Time Calculations
Time calculations work in sixties, not tens: 60 seconds make a minute and 60 minutes make an hour. This NSW Year 7 maths subtopic consolidates time skills from primary school before they are used in rates, timetables and travel problems.
You will convert between seconds, minutes, hours, days and weeks, add and subtract hours and minutes by carrying and borrowing 60, change minutes to decimal hours (\(45\text{ min} = 0.75\text{ h}\)), and find the elapsed time from a start to a finish time. Working out the length of a shift or a long flight uses these steps. This subtopic is part of Year 7 Ratios, Rates and Time.
Every question with a fully worked solution.
- Time Calculations - Video - Converting Units of Time Watch
Theory
Time is measured in seconds, minutes, hours, days and weeks. An hour has \(60\) minutes, not \(100\), so time calculations carry and borrow in \(60\)s. This Year 7 maths page shows how to convert units of time, add and subtract hours and minutes, use decimal hours and find elapsed time.
The facts: \(1\) min \(= 60\) s, \(1\) h \(= 60\) min, \(1\) day \(= 24\) h, \(1\) week \(= 7\) days.
Converting. A bigger unit to a smaller unit: multiply (\(3\) min \(= 3 \times 60 = 180\) s). A smaller unit to a bigger unit: divide, and the minutes left over stay as minutes: \(200\) min \(= 3\) h \(20\) min, because \(3 \times 60 = 180\).
Adding. Add the hours and the minutes separately. Then every \(60\) minutes make \(1\) hour: \(3\) h \(75\) min \(= 4\) h \(15\) min.
Subtracting. If there are not enough minutes, borrow \(1\) hour \(= 60\) minutes: \(5\) h \(10\) min \(= 4\) h \(70\) min.
Decimal hours. Minutes to part of an hour: divide by \(60\) (\(30\) min \(= 0.5\) h). Part of an hour to minutes: multiply by \(60\) (\(0.2\) h \(= 12\) min).
Elapsed time (how long from a start to a finish): count on to the next o’clock, then whole hours, then the minutes left.
Common minutes as decimal hours (minutes ÷ 60):
| Minutes | Hours |
|---|---|
| \(6\) min | \(0.1\) h |
| \(15\) min | \(0.25\) h |
| \(30\) min | \(0.5\) h |
| \(45\) min | \(0.75\) h |
How to add or subtract hours and minutes
- Line up hours with hours and minutes with minutes.
- Adding: add each part, then change every \(60\) minutes into \(1\) hour.
- Subtracting: if the minutes are too small, borrow \(1\) hour \(= 60\) minutes first.
- Check by adding back, or by working in minutes.
How to find elapsed time
- Count on from the start to the next o’clock.
- Jump whole hours, then the minutes left.
- Add the jumps.
(i) \(350\) minutes into hours and minutes
(ii) \(2\) days \(5\) hours \(20\) minutes into hours and minutes
| \(5 \times 60\) | \(=\) | \(300\) |
| \(350 - 300\) | \(=\) | \(50\) |
| \(2 \times 24 + 5\) | \(=\) | \(53\) |
(i) \(5\) h \(50\) min
(ii) \(53\) h \(20\) min (the minutes stay as minutes)
(ii) Convert \(285\) minutes into hours and minutes.
(iii) Convert \(1\) day \(7\) h \(40\) min into hours and minutes.
| \(9 \times 60\) | \(=\) | \(540\) |
| \(4 \times 60\) | \(=\) | \(240\) |
| \(285 - 240\) | \(=\) | \(45\) |
| \(24 + 7\) | \(=\) | \(31\) |
(i) \(540\) s
(ii) \(4\) h \(45\) min
(iii) \(31\) h \(40\) min
(i) \(2\) h \(26\) min \(+\) \(3\) h \(47\) min
(ii) \(4\) h \(4\) min \(-\) \(2\) h \(12\) min
(i) Hours: \(2 + 3 = 5\). Minutes: \(26 + 47 = 73\) min \(= 1\) h \(13\) min.
(ii) \(4\) min is less than \(12\) min, so borrow: \(4\) h \(4\) min \(= 3\) h \(64\) min.
| \(26 + 47\) | \(=\) | \(73\) |
| \(64 - 12\) | \(=\) | \(52\) |
| \(3 - 2\) | \(=\) | \(1\) |
(i) \(6\) h \(13\) min
(ii) \(1\) h \(52\) min
(i) \(2\) h \(47\) min \(+\) \(3\) h \(38\) min
(ii) \(7\) h \(20\) min \(-\) \(4\) h \(45\) min
| \(47 + 38\) | \(=\) | \(85\) |
| \(80 - 45\) | \(=\) | \(35\) |
(i) \(85\) min \(= 1\) h \(25\) min, so \(6\) h \(25\) min.
(ii) \(7\) h \(20\) min \(= 6\) h \(80\) min, so \(2\) h \(35\) min. Check: \(2\) h \(35\) min \(+\) \(4\) h \(45\) min \(= 7\) h \(20\) min.
(ii) Write \(1.6\) h in hours and minutes.
| \(45 \div 60\) | \(=\) | \(0.75\) |
| \(0.6 \times 60\) | \(=\) | \(36\) |
(i) \(3.75\) h
(ii) \(1\) h \(36\) min
Count on from 9:35 am (see the time line in Diagrams): \(25\) min \(+ 4\) h \(+ 5\) min \(= 4\) h \(30\) min. Take away the lunch break, borrowing \(1\) hour: \(3\) h \(90\) min \(- 45\) min.
| \(4 \times 60 + 30\) | \(=\) | \(270\) |
| \(270 - 45\) | \(=\) | \(225\) |
| \(225 \div 60\) | \(=\) | \(3.75\) |
They walk for \(3\) h \(45\) min \(= 3.75\) hours.
Common pitfalls
Frequently asked questions
How do you convert minutes to hours and minutes?
Divide by \(60\). The whole number is the hours and the remainder is the minutes: \(285\) min \(= 4\) h \(45\) min.
How do you add hours and minutes?
Add the hours and the minutes separately, then change each \(60\) minutes into an hour.
How do you subtract times when there are not enough minutes?
Borrow \(1\) hour and add \(60\) to the minutes.
How do you write minutes as a decimal of an hour?
Divide by \(60\). \(45\) min \(= 0.75\) h.
How do you find how long something takes?
Count on from the start time to the next o’clock, then whole hours, then the minutes left.