Calculating with Time — KS3 Maths

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:

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?

1. Add the hours: 14 + 1 = 15
2. Add the minutes: 35 + 50 = 85
3. 85 minutes ≥ 60, so convert: 85 = 1 hour 25 minutes
4. Add the extra hour: 15 + 1 = 16 hours
5. Finish time: 16:25

Worked example 2: 3 hours 47 minutes + 2 hours 28 minutes

1. Hours: 3 + 2 = 5
2. Minutes: 47 + 28 = 75
3. 75 minutes = 1 hour 15 minutes
4. 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:

1. We cannot subtract 45 from 10, so borrow 1 hour (= 60 minutes): the first time becomes 4 hours 70 minutes.
2. Minutes: 70 − 45 = 25 minutes
3. Hours: 4 − 2 = 2 hours
4. 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.

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