Worksheet for converting between 12-hour and 24-hour time formats.

To solve the problem of converting between 12-hour and 24-hour time formats, we need to understand the rules for each format:

Key Rules:

1. 12-hour clock:
- Uses a 12-hour cycle with "AM" (morning) and "PM" (afternoon/evening).
- Times range from 12:00 AM to 11:59 AM (morning) and 12:00 PM to 11:59 PM (evening).

2. 24-hour clock:
- Uses a 24-hour cycle.
- Times range from 00:00 (midnight) to 23:59.
- No need for AM/PM indicators.

Conversion Rules:

- From 12-hour to 24-hour:
- For times in the AM, keep the hour as is (except 12:00 AM becomes 00:00).
- For times in the PM, add 12 to the hour (except 12:00 PM remains 12:00).

- From 24-hour to 12-hour:
- For hours 00 to 11, convert to AM (00:00 becomes 12:00 AM, 01:00 becomes 1:00 AM, etc.).
- For hours 12 to 23, subtract 12 from the hour and convert to PM (12:00 becomes 12:00 PM, 13:00 becomes 1:00 PM, etc.).

---

Given Table:

| 12-hour time | 24-hour time |
|--------------|--------------|
| 6:00 pm | |
| | 02:15 |
| 12:30 pm | |
| | 17:15 |
| | 14:20 |
| 7:30 pm | |
| 9:00 am | |

---

Step-by-Step Solution:

#### 1. Convert 6:00 pm to 24-hour time:
- In the 12-hour format, 6:00 pm is in the PM period.
- Add 12 to the hour: \( 6 + 12 = 18 \).
- The minutes remain the same: 00.
- Result: 18:00

#### 2. Convert 02:15 (24-hour) to 12-hour time:
- In the 24-hour format, 02:15 is in the early morning (before 12:00).
- Since it is less than 12, it is in the AM period.
- The hour remains 2, and the minutes remain 15.
- Result: 2:15 AM

#### 3. Convert 12:30 pm to 24-hour time:
- In the 12-hour format, 12:30 pm is in the PM period.
- 12:00 PM remains 12:00 in the 24-hour format.
- The minutes remain the same: 30.
- Result: 12:30

#### 4. Convert 17:15 (24-hour) to 12-hour time:
- In the 24-hour format, 17:15 is in the afternoon (after 12:00).
- Subtract 12 from the hour: \( 17 - 12 = 5 \).
- The minutes remain the same: 15.
- Result: 5:15 PM

#### 5. Convert 14:20 (24-hour) to 12-hour time:
- In the 24-hour format, 14:20 is in the afternoon (after 12:00).
- Subtract 12 from the hour: \( 14 - 12 = 2 \).
- The minutes remain the same: 20.
- Result: 2:20 PM

#### 6. Convert 7:30 pm to 24-hour time:
- In the 12-hour format, 7:30 pm is in the PM period.
- Add 12 to the hour: \( 7 + 12 = 19 \).
- The minutes remain the same: 30.
- Result: 19:30

#### 7. Convert 9:00 am to 24-hour time:
- In the 12-hour format, 9:00 am is in the AM period.
- Keep the hour as is: 9.
- The minutes remain the same: 00.
- Result: 09:00

---

Final Answer:

| 12-hour time | 24-hour time |
|--------------|--------------|
| 6:00 pm | 18:00 |
| 2:15 AM | 02:15 |
| 12:30 pm | 12:30 |
| 5:15 PM | 17:15 |
| 2:20 PM | 14:20 |
| 7:30 pm | 19:30 |
| 9:00 am | 09:00 |

$$
\boxed{
\begin{array}{|c|c|}
\hline
\text{12-hour time} & \text{24-hour time} \\
\hline
6:00 \text{ pm} & 18:00 \\
2:15 \text{ AM} & 02:15 \\
12:30 \text{ pm} & 12:30 \\
5:15 \text{ PM} & 17:15 \\
2:20 \text{ PM} & 14:20 \\
7:30 \text{ pm} & 19:30 \\
9:00 \text{ am} & 09:00 \\
\hline
\end{array}
}
$$