Two times called 9:00
Nine in the morning and nine at night both show 9:00 on a clock face. On a 12-hour clock they share the name 9:00, and the am or pm after it says which one is meant: 9:00 am is in the morning, and 9:00 pm is at night.
9:00 pm is in the second lap, directly below 9:00 am in the first.
Keep counting past 12
The 24-hour clock gives every hour of the day its own number. It starts at 00 at midnight and counts the hours straight through the day: 01, 02, 03, and on up to 12 at noon.
After noon it does not start again at 1. It keeps counting: 13, 14, 15, and on up to 23. Nine at night comes 21 hours after midnight, so on the 24-hour clock it is 21:00.
No two hours of the day share a number, so a 24-hour time needs no am or pm. The hour is always written with two digits, so seven in the morning is 07:00.
Both numberings on one chart. In the second lap the hours carry on from 12, and 9 pm is 21.
Add 12 after noon
In the first lap, from midnight to noon, the 24-hour hour is the same as the 12-hour one: 7:30 am is 07:30.
In the second lap, a whole lap of 12 hours has already gone by, so each hour is 12 more than its 12-hour name. Half past two in the afternoon is 2:30 pm, and 2 + 12 = 14, so it is 14:30. The minutes stay the same.
2:30 pm is a whole 12 hours and then 2 hours 30 minutes more: 14:30.
7:30 am = 07:30: before midday the 24-hour name is the face's hour with a leading zero, and the minute hand moves 12 times as fast as the hour hand
Make the clock show 15:45
The clock opens at 7:30 am, which is 07:30. Turn the hour hand to a quarter to four and choose pm. The hour becomes 3 + 12 = 15, so 3:45 pm is 15:45.
Back to the 12-hour clock
To change a 24-hour time back, look at the hour. From 00 to 11 it is a morning time, am. From 13 to 23 it is an afternoon or evening time, pm, and you take 12 away: 16:45 is 16 − 12 = 4, so it is 4:45 pm.
The hour 12 is noon, so 12:00 is 12:00 pm. The hour 00 is midnight, so 00:00 is 12:00 am.
Three ways to slip
Reading 16:45 as 6:45 pm drops the 1 from the front of 16. That takes away 10, but the step between the two clocks is 12.
Counting back from 24 gives the wrong hour too. 3:00 pm is not 24 − 3 = 21:00, because the afternoon counts on from 12: 3:00 pm is 15:00.
Writing 3:00 pm as 03:00 drops the pm. On the 24-hour clock, 03:00 is three o’clock in the middle of the night.
After 23:59
The last minute of the day is 23:59. One minute later it is midnight, 00:00, and the count starts again from 00 on the next day. So going 4 hours on from 22:00 passes midnight: 2 hours reach 00:00, and 2 more reach 02:00 the next morning.
Worked example: The Same Moment in Two Cities
Question The time in Dubai is 4 hours behind the time in Singapore. (a) Lina in Singapore calls her aunt in Dubai at 3.30 p.m. What is the time in Dubai? (b) Her aunt calls back at 21:45 on Friday, by the time in Dubai. What are the time and the day in Singapore?
1.Go back 4 h from 3.30 p.m. Going back 3 h 30 min reaches 12 noon. Going back the other 30 min reaches 11.30 a.m.
Going back 3 h 30 min from 3.30 p.m. reaches 12 noon. The other 30 min reaches 11.30 a.m. 2.(a) The time in Dubai is 11.30 a.m.
(a) The time in Dubai is 11.30 a.m. 3.Singapore is 4 h ahead of Dubai, so go forward 4 h from 21:45 on Friday. The first 2 h 15 min reaches midnight, and Saturday begins.
From 21:45 it is 2 h 15 min to midnight, and then Saturday begins. 4.The part that is left is 4 h − 2 h 15 min = 1 h 45 min. That is 01:45 on Saturday.
The part that is left is 4 h − 2 h 15 min = 1 h 45 min, so the time is 01:45. 5.(b) In Singapore it is 01:45 on Saturday.
(b) In Singapore it is 01:45 on Saturday.
Answer: (a) 11.30 a.m.; (b) 01:45 on Saturday
Common mistakes
- Going forward 4 h in part (a) and answering 7.30 p.m. Dubai is behind Singapore, so the time there is earlier, not later.
- Writing 25:45 on Friday in part (b). The hours stop at 23. After midnight the clock starts again at 00:00 and the day becomes Saturday.