Percentages

A percentage is a part of one hundred. If we choose 30 packs out of 100, this is written as 30%, which is the same as \frac { 30 }{ 100 } =\frac { 3 }{ 10 }


We see percentages very often. I scored 75% in my Maths test, prices of cars decreased by 10%, there is an increase of 25% in the prices of milk and so on.


To find 10% of a number, we do \frac { 10 }{ 100 } \times the number.
Find 10% of 120.
10% of 120=\frac { 10 }{ 100 } \times 120.
= 12.

Examples


Find 5\frac { 1 }{ 2 }% of £200.
5\frac { 1 }{ 2 }% =\frac { 11 }{ 200 } \times £200=11.
Notice the 200 in the denominator because \frac { 11\div 2 }{ 100 }


Calculate 3\frac { 1 }{ 7 }% of £2100.
3\frac { 1 }{ 7 }% =\frac { 22 }{ 7 }
So, 3\frac { 1 }{ 7 }% of £2100=\frac { 22 }{ 700 } \times £2100=£66.


0.2% of a population were over 9 years old. How many were over 9 years old? When the population of the country was 13.1 million.
0.2% of 13,100,000=\frac { 0.2 }{ 100 } \times 13,100,000
=0.2\times 131,000
=2\times 13,100
= 26200



In a sale, all prices have been decreased by 15%. Find the new price of a toy which costs £20.
15% of £20\times \frac { 15 }{ 100 } \times £20
= £3
So the new price of the toy is £20 - £3 = £17.


When answering questions on percentages, we should read the question carefully. Consider the next few examples.


During a sale, all prices have decreased by 15%. Find the price of a toy which costs £17.
We reason as follows; Since prices have gone down by 15%, this means that the £17 represents 85%(100 - 15).
\frac { 85 }{ 100 } of a price = £17
Price =£17\times \frac { 100 }{ 85 }
= £20
So the price of the toy was £20 before the sale.


Due to Covid-19, prices of cars in a showroom have increase by 25%. David bought his new car for £30,000. What was the price of David’s car before the prices increased?
Here £80,000 represents 125%, because the price is 25% higher.
So, \frac { 125 }{ 100 } of price = £80,000
Price =£80,000\times \frac { 100 }{ 125 }
= £64,000

We can check that we are correct by calculating 25% of £64,000 and find the price of the car due to the Covid-19 price increment.
\frac { 25 }{ 100 } =£64,000=£16,000
So, the new price of the car = £64,000 + £16000
= £80,000



In 2020, income tax at the rate of 40%, was deducted from John, out of of £400. How much did John receive?
We can calculate 60% of £400 and this would be John’s fee.
\frac { 60 }{ 100 } \times £400=£240
John received £240.



What percentage of £360 is £54?
We calculate \frac { 54 }{ 360 } \times 100% =15%



What percentage of £12 is 18 pence?
We should convert the figures into the same unit. We can either say £12 = £1200 pence or 18 pence = £0.18. We shall use £12 = 1200p.
\frac { 18 }{ 1200 } \times 100% =1.5