Units of time
This list below shows the units we use to measure time.
It also shows the conversion from one unit to another.
\(60\) seconds = \(1\) minute
\(60\) minutes = \(1\) hour
\(24\) hours = \(1\) day
\(7\) days = \(1\) week
\(365\) days = \(1\) year (\(366\) days in a leap year)
Question
a) How many minutes are there in \(6\) hours?
b) How many hours are there in a week?
c) How many weeks make up \(63\) days?
Answer
a) \(60 \times 6 = 360\) minutes
b) \(24 \times 7 = 168\) hours in one week
c) \(63 \div 7 = 9\) weeks (there are \(7\) days in a week)
You must be careful when using fractions and decimals with units of time
For example, \(0.5\) hours equals \(30\) minutes, not \(50\) minutes.
This is because decimals show fractions of tenths, hundredths, thousandths and so on.
But minutes are measured in sixtieths of an hour.
Similarly, \(\frac{1}{4}\) hour = \(\frac{1}{4}\) of 60 = \(15\) minutes and \(\frac{1}{10}\) hour = \(\frac{1}{10}\) of 60 = \(6\) minutes.
12-hour and 24-hour clock
Time is measured using either the \(12\)-hour clock or the \(24\)-hour clock.
12-hour clock
The \(12\)-hour clock notation uses am and pm to indicate morning and afternoon.
- \({am}\) is the time from \(12\) midnight to \(12\) noon
- \({pm}\) is the time from midday and before midnight
(\(12.00am\) is midnight and \(12.00pm\) is midday, however, this is rarely used as it causes confusion.)
For example
\(6.23am\)
\(7.45pm\)
24-hour clock
The \(24\)-hour clock does not require the use of am or pm.
The time starts at 0000 and continues throughout the day up to 2359.
Afternoon is indicated by a number bigger than \(12\).
When converting from the 12-hour clock to the 24-hour clock remember: for any time after 12.59pm, add 12 to the hours.
For example
\(6.23pm\) becomes \((6.23 + 12) = \text{18:23}\)
\(7.45pm\) becomes \((7.45 + 12) = \text{19:45}\)
The \(24\)-hour clock always uses \(4\) digits, so for any time before \(\text{10:00}\) a zero is placed at the beginning.
For example:
- \(\text{01:00}\) means \(1.00am\)
- \(\text{13:00}\) means \(1.00pm\)
- \(\text{04:00}\) means \(4.00am\)
- \(\text{16:00}\) means \(4.00pm\)
Question
Copy and complete the following table, then check your answers.
Answer
Time intervals
Question
Amelia falls asleep at \(11.05\) pm and wakes up at \(7.15\) am. How long has she been asleep?
Answer
\(11.05\) - midnight = \(55\) minutes
Midnight - \(7\) am = \(7\) hours
\(7\) am - \(7.15\) am = \(15\) minutes
Add the minutes first.
\(55 + 15 = 70\) minutes
\(= 1\) hour \(10\) minutes
Add on the hours
\(1\) hour \(10\) minutes + \(7\) hours = \(8\) hours and \(10\) minutes
Amelia was asleep for \(8\) hours and \(10\) minutes.
You must be careful when adding or subtracting hours and minutes.
For example, \(1\) hour \(50\) minutes is not the same as \(1.50\) hours.
Question
Ryan starts work at \(08.25\) and finishes at \(14.50\).
He is allowed two breaks of \(20\) minutes each.
How long has worked?
Answer
\(08.25 - 09.00 = 35\) minutes
\(09.00 - 14.00 = 5\) hours
\(14.00 - 14.50 = 50\) minutes
Add the minutes
\(35 + 50 = 85\)
Subtract the breaks
\(85 - 40 = 45\) minutes
Add the \(5\) hours
Ryan has worked for \(5\) hours and \(45\) minutes
Reading timetables
Look at the train timetable from Bangor to Belfast:
Question
a) Anna is meeting a friend at the Folk museum in Cultra. Which train should she get from Bangor West?
b) The 0831 train from Bangor is running 6 minutes late, at what time will it arrive in Holywood?
c) How long is the train journey from Helen’s Bay to Titanic Quarter?
d) Rory needs to be at the airport in Sydenham by 9.30am. It will take 15 minutes to walk from the station to the airport. Which train should he get from Bangor?
Answer
a) The only train that stops at Cultra leaves Bangor West at 0840.
b) The 0831 usually arrives in Holywood at 0843. If it is running 6 minutes late it will arrive at 0849.
c) The train leaves Holywood at 0846 and arrives at the Titanic quarter at 0905. It takes 19 minutes.
d) Working backwards, Rory needs to be at the airport for 0930. It will take 15 minutes to walk from the station so the latest time he can arrive at Sydenham station is 0915. The train that arrives at 0921 is too late so Rory should get the train which leaves Bangor at 0837 and arrives in Sydenham at 0901.
Days, months and years
Use this rhyme to help you remember how many days there are in each month:
\(30\) days has September,April, June and November.All the rest have \(31\),Except February alone,Which has \(28\) days clear,And \(29\) in each leap year.
Question
If March \({28}^{th}\) is a Tuesday, what day is the April \({6}^{th}\) in the same year?
Answer
There are \(31\) days in March.
| Tues | Wed | Thurs | Fri | Sat | Sun | Mon |
|---|---|---|---|---|---|---|
| 28 | 29 | 30 | 31 | 1 | 2 | 3 |
| 4 | 5 | 6 |
By counting through the days you can see that \({6}^{th}\) April will be a Thursday.
Leap years
There are \(365\) days in a year.
A leap year, with its extra day in February, has \(366\).
Leap years occur every four years, and are divisible by \(4\).
This remains true, except for every year that is divisible by \(100\), however it will still be a leap year if the year is divisible by \(400\).
For example:
1996 was a leap year because \(1996 \div 4 = 499\)
1934 was not a leap year because \(1934 \div 4 = 483.5\)
\(1700\) wasn’t a leap year, because although it is divisible by \(4\) \(({1700} \div {4} = {425})\), it is also divisible by \(100\) \(({1700} \div {100} = {17})\).
However it isn’t divisible by \(400\) \(({1700} \div {400} = {4.25})\).
\(2000\) was a leap year as it is divisible by \(4\), \(100\) and also by \(400\) \(({2000} \div {400} = {5})\).
Flying around the world: Working out time
A delay at the airport turns into a time difference challenge for one girl as she waits for her father. See how she works out the time difference between various countries.
(PHONE RINGS)
Oh no, it’s Mum.
Hello!
Dad’s not here. He must have missed his connection.
No I can easily work out the next flight.
I can do all the maths. No, it’s no problem. Bye.
What’s he say? Emirates via Dubai, he told me he usually gets in early.
So see you at four o’clock.
What time is it now?
It’s after five. Where is he?
Well I’ve got a great phone app for looking up flight times.
So this is the only Emirates flight from Perth.
Landing at 13:07 local time in Dubai.
So he was in Dubai at lunch time. He’s not going to get here for ages.
Oh no, there’s a time difference.
I can work this out and I’m going to use his present.
Serves him right for not giving me a ring.
Now it may be long winded but I’m going to work out all the flight times in UKtime.
Then using my app, I’ve got a chance of working out where he is and whatflight he’s on.
It’s all about time zones.
He flew from Perth to Dubai.
With a stopover in Dubai and then arriving in the UK.
Now the world spins anti-clockwise.
You count the time differences from Greenwich, which is Greenwich MeanTime at zero.
Anything to the east you add on hours and anything to the west you takeaway hours. Cool!
As the world spins once a day, the world is split into 24 time zones.
I know Dubai is four hours ahead and Perth is eight hours ahead.
So travelling from Perth to Dubai is like travelling back in time.
So let’s get back to the app and find a flight from Perth to Dubai.
Here’s one. That left Perth at 05:54 local time and that’s eight hours ahead.So 05:54 minus eight hours.
The first five hours take us to 00:54 hours.
Which in the 24 hour clock is 00:54 and then the next three hours takes us to three hours before that which is 21:54.
Hmm, 21:54. Let’s check this on a 12 hour clock.
From 05:54 going back eight hours.
Eight turns of the dial, round and round past midnight.
Takes us to 21:54 in the evening, that’s PM.
So he’s been travelling since about ten o’clock last night and he arrived in Dubai while I was having breakfast.
That makes more sense.
Let’s just look at this on the globe.
13:07 local time in Dubai.
Four hours back would be 09:07 UK time.
So he’s had all day to get here!
So what I’m looking for is a flight that left Dubai after 13:07 Dubai time.
That he would have had a chance to catch to fly to London.
And there it is, leaving Dubai at 14:05, arriving in London late at 17:07.
That’s now!
Oops! Better wrap his present.
Mmm, tasty
Test section
Question 1
How many minutes are there in \(\text{3-and-a-half~hours}\)?
Answer
There are \({60}~{minutes}\) in an hour, and therefore that \({60}\times{3.5}={210}~{minutes}\).
Question 2
How many days are there in \({108}~{hours}\)?
Answer
There are \({24}~{hours}\) in a day, and therefore that \({108}\div{24}={4.5}~{days}\).
Question 3
How many days are there in \({8}~{weeks}\)?
Answer
There are \({7}~{days}\) in a week, and therefore that \({8}\times{7}={56}~{days}\).
Question 4
What is \({7.15pm}\) on the \({24}\)-hour clock?
Answer
You need to count on from \({12}\) midday on a \({24}\)-hour clock to get \(\text{19:15}\) for \({7.15pm}\).
Question 5
What is \(\text{17:03}\) on the \({12}\)-hour clock?
Answer
You have to go back to \({1}\) after \({12}\) midday on a \({12}\)-hour clock to get \({5.03pm}\) for \(\text{17:03}\).
Question 6
Look at the train timetable from Bangor to Belfast.
How many trains stop at Seahill?
Answer
2 trains stop at Seahill.
Question 7
Look at the bus timetable from Lisburn to Newcastle.
How long does it take to travel from Lisburn bus station to Annahilt, West Winds Terrace?
Answer
\(40\) mins.
There are two buses from Lisburn to Annahilt, West Winds Terrace.
\(0705\) and \(0905\).
Both take \(40\) mins
Question 8
Look at the train timetable from Belfast to Dublin.
Louie needs to be in Dublin for \(2\)pm. What is the latest train he can get from Lanyon Place?
Answer
Louie should get the \(1035\) train from Lanyon Place. He will arrive in Dublin at \(1240\). The next train arriving in Dublin is too late.
Question 9
Which of these three months doesn't have \({31}~{days}\)?
a) August
b) September
c) October
Answer
September is the only one of these three months which doesn't have \({31}~{days}\).
Question 10
Which of the following years, was a leap year?
a) \({2002}\)
b) \({2003}\)
c) \({2004}\)
Answer
A leap year is divisible by \({4}\).
In this case, \({2004}\div{4}={501}\), therefore \({2004}\) was a leap year.
