Parts of an hour:

• One hour = 60 minutes
• Half an hour = 30 minutes
• A quarter hour = 15 minutes
• Three-quarters of an hour = 45 minutes

Reading an analogue clock:

• The short hand points to the hour.
• The long hand points to the minutes (when it points to 12 = 0 minutes; to 3 = 15 minutes; to 6 = 30 minutes; to 9 = 45 minutes).

Writing a time: we write hours:minutes, for example \( 08:45 \) means 8 in the morning and 45 minutes.

Calculating elapsed time:

\[ \text{Elapsed time} = \text{End time} - \text{Start time} \]

If the end minutes are less than the start minutes — "borrow" one hour (60 minutes) from the hours.

Example 1: Reading a Clock — Exact Hour

Problem: The short hand points exactly to 7 and the long hand points to 12. What time is it?

Solution:

1. Short hand on 7 → 7 o'clock.
2. Long hand on 12 → 0 minutes.
3. The time is 7:00.

Answer: The time is 7:00 (seven in the morning).

Example 2: Reading a Clock — Quarter Past

Problem: The short hand is between 10 and 11, and the long hand points to 3. What time is it?

Solution:

1. Long hand on 3 → 15 minutes.
2. Short hand has passed 10 but not yet reached 11 → 10 hours.
3. The time is 10:15.

Answer: The time is 10:15 (quarter past ten).

Example 3: Calculating Elapsed Time — No Borrowing

Problem: The film started at 14:20 and ended at 16:50. How long did the film last?

Solution:

1. End time: 16:50 — Start time: 14:20.
2. Minutes: \( 50 - 20 = 30 \) minutes.
3. Hours: \( 16 - 14 = 2 \) hours.
4. Duration: 2 hours and 30 minutes.

Answer: The film lasted two and a half hours (2 hours and 30 minutes).

Example 4: Calculating Elapsed Time — With Borrowing

Problem: A lesson started at 09:45 and ended at 10:30. How long did the lesson last?

Solution:

1. End time: 10:30 — Start time: 09:45.
2. Minutes: \( 30 - 45 \) — problem! 30 is less than 45.
3. Borrow: end time becomes \( 9:90 \) (subtract 1 from hours: \( 10-1=9 \), add 60 to minutes: \( 30+60=90 \)).
4. Minutes: \( 90 - 45 = 45 \) minutes.
5. Hours: \( 9 - 9 = 0 \) hours.
6. Check: \( 09:45 + 45 \text{ minutes} = 10:30 \) — correct!

Answer: The lesson lasted 45 minutes.

Example 5: Finding the End Time

Problem: A walk started at 15:35 and lasted 50 minutes. When did it end?

Solution:

1. Start time: 15:35; add 50 minutes.
2. Minutes: \( 35 + 50 = 85 \).
3. 85 minutes = 1 hour (60 minutes) + 25 minutes.
4. Add one hour: \( 15 + 1 = 16 \); 25 minutes remain.
5. End time: 16:25.

Answer: The walk ended at 16:25.

✗ Common mistake: Confusing the minute hand with the hour hand and reading the wrong time.

✓ The correct way: Short hand = hours; long hand = minutes. Memory trick: "long ↔ lots of minutes."

✗ Common mistake: When calculating elapsed time, subtracting only the hours and forgetting to calculate the minutes separately.

✓ The correct way: Always work in two separate steps: minutes first, then hours. If the end minutes are smaller — borrow 60 minutes.

✗ Common mistake: When finding the end time, forgetting to convert minutes above 60 into an extra hour.

✓ The correct way: After adding the minutes — if the total is more than 60, subtract 60 and add 1 to the hours.

Key points:

• 1 hour = 60 min | half hour = 30 min | quarter hour = 15 min
• Short hand = hours; long hand = minutes.
• Elapsed time = end time \( - \) start time (minutes separately, hours separately).
• If end minutes < start minutes: borrow 60 minutes (and subtract 1 from end hours).
• Check: \( \text{Start} + \text{Duration} = \text{End} \).