Convert clocks and calculate time intervals
Read 12-hour and 24-hour time · Calculate across an hour or midnight boundary · Use stated duration conversions
Section Paper 2 · Historical Extended · non-calculator
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Integer arithmetic
- Hours and minutes
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Read 12-hour and 24-hour time
- Calculate across an hour or midnight boundary
- Use stated duration conversions
Clock notation is not a decimal
There are 60 seconds in a minute, 60 minutes in an hour and 24 hours in a day. 1 hour 30 minutes is 1.5 hours, not 1.30 hours. 12 am is midnight (00:00); 12 pm is noon (12:00). For afternoon times other than noon, add 12 to the hour to get 24-hour notation.
Schedules and longer units
Calculate a duration by counting to the next hour or converting both times to minutes on a dated timeline. A journey ending after midnight needs the next day's offset. A displayed clock time alone does not identify the date or time zone.
0444 uses 1 year = 365 days for syllabus calculations. Months have unequal calendar lengths, so do not assume every month is 30 days unless the problem says so. For a real dated schedule, follow its supplied dates rather than inventing a month conversion.
Sources for this lesson
Pause and explain
What is 1 hour 30 minutes in decimal hours?
Worked example
A journey starts at 23:35 and ends at 01:10 the next day. Find its duration.
Show the worked solution
- 23:35 to midnight is 25 minutes.
- Midnight to 01:10 is 70 minutes; total 95 minutes.
Answer 1 hour 35 minutes.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Convert 7:45 pm to 24-hour notation and 00:20 to 12-hour notation.
Give me a hint
Use the noon/midnight distinction.
Compare my reasoning
- 7:45 pm becomes 19:45.
- 00:20 is 12:20 am.
19:45 and 12:20 am.
Look for these in your work
- Keep the minutes
- Label am/pm correctly
A class runs from 14:50 to 16:05 on the same day. Find its duration in minutes and hours.
Give me a hint
Count to 15:00, then to 16:05.
Compare my reasoning
- 10 + 65 = 75 minutes.
- 75/60 = 1.25 hours.
75 minutes = 1.25 hours.
Look for these in your work
- Use a common duration unit
- Divide by 60
A service runs from 22:48 to 00:12 the next day. Find its duration; separately convert two syllabus years into days using 365 days per year.
Give me a hint
Handle the midnight boundary and the stated yearly rule separately.
Compare my reasoning
- 22:48 to midnight is 72 minutes; add 12 to get 84.
- 2×365 = 730 days under the supplied rule.
84 minutes = 1 hour 24 minutes; two syllabus years = 730 days.
Look for these in your work
- Use the dated timeline
- State the yearly assumption
Common mistakes
- Clock minutes are not hundredths of an hour.
- Specify the next day when crossing midnight.
What can you explain now?
What is 1 hour 30 minutes in decimal hours?
Compare with the explanation
1.5 hours.
30 minutes is 30/60 = 0.5 hour.
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Make it stick
What is 1 hour 30 minutes in decimal hours?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.