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Year 5 Maths Time

Convert 12 to 24-hour

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Theory

To change a pm time to 24-hour time, add 12 to the hour; to change back, subtract 12. Morning times keep their hour, with a zero in front. The two \(12\) o’clock hours are the special cases. This Year 5 maths page shows every case with examples.

am times run from midnight to just before midday. pm times run from midday to just before midnight.

am to 24-hour: keep the hour and write four digits: \(\text{10:25 am} = \text{10:25}\), \(\text{3:10 am} = \text{03:10}\).

pm to 24-hour: add \(12\) to the hour: \(\text{5:40 pm} = \text{17:40}\).

Special cases: the \(12\) am hour is \(00\) (\(\text{12:35 am} = \text{00:35}\)); the \(12\) pm hour stays \(12\) (\(\text{12:05 pm} = \text{12:05}\)).

24-hour to 12-hour: hours \(13\) to \(23\): subtract \(12\) and write pm. Hour \(12\): pm. Hour \(00\): write \(12\) and am. Other hours: drop the leading zero and write am.

12-hour and 24-hour times on one timeline A timeline from midnight to midnight with 24-hour hours above and 12-hour hours below. A red dot at 17:40, labelled 5:40 pm, and one at 03:10, labelled 3:10 am. am (midnight to midday)pm (midday to midnight) 000306091215182100 123691236912 24-hour (top) and 12-hour (bottom) 3:10 am 5:40 pm
Below the line: 12-hour; above: 24-hour. \(\text{5:40 pm}\) sits above \(17\).
Converting a pm time A box 5:40 (pm) with an arrow labelled pm, plus 12 on the hour, to a box 17:40. A red arrow back is labelled minus 12, write pm. 5:40 17:40 pm: +12 −12, write pm
\(\text{5:40 pm}\): add \(12\) to the hour to get \(\text{17:40}\); subtract \(12\) to come back.

Conversion table for the hours:

12-hour24-hour
\(12\) am (midnight hour)\(00\)
\(1\) am to \(11\) am\(01\) to \(11\)
\(12\) pm (midday hour)\(12\)
\(1\) pm to \(11\) pm\(13\) to \(23\) (add \(12\))
Only pm hours get +12. \(\text{6:20 am}\) stays \(\text{06:20}\).
Watch the 12s. \(\text{12:35 am}\) is just after midnight: \(\text{00:35}\).

12-hour to 24-hour

  1. am: keep the hour (but \(12\) am becomes \(00\)).
  2. pm: add \(12\) to the hour (but \(12\) pm stays \(12\)).
  3. Write four digits.

24-hour to 12-hour

  1. Hour 13 to 23: subtract \(12\), write pm.
  2. Hour 12: write pm. Hour 00: write \(12\) and am.
  3. Hour 01 to 11: drop the leading zero, write am.
Example 1 — pm to 24-hour
Write \(\text{5:40 pm}\) in 24-hour time.
Solution
\(5 + 12\)\(=\)\(17\)
5+12=17

\(\text{17:40}\).

Example 2 — am to 24-hour
Write each time in 24-hour time.
(i) \(\text{10:25 am}\)
(ii) \(\text{3:10 am}\)
Solution

(i) \(\text{10:25}\)
(ii) \(\text{03:10}\)

Example 3 — 24-hour to pm
Write \(\text{16:55}\) as a 12-hour time.
Solution
\(16 - 12\)\(=\)\(4\)
16−12=4

\(\text{4:55 pm}\).

Example 4 — Night times
Write each as a 12-hour time.
(i) \(\text{23:35}\)
(ii) \(\text{21:20}\)
Solution
\(23 - 12\)\(=\)\(11\)
\(21 - 12\)\(=\)\(9\)
23−12=11,21−12=9

(i) \(\text{11:35 pm}\)
(ii) \(\text{9:20 pm}\)

Example 5 — Just after midnight
Write \(\text{12:35 am}\) in 24-hour time.
Solution

The midnight hour is \(00\): \(\text{00:35}\).

Example 6 — Just after midday
Write \(\text{12:05 pm}\) in 24-hour time.
Solution

The midday hour stays \(12\): \(\text{12:05}\).

Example 7 — Timetable
A ferry timetable shows departures at \(\text{06:15}\), \(\text{12:00}\) and \(\text{19:50}\). Write them as 12-hour times.
Solution

\(\text{6:15 am}\), \(\text{12:00 pm}\) (midday), \(\text{7:50 pm}\).

Example 8 — Find the mistake
Zoe wrote \(\text{4:15 am}\) as \(\text{16:15}\). What went wrong?
Solution

She added \(12\) to a morning time. It should be \(\text{04:15}\); \(\text{16:15}\) is \(\text{4:15 pm}\).

Common pitfalls

Adding 12 to am times. Only pm hours from \(1\) to \(11\) get \(+12\).
Writing 12 am as 12. The midnight hour is \(00\).
Writing 12 pm as 24. Midday is \(\text{12:00}\).
Keeping am or pm in 24-hour time. \(\text{17:40 pm}\) is wrong; just write \(\text{17:40}\).

Frequently asked questions

How do you change a pm time to 24-hour time?

Add \(12\) to the hour: \(\text{5:40 pm} = \text{17:40}\).

How do you change 24-hour time to pm?

Subtract \(12\) from hours \(13\) to \(23\): \(\text{16:55} = \text{4:55 pm}\).

What is 12:35 am in 24-hour time?

\(\text{00:35}\).

What is 12:05 pm in 24-hour time?

\(\text{12:05}\).

Why do morning times start with 0?

24-hour times always have four digits, so \(3{:}10\) am is \(\text{03:10}\).

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