Alright, let's solve this problem step-by-step.
You are given a ratio that represents time: [tex]\( \frac{13}{18} \)[/tex].
1. Convert the ratio to a fraction of an hour:
[tex]\[
\frac{13}{18}
\][/tex]
2. Convert the fraction to minutes:
To convert a fraction of an hour to minutes, you multiply by 60 (since there are 60 minutes in an hour):
[tex]\[
\frac{13}{18} \times 60
\][/tex]
3. Simplify the multiplication:
First, calculate [tex]\( \frac{13 \times 60}{18} \)[/tex]:
[tex]\[
\frac{13 \times 60}{18} = \frac{780}{18} \approx 43.33 \text{ minutes}
\][/tex]
4. Round to the nearest quarter-hour:
The nearest quarter-hour intervals are 15, 30, 45, and 60 minutes. We compare 43.33 minutes to these intervals:
- 43.33 is closer to 45 than to 30 or 60.
So, as a result of rounding to the nearest quarter-hour, the time is closest to:
[tex]\[
\boxed{45}
\][/tex]
Thus, the closest given time is:
- 5:45
