Time (IV): 24-hour clock

Foundation

3 pm = 15:00.

For:Primary 3 Mathematics · Unit:Measures · Lesson 19 of 23 in the learning path

After this lesson, you can:
  • The 24-hour clock runs 00:00 to 23:59
  • Morning times stay the same: 9 am = 09:00
  • Afternoon and evening add 12: 3 pm = 15:00
數學Mathematics

1Summary 重點摘要

3 pm = 15:00.

2Vocabulary cards Vocabulary

2
24-hour clock24 小時制

Counting 00:00 to 23:59, used in train timetables.

1
12-hour clock12 小時制

Splitting the day into a.m. and p.m.

a
a.m. (morning)上午

From midnight to 11:59 am; written the same in 24-hour form, e.g. 9:00.

p
p.m. (afternoon/evening)下午/晚上

From noon to midnight; add 12 in 24-hour form, e.g. 3 pm = 15:00.

n
noon (12:00)中午 12 時

12:00, the divide between morning and afternoon.

m
midnight (00:00)午夜 12 時

00:00, the start of the day, written 00:00.

t
timetable時間表

A list of times for trains or events, often in 24-hour form.

a
add 12加 12

The rule for pm times: 3 + 12 = 15.

3Step by step Steps

  1. Part 1: Why 24-hour timeThe 12-hour clock can confuse people: a train at 3 pm and a train at 3 am both look like 3:00, and the numbers alone cannot tell day from night, so mistakes happen. The 24-hour clock is much clearer: 3 pm is 15:00 and 3 am is 03:00, and there is no mixing them up. Why learn both systems? Daily life uses both, and station and airport timetables mostly use the 24-hour clock. Take care that 12-hour times must state am or pm; without those words the time is incomplete and nobody can be sure.
  2. Part 2: Morning times stay the sameMorning times need no change, just write them as they are, the easiest part of the 24-hour clock. 9 am is 09:00, and 11:30 am is 11:30. All times from 00:00 to 11:59 belong to the morning, so write them exactly as on the clock face, with no adding and no subtracting. Take care that morning hours are usually padded to two digits in the 24-hour clock; 9 am is written 09:00, the leading 0 keeping the format tidy, and though 9:00 is understandable, the formal form pads the 0.
  3. Part 3: Afternoon times add 12For afternoon and evening times, add 12 to the hour, the core rule for turning 12-hour time into 24-hour time. Why add 12? Twelve hours have passed since noon, and those 12 hours must be counted in. 3 pm = 3 + 12 = 15:00; 5:30 pm = 5 + 12 = 17, that is 17:30; 8 pm in the evening = 20:00. The rule to remember is: after noon, add 12 to the hour. Take care that only the hours change while the minutes stay; 3:30 pm is 15:30, not 15:42.
  4. Part 4: Two special momentsTwo special moments must be remembered. Noon is written 12:00, with no adding needed, because it is exactly the dividing point between morning and afternoon. Midnight is written 00:00, not 24:00, because a new day begins at 00:00, making midnight the starting point of the day. The usual error is writing noon as 24:00, or writing midnight as 12:00 and mixing it with noon; remember 12:00 belongs to noon and 00:00 to midnight, each holding one end of the day, and never swap them.
  5. Part 5: Convert back to 12-hour timeTo change 24-hour time back, subtract 12 when the hour is bigger than 12, and mark it afternoon or evening. Seeing 19:00, work out 19 - 12 = 7, so it is 7 pm. Seeing 08:00, the 8 is smaller than 12, so read it directly as 8 am, with no subtracting. Take care that after subtracting 12 the words pm or evening must be added; writing only 7:00 confuses it with the morning. Hours below 12 should be left alone and read as am; applying the rule in the wrong direction only creates errors.
  6. Part 6: Reading a timetableTimetables often use the 24-hour clock, and converting lets you read the services. A train list shows 13:45 and 21:10: 13:45 minus 12 is 1:45 pm, and 21:10 minus 12 is 9:10 pm. The two trains are 21:10 - 13:45 = 7 hours 25 minutes apart, and from this you can estimate the wait. Take care that the gap between two trains is safest worked directly with the 24-hour numbers; converting to 12-hour time first only invites mistakes, because the border between morning and afternoon adds trouble.

4Diagrams Diagrams

24 小時制 The 24-hour clock123456789101112下午 2:30+12下午的鐘數 +122:30 下午 → 14:30上午時間不用變:9:00 上午 = 09:00火車・機場・手機全部用 24 小時制00:00 午夜 → 06:00 清晨 → 12:00 中午 → 18:00 傍晚 → 23:59 差一分午夜
Fig. 1: The 24-hour clock

5Worked example Example

Example: write these in 24-hour form: (1) 2:15 pm (2) 10 pm (3) midnight.

  1. Question 1: 2:15 pm, so 2 + 12 = 14, written 14:15.
  2. Question 2: 10 pm, so 10 + 12 = 22, written 22:00.
  3. Question 3: midnight needs no adding; it starts the new day, so write 00:00.
  4. Check the rule: afternoon and evening hours add 12 first, while morning times stay the same.
  5. Answer: Answer: the three times are 14:15, 22:00 and 00:00. When converting to the 24-hour clock, first decide whether the time is am or pm: am times stay the same, pm times add 12 to the hour, and midnight is 00:00.

6Common mistakes Mistakes

✗ Writing 3 pm as 3:00
✓ pm times add 12: 3 + 12 = 15:00
✗ Writing midnight as 24:00
✓ Midnight is 00:00 — the day starts there
✗ Writing 9 am as 21:00
✓ am times never add 12: 9 am is 09:00
✗ Reading 19:00 as 7 am
✓ 19 > 12, so subtract 12: it is 7 pm

7Quick check Quick check

Q11 pm = ?

Q2Midnight = ?

Q3What is 18:30 in 12-hour time?

Q4Class starts at 8 am. Write it in 24-hour form.

Q5How far apart are 20:00 and 20:45?

8Recap Recap

  • The 24-hour clock runs 00:00 to 23:59
  • Morning times stay the same: 9 am = 09:00
  • Afternoon and evening add 12: 3 pm = 15:00
  • Midnight is 00:00 and noon is 12:00
  • To go back, subtract 12 from times over 12:00

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