The word ‘percentage’ is very familiar to us as it is used regularly in the media to describe anything from changes in the interest rate, to the number of people taking holidays abroad, to the success rate of the latest medical procedures or exam results. Percentages are a useful way of making comparisons, apart from being used to calculate many taxes that we pay such as VAT, income tax, domestic fuel tax and insurance tax, to name but a few. So percentages are very much part of our lives.
What does percentage actually mean? ‘Per cent’ means ‘out of 100’; and ‘out of’, in mathematical language, means ‘divide by’. So if you score
So,
A few more examples:
Thus, all percentage amounts have their fractional and decimal equivalents.
It is worth noting that 50% can be found by dividing by 2, and that 10% is easily found by dividing by 10.
Now, let us look at writing fractions as percentages.
For example, say you get 18 marks out of 20 in a test. What percentage is this?
First, write the information as a fraction. You gained 18 out of 20 marks, so the fraction is
Since we are multiplying both the numerator and the denominator by
In that example it was easy to see that, in order to make the denominator
Although it is easier to use a calculator for this type of calculation, it is advisable not to use the % button at this stage. We shall look at using the percentage button on a calculator at the end of this lesson.
Thus the key point in this discussion is that : percentage means ‘out of 100’, which means ‘divide by
Example: 7 out of every 10 people questioned who expressed a preference liked a certain brand of cereal. What is this as a percentage?
Solution: 7 out of 10 people liked the brand of cereal. Now, 7 out of 10 expressed as a fraction is
Find percentages
For many calculations, we need to find a certain percentage of a quantity.
For example, it is common in some countries to leave a tip of
As mentioned before, an easy way to find
For example, in one month he secures
Solutuion:
Find original amount before percentage change
Let us look at a situation where we need to find an original amount before a percentage increase has taken place.
Example: An insurance company charges a customer
Solution: Here, the
Here is one more similar calculation, but this time there has been a reduction in cost.
Example: A shop has reduced the cost of a coat by
Solution: In this case,
We divide by
The key point which has to be noted here is that if you are given a percentage change and the final amount, write the final amount as
Expressing change as percentage
We might wish to calculate the percentage by which something has increased or decreased.
To do this we use the rule:
So we write the amount of change as a fraction of the original amount, and then turn it into a percentage.
Example: Four years ago, a couple paid
Solution:
Example: A car costs
Solution:
Point to note: To write an increase or decrease as a percentage, use the formula:
Understanding percentage on calculator
The
- Pressing “
” gives an answer of . Now , so pressing the button has had the effect of multiplying by . This has found 48 as a percentage of 400. - Pressing “
” gives the answer . Now , so pressing the button here has divided by . This has found of the faction . - Pressing “
” gives an answer of . Now , so pressing here has divided by 100. This has found . - Pressing “
” results in on the display, requiring “ ” to be pressed to display an answer of . So pressing the button here has had no effect.
Exercise
- In a test you gained
marks out of . What percentage is this? out of gambling sites on the Internet failed to recognise the debit card of a child. What is this as a percentage?- At the end of
you bought shares in a company for . During the shares increased in value by . During the shares decreased in value by . How much were the shares worth at the end of ? - What is the amount of Value Added Tax or VAT (at a rate of
) which must be paid on an imported computer game costing ? - A batsman scored
runs which included boundaries and sixes. What percent of his total score did he make by running between the wickets?