Even otherwise highly numerate people have been known to throw up their hands in horror at the thought of adding together times. Show A system like time, which is not decimal, can be counter-intuitive and requires concentration. However, with a bit of application, you too can learn how to calculate with time, and gain confidence in manipulating hours, minutes and seconds. Basic Units of TimeThe basic units of time, which allow you to do calculations involving time, are:
Years are commonly split into quarters, especially in business and education settings, with each quarter being three months or approximately 90 days. Quarters in a specific business or sector may not necessarily be the same as those indicated below: The number of days in a month varies. All months have the same number of days each year except for February which has 28 days in a common year and 29 in a leap year.
As the number of days in a month varies, this also means that the number of weeks in a month varies too. People often use approximations when calculating the number of days in months. For example, it is common to use the assumption that a month contains four weeks, even though only February in a common year actually does so. This makes it hard to convert from months to weeks and vice versa, unless you know which months are being used, because there is no immediate ‘conversion factor’.
Top Tip! If you are converting between months and weeks, the best way to do so is via years, because they always contain 12 months (even in a leap year).
The answers you get will be good approximations. There are many different ways to write time. The simplest (digital) form is as written hh.mm or hh:mm, for example 10.21 or 10:21. Hours may be either divided into 24 (known as the 24-hour clock) or two lots of 12 (often referred to as the 12-hour clock). When using the 24-hour clock, the 24 hour cycle starts with the time 00:00 (midnight) and runs all the way through to 23:59, before rolling over to 00:00 again. We never write ‘24:00’. You will often see the time in 24-hour clock written without a separator (‘.’ or ‘:’) between the hours and minutes. For example 1400, which may be referred to as fourteen hundred hours. This is especially common in military and seafaring situations. When using the 12-hour clock the 24 hour period is divided into two 12-hour periods. Both midnight and midday are 12:00. Time before midday (noon) is designated am (ante meridiem) and time after noon is referred to as pm (post meridiem). For example, 4:10pm is the same time as 16:10. Note that we never write ‘16:10pm’ The use of am and pm is only for the 12-hour clock. You can also describe time in words, such as 'ten minutes past/after twelve', or 'ten past twelve'. Up to half way through an hour, we describe ‘minutes past’ the hour; beyond ‘half past’ we talk about minutes to/before the next hour. A time ‘on the hour’, for example 2:00pm, can be referred to as ‘two pm’, ‘fourteen hundred’, or ‘two o’clock’.
Calculations of How Much Time has Passed You may need to do calculations of how much time has passed, for example, to work out the end time of an examination, how long you will have to wait for a train, or perhaps to calculate race results. If time is described in words, you will need to convert it into a digital form in order to do any calculations. It is also simpler to use the 24 hour clock to avoid any confusion, unless all your figures are either am or pm. Example time formats:
Calculating the Passage of TimeIn the normal way of things, to calculate how much one thing is greater than another you would simply subtract one from another. However, subtracting time is complicated because it’s not decimal. Instead of the columns being hundreds, tens and units, they are hours, minutes and seconds. Top Tip If you have a scientific electronic calculator, you will almost certainly have a button that will calculate time. Technically, it’s for degrees but as there are 60 minutes in a degree, and 60 seconds in a minute, you can also use it to calculate time. The button will have a symbol like this: At the very least, you should be able to use that to convert time to decimals and back again, making calculations much easier. The other way of calculating how much time has passed between Time A and Time B is:
Calculating the total amount of time spentSometimes you might need to add up how much time you have spent on a task that you have completed over several days or sessions. Adding a list of hours and minutes isn’t as straightforward as doing a normal addition calculation, because (as above) we are not working with a decimal system. For example, you may be doing a gardening job for a neighbour, who has agreed to pay you an hourly rate of £10 per hour. On the first day you spend 3 hours and 25 minutes on the task, on the second day you spend 2 hours and 50 minutes and on the third day you finish it off in an hour and a quarter. You need to add together the three amounts of time 3:25, 2:50 and 1:15. The first step is to add together all of the minutes: 25 + 50 + 15 = 90 minutes. If you need to remind yourself how to perform an addition calculation, have a look at our page on addition. As there are only 60 minutes in an hour, the next step is to convert 90 minutes into hours and minutes: 90 ÷ 60 = 1.5 hours The answer is a decimal, so we can convert it back into hours and minutes. You can use a scientific calculator with a degrees function as described above, or you can do a bit more maths. We can convert 0.5 hours into minutes. 0.5 × 60 = 30 1.5 hours is therefore 1 hour and 30 minutes. Next we need to add together the whole hours we have spent, which was 3 on the first day, 2 on the second day and 1 on the third day: 3 + 2 + 1 = 6 hours. Add the total hours to the total minutes (in hours and minutes): 6h + 1h 30m = 7 hours and 30 minutes, or 7:30 spent gardening. In decimal form, this is 7.5 hours. In order to calculate how much you have earned, we multiply the time (in decimals) by the hourly rate: 7.5 × 10 = 75. You have therefore earned $75. ConclusionThe most important thing when calculating with time is to check whether the answer looks about right? If your two numbers are less than an hour apart, is your answer less than an hour? If they are about 2 hours apart when you look at them, is your answer? If not, you may have lost or gained some time somewhere! If you want to know more about ‘about right’ take a look at our page on Estimation, Approximation and Rounding. |