction, recall that:
[tex]\[
\frac{3.4}{12} \approx 0.28333
\][/tex]
5. Matching the calculated amount with multiple choices:
It’s helpful to compare the simplified decimal back to the given fraction options:
- [tex]\(\frac{17}{60} \approx 0.28333\)[/tex]
- [tex]\(\frac{15}{62} \approx 0.24194\)[/tex]
- [tex]\(\frac{3}{19} \approx 0.15789\)[/tex]
- [tex]\(\frac{17}{67} \approx 0.25373\)[/tex]
Since [tex]\(\frac{17}{60} \approx 0.28333\)[/tex], it matches our calculated approximate value of the administered medicine.
Therefore, O. Andrea should administer [tex]\(\boxed{\frac{17}{60}}\)[/tex] fluid ounces of medicine.
