The 24-hour clock and durations

Read the 24-hour clock

In the 24-hour clock, 00:00 is the start of a day and 12:00 is noon. After noon, 13:00 is 1:00 pm, 14:00 is 2:00 pm, and so on up to 23:59 before the next midnight.

07:25 is 7:25 am. 19:25 is 7:25 pm. Hours after noon use 12 more than the corresponding 12-hour number; the minute value stays the same.

12:15 means 12:15 pm, while 00:15 means 12:15 am. Do not add 12 to every am time or turn midnight into an extra hour of duration.

In 12-hour notation, 12:00 am is midnight and 12:00 pm is noon. For other morning hours, keep the hour number when changing to the 24-hour clock. For other afternoon or evening hours, add twelve. 12 am changes to 00; 12 pm stays 12. In each case, keep the minutes unchanged.

To go back from the 24-hour clock, hours 00–11 are before noon and use am. Change hour 00 to 12. Hours 12–23 use pm; keep hour 12, and subtract twelve from hours 13–23. The two notations name the same time of day.

Check your understanding 1 Change the hour and keep the minutes

Write 8:40 pm using the 24-hour clock. Enter its hour and minutes separately.

Hour (24-hour clock)

Clock minutes

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20:40. The hour is 8 + 12 = 20; the minutes stay 40. Both 8:40 pm and 20:40 name the same evening time.

Check your understanding 2 Distinguish the two twelves

Write 12:05 am using the 24-hour clock. Then write the 24-hour time 12:05 using the 12-hour clock, including am or pm. Explain why the two answers refer to different parts of the day.

Your two times and explanation, or work on paper

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12:05 am becomes 00:05, five minutes after midnight. A 24-hour time of 12:05 becomes 12:05 pm, five minutes after noon. The minutes agree, but the times are twelve hours apart. The words noon and midnight on their own mean twelve exactly, not five minutes past it.

Find a duration by counting forward

The start time and finish time label when events happen. The duration is how long passes between them. If you know any two of these quantities, you can find the third. Keep the day with each clock time when a journey crosses midnight.

A journey starts at 14:45 and ends at 16:10 on the same day. From 14:45 to 15:00 is 15 min, then 60 min to 16:00, then 10 min to 16:10.

The duration is 15 + 60 + 10 = 85 min, or 1 h 25 min. Subtracting written clock numbers as ordinary decimal numbers would mishandle the 60 minutes in an hour.

Check your understanding 3 Keep hours and minutes together

A class starts at 19:35 and finishes at 21:10 on the same day. Give its duration in whole hours and the minutes left over.

Whole hours

Minutes left over

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1 h 35 min. The jumps take 25 + 60 + 10 = 95 min. One complete hour uses 60 min, leaving 35 min. Check: 19:35 plus one hour is 20:35, and 35 more minutes reaches 21:10.

Work backwards for a start time

A film ends at 17:20 and lasts 1 h 45 min. Take away one hour to reach 16:20. Take away 20 min to reach 16:00, then the 25 min still to remove. The start time was 15:35.

Check by going forward: 15:35 to 16:35 is one hour, then 45 min to 17:20.

When you go backwards through 00:00, you enter the previous day. For example, 15 minutes before 00:05 is 23:50 on the previous day: take away five minutes to reach midnight, then ten more. The clock’s smaller hour number does not tell you which day you are on.

Check your understanding 4 Find what happened before midnight

A journey finishes at 00:10 and lasts 40 min. Find its starting time and day, relative to the finishing day. Check by counting forward.

Your starting time, day and forward check, or work on paper

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The start is 23:30 on the previous day. Going backwards, ten minutes reaches 00:00; another thirty minutes reaches 23:30. Going forward, 23:30 to midnight takes thirty minutes, then ten more minutes reaches 00:10. That is forty minutes altogether.

Check your understanding 5 Cross midnight carefully

A journey starts at 23:40 and lasts 50 min. What is its finishing time, and on which day?

Your finishing time, day and check, or work on paper

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Twenty minutes reaches 00:00 at the start of the next day. Thirty minutes remain, so the finish is 00:30 on the next day. A date change does not reset the duration already travelled.

For each problem, label which two quantities you know: start time, finish time or duration. Choose a forward or backward jump to find the missing one.