The term ‘per cent’ implies ‘out of a hundred’. In mathematics, percentperiods are supplied choose fractions and decimals, as means to define components of a whole. When you are making use of percentperiods, the whole is thought about to be comprised of a hundred equal components. The symbol % is offered to display that a number is a portion, and much less commonly the abbreviation ‘pct’ may be provided.

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You will certainly watch percentperiods practically everywhere: in shops, on the internet, in advertisements and in the media. Being able to understand what percentages expect is a vital ability that will certainly perhaps save you time and money and will additionally make you even more employable.

The Meaning of Percentages

Percentage is a term from Latin, meaning ‘out of one hundred’.

You have the right to therefore consider each ‘whole’ as broken up right into 100 equal parts, each one of which is a solitary percent.

The box below mirrors this for a basic grid, yet it works the exact same way for anything: youngsters in a course, prices, pebbles on the beach, and so on.

Visualising Percentages

The grid listed below has 100 cells.

Each cell is equal to 1% of the entirety (the red cell is 1%). Two cells are equal to 2% (the green cells). Five cells are equal to 5% (the blue cells). Twenty five cells (purple cells) are equal to 25% of the entirety or one quarter (¼). Fifty cells (yellow cells) are equal to 50% of the totality or fifty percent (½).

How many type of unshaded (white) cells are there? What is the percentage of unshaded cells?

Answer: There are 2 methods to work this out.

Count the white cells. Tbelow are 17 of them. Out of 100 cells, 17% are therefore white. Add up the number of various other cells, and also take them from 100. Tbelow is one red cell, two green, five blue, 25 purple, and 50 yellow. That adds up to 83. 100−83 = 17. Again, out of 100 cells, 17 are white, or 17%.

It is basic to job-related out the portion once there are 100 individual ‘things’ consisting of the totality, as in the grid over. But what if tbelow are even more or less?

The answer is that you convert the individual aspects that comprise the entirety right into a portion. For example, if there had actually been 200 cells in the grid, each portion (1%) would be 2 cells, and eexceptionally cell would be fifty percent a percent.

We use percenteras to make calculations simpler. It is a lot much easier to occupational via parts of 100 than thirds, twelfths and so on, specifically because fairly a lot of fractions carry out not have a precise (non-recurring) decimal indistinguishable. Importantly, this likewise makes it a lot simpler to make comparisons between percentages (which all efficiently have the widespread denominator of 100) than it is in between fractions with various denominators. This is partially why so many type of nations use a metric system of measurement and decimal currency.

Finding the Percentage

The basic preeminence for finding a given percent of a given entirety is:

Work out the value of 1%, then multiply it by the portion you must discover.

This is easiest to understand via an instance. Let’s intend that you desire to buy a new lapoptimal computer system. You have actually checked local companies and also one company has actually readily available to provide you 20% off the list price of £500. How much will certainly the lappeak expense from that supplier?

In this example, the entirety is £500, or the cost of the laptop prior to the discount is applied. The percent that you must discover is 20%, or the discount available by the supplier. You are then going to take that off the complete price to discover out what the lapoptimal will certainly expense you.

Start by working out the value of 1%

One percent of £500 is £500 ÷ 100 = £5.

Multiply it by the percent you are looking for

Once you have functioned out the worth of 1%, you ssuggest multiply it by the portion you are looking for, in this situation 20%.

£5 × 20 = £100.

You now understand that the discount is worth £100.

Complete the calculation by including or subtracting as vital.

The price of the lappeak, including the discount, is £500−20%, or £500−£100 = £400.

The straightforward method to work-related out 1% of any kind of number

1% is the entirety (whatever that may be) split by 100.

When we divide somepoint by 100, we ssuggest move the place values two columns to the right (or relocate the decimal suggest 2 places to the left).

You can discover out more around numbers and also area values on our Numbers web page, yet here’s a quick recap:

£500 is made up of 5 hundreds, zero tens and also zero devices. £500 also has actually zero pence (cents if you are functioning in dollars) so can be written as £500.00, with zero tenths or hundredths.

When we divide by 100, we move our number 2 columns to the appropriate. 500 separated by 100 = 005, or 5. Leading zeros (zeros on the ‘outside left’ of a number, such as those in 005, 02, 00014) have no worth, so we carry out not should compose them.

You can likewise think of this as moving the decimal point 2 locations to the left.

This preeminence applies to all numbers, so £327 divided by 100 is £3.27. This is the exact same as saying that £3.27 is 1% of £327. £1 divided by 100 = £0.01, or one pence. There are one hundred pence in a pound (and also one hundred cents in a dollar). 1p is therefore 1% of £1.

Once you have calculated 1% of the totality, you deserve to then multiply your answer to the percent you are trying to find (view our page on multiplication for help).

Mental Maths Hacks

As your maths abilities construct, you deserve to start to watch other methods of getting here at the same answer. The lapheight example above is rather straightforward and also through practise, you can use your psychological maths skills to think about this difficulty in a different way to make it much easier. In this situation, you are trying to discover 20%, so rather of finding 1% and also then multiplying it by 20, you can discover 10% and then sindicate double it. We know that 10% is the very same as 1/10th and also we have the right to divide a number by 10 by moving the decimal location one area to left (removing a zero from 500). As such 10% of £500 is £50 and 20% is £100.

A beneficial mental maths hack is that percentperiods are reversible, so 16% of 25 is the very same as 25% of 16. Invariably, one of those will certainly be much much easier to occupational out in our head…attempt it!

Working through Percentages

We calculated a 20% discount in the example over and also then subtracted this from the totality to occupational out exactly how a lot a brand-new laptop would certainly expense.

As well as taking a percent ameans, we have the right to likewise include a percent to a number. It functions exactly the very same means, but in the last step, you sindicate add instead of subtracting.

For example: George is supported and gets a 5% pay climb. George presently earns £24,000 a year, so how a lot will he earn after his pay rise?

Work out 1% of the whole

The entirety in this example is George"s current salary, £24,000. 1% of £24,000 is 24,000 ÷ 100 = £240.

Multiply that by the percent you are looking for

George is acquiring a 5% pay increase, so we must understand the worth of 5%, or 5 times 1%.

£240 × 5 = £1,200.

Complete the calculation by adding to the original amount

George’s pay rise is £1,200 per year. His brand-new salary will therefore be £24,000 + £1,200 = £25,200.

Percenteras over 100%

It is possible to have actually percentages over 100%. This example is one: George’s brand-new salary is actually 105% of his old one.

However before, his old salary is not 100% of his brand-new one. Instead, it is just over 95%.

When you are calculating percentages, the vital is to examine that you are working via the correct totality. In this case, the ‘whole’ is George’s old salary.

Percentages as Decimals and Fractions

One percent is one hundredth of a totality. It can therefore be created as both a decimal and a portion.

To write a percent as a decimal, sindicate divide it by 100.

For example, 50% becomes 0.5, 20% becomes 0.2, 1% becomes 0.01 and so on.

We have the right to calculate percenteras utilizing this understanding. 50% is the same as a fifty percent, so 50% of 10 is 5, bereason 5 is half of 10 (10 ÷ 2). The decimal of 50% is 0.5. So an additional means of finding 50% of 10 is to say 10 × 0.5, or 10 halves.

20% of 50 is the exact same as saying 50 × 0.2, which equals 10.

17.5% of 380 = 380 × 0.175, which equates to 66.5.

George’s salary rise over was 5% of £24,000. £24,000 × 0.05 = £1,200.

The conversion from decimal to percentage is simply the reverse calculation: multiply your decimal by 100.

0.5 = 50% 0.875 = 87.5%

To create a percent as a fraction, put the portion value over a denominator of 100, and divide it down right into its lowest feasible form.

50% = 50/100 = 5/10 = ½ 20% = 20/100 = 2/10 = 1/5 30% = 30/100 = 3/10


It is feasible to transform fractions to percentperiods by converting the denominator (the bottom variety of the fraction) right into 100.

However, it is harder to convert fractions to percenteras than percenteras to fractions bereason not eincredibly fraction has actually a precise (non-recurring) decimal or portion.

If the denominator of your fractivity does not divide a whole number of times right into 100, then tbelow will certainly not be a basic convariation. For instance, 1/3, 1/6 and also 1/9 execute not make ‘neat’ percentages (they are 33.33333%, 16.66666% and 11.11111%).

Working out Percenteras of a Whole

So far we have looked at the basics of percenteras, and also how to include or subtract a percentage from a whole.

Sometimes it is valuable to be able to work-related out the percenteras of a whole as soon as you are provided the numbers came to.

For example, let’s intend that an organisation employs 9 supervisors, 12 administrators, 5 accountants, 3 huguy resource specialists, 7 cleaners and also 4 catering staff. What percentage of each kind of staff does it employ?

Start by functioning out the whole.

In this situation, you perform not understand the ‘whole’, or the total variety of staff in the organisation. The first step is therefore to add together the various types of staff.

9 managers + 12 administrators + 5 accountants + 3 HR professionals + 7 cleaners + 4 catering staff = 40 members of staff.

Convert the fractivity of the whole into a percentage

0.225 is the fractivity of staff that are managers, expressed as a decimal. To convert this number to a portion, we must multiply it by 100. Multiplying by 100 is the very same as separating by a hundred other than you move the numbers the other way on the place values scale. So 0.225 becomes 22.5.

In other words, 22.5% of the organisation’s employees are supervisors.

We then perform the very same 2 calculations for each other category.

TOP TIP! Check you have actually a full of 100%

When you have finiburned calculating your percenteras, it is a great idea to add them together to make sure that they equal 100%. If they do not, then check your calculations.

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Roles Number of Staff % of Staff
Managers 9 22.5%
Administrators 12 30%
Accountants 5 12.5%
HR professionals 3 7.5%
Cleaners 7 17.5%
Catering staff 4 10%
Total 40 100%

It deserve to be useful to present portion information representing a entirety on a pie chart. You can conveniently check out the proparts of categories of staff in the instance.


Points to remember

Percentperiods are a means to describe components of a entirety.They are a little bit choose decimals, except that the totality is always break-up right into 100, instead of tenths, hundredths, thousandths and so on of a unit.Percentperiods are designed to make calculations simpler.