Calculating with time is trickier than calculating with decimals because time uses base 60 — there are 60 seconds in a minute and 60 minutes in an hour, not 100. Adding and subtracting hours and minutes requires careful conversion before you can apply standard column methods.
Why is time different from decimals?
In our decimal number system, 10 units at one level make 1 unit at the next. Time breaks that pattern: 60 seconds make a minute, 60 minutes make an hour, 24 hours make a day. This means you cannot simply treat a time such as 2:45 as the decimal 2.45 — the minutes part runs from 0 to 59, not 0 to 99.
Key conversions to know:
| Unit | Equivalence |
|---|---|
| 1 minute | 60 seconds |
| 1 hour | 60 minutes = 3600 seconds |
| 1 day | 24 hours |
| 1 week | 7 days |
How do you add two times together?
The safest method is to add hours and minutes separately, then convert if the minutes total 60 or more.
Worked example 1: A film starts at 14:35 and lasts 1 hour 50 minutes. When does it finish?
- Add the hours: 14 + 1 = 15
- Add the minutes: 35 + 50 = 85
- 85 minutes ≥ 60, so convert: 85 = 1 hour 25 minutes
- Add the extra hour: 15 + 1 = 16 hours
- Finish time: 16:25
Worked example 2: 3 hours 47 minutes + 2 hours 28 minutes
- Hours: 3 + 2 = 5
- Minutes: 47 + 28 = 75
- 75 minutes = 1 hour 15 minutes
- Total: 5 + 1 = 6 hours 15 minutes
How do you subtract times to find elapsed time?
The number-line (bridging) method avoids borrowing and is the clearest approach.
Worked example 3: A journey starts at 09:48 and ends at 12:15. How long does it take?
Use a number line, counting in stages:
- 09:48 → 10:00: that is 12 minutes
- 10:00 → 12:00: that is 2 hours
- 12:00 → 12:15: that is 15 minutes
- Total: 2 hours + 12 minutes + 15 minutes = 2 hours 27 minutes
Worked example 4: 5 hours 10 minutes − 2 hours 45 minutes
Method — borrow a minute-hour:
- We cannot subtract 45 from 10, so borrow 1 hour (= 60 minutes): the first time becomes 4 hours 70 minutes.
- Minutes: 70 − 45 = 25 minutes
- Hours: 4 − 2 = 2 hours
- Answer: 2 hours 25 minutes
How do you convert between 12-hour and 24-hour clock?
- 12-hour to 24-hour (pm times): add 12 to the hours. 3:45 pm → 15:45. (Exception: 12:00 pm noon stays 12:00; 12:00 am midnight becomes 00:00.)
- 24-hour to 12-hour: subtract 12 from any hour ≥ 13 and add "pm". 17:20 → 5:20 pm.
- am times: the hours stay the same. 08:30 stays 08:30 in 24-hour clock (written with a leading zero).
How do you convert minutes to a fraction or decimal of an hour?
Divide the minutes by 60.
- 30 minutes = 30/60 = 0.5 hours (or ½)
- 45 minutes = 45/60 = 0.75 hours (or ¾)
- 15 minutes = 15/60 = 0.25 hours (or ¼)
- 20 minutes = 20/60 = ⅓ hours ≈ 0.333 hours
This conversion is essential for speed-distance-time calculations where speed is measured in kilometres per hour — you must convert minutes to hours first.
What mistakes should you avoid?
- Treating time like a decimal. 1.5 hours is 1 hour 30 minutes, not 1 hour 50 minutes. 2.75 hours is 2 hours 45 minutes, not 2 hours 75 minutes.
- Forgetting to convert when adding minutes. If your minute total exceeds 59, always carry 1 hour.
- Subtracting in the wrong direction. Always subtract the earlier time from the later time. If you get a negative result for the hours, swap the order or check your starting values.
- Mixing 12-hour and 24-hour times. Write all times in the same format before calculating.
Frequently asked questions
Can I use a calculator for time arithmetic?
On a non-calculator paper you cannot. On a calculator paper, most standard calculators treat 2.3 as 2.3 hours, not 2 hours 30 minutes. You must convert to decimal hours first (e.g. 2 h 15 min = 2.25 hours) before entering values. Some scientific calculators have a dedicated time function — check your manual, but the manual conversion method is more reliable under exam conditions.
How do I work with seconds as well as minutes?
Use the same principle: add seconds, convert 60+ seconds to minutes; add minutes, convert 60+ minutes to hours. The bridging method works at each level. For example, 1 min 35 s + 2 min 50 s: seconds 35 + 50 = 85 s = 1 min 25 s; minutes 1 + 2 + 1 = 4 min; total 4 min 25 s.
My elapsed time calculation crosses midnight — what do I do?
Count forward in the same stages. For example, from 22:40 to 01:15: 22:40 → 23:00 = 20 min; 23:00 → 24:00 (= 00:00) = 1 hour; 00:00 → 01:15 = 1 hour 15 min; total = 2 hours 35 minutes. The key is not to panic — the number line is just extended beyond 24:00.
Is 12:00 midday written as 12:00 or 12:00 pm?
In everyday speech, 12:00 noon is written "12:00 pm" (or "12 noon"), and midnight is "12:00 am" (or "12 midnight"). In 24-hour notation, noon is 12:00 and midnight is 00:00 (the start of the day) or 24:00 (the end). In exam questions the problem will usually make it clear from context — "the train departs at midday" leaves no ambiguity.
For guided KS3 number and measurement practice with Professor Pi, visit AI Tutors.