'Percent' means 'out of 100'. If 90 per cent of the population owns a mobile phone, this means 90 out of every 100 people have one. The symbol '%' means per cent.
A percentage is a fraction of 100.
30% (30 in each 100) as a fraction is 30/100
30% as a decimal is 0.3.
Often, in real life - and maths exams - you must find a percentage of a quantity. First, write the percentage as a fraction or a decimal, then multiply by the quantity.
Have a look at this question:
Find 40% of £50.
First, write 40% as a fraction: 40% = 40/100 = 4/10 = 2/5
Now multiply by the quantity:
2/5 × 50 = £20.
Practise converting percentages to fractions. Then try the questions below.
Sarah is buying a pair of jeans. The original price was £75, but there is a discount of 30%. How much will the discount be?
Discount = 30% of 75
= 30/100 × 75
= 0.3 × 75
Note that if the question asked for the discount price, you would subtract the discount from the original price : £75 - £22.50 = £52.50.
Sometimes both the percentage and amount of money will not be whole numbers.
A car costs £9,999.90 before VAT (value added tax). Work out the cost of the VAT if it is charged at 20%.
VAT = 20% of £9,999.90
= 20/100 × 9,999.90
Since the answer is a price, it must be rounded to two decimal places.
The answer is £1,999.98
People pay tax on the income they earn. The basic rate of income tax is 20% (as of 2011).
Value Added Tax is added to the cost of most things you buy. It is charged at 20% (as of 2011).
In some questions you are given the cost price and the selling prices and have to find the percentage increase or decrease. This means you need to find one amount as a percentage of another. You form a fraction from the two amounts and multiply this by 100. Try these questions.
With simple interest the amount of money borrowed remains fixed.
For example £400 is borrowed for 3 years at an interest rate of 5% pa (pa means per annum, or each year).
Interest for one year = 5% of £400
= (5/100 ) × 400
Interest for 3 years = £20 × 3 = £60.
You can write this in a formula.
Interest = P × R × T
People often buy something at one price, and sell it on for another - eg, when they are selling things at a car boot sale.
If the selling price is greater than the buying price, a profit is made.
If the selling price is less than the buying price, there is a loss.
Ajay is dealing in electrical goods. He buys a radio for £45 and sells it for £63. What is his percentage profit?
Here the cost price is £45 and the selling price £63.
The profit is £63 - £45 = £18
To calculate the percentage profit you have to find what the profit is as a percentage of the original price. So divide the profit by the original price and multiply by 100.
18 ÷ 45 x 100 = 40%.
Charlotte buys a coat in a sale for £60. The original cost of the coat was £80. What is the percentage decrease?
The coat was bought for £60, and the original price was £80.
The decrease is £80 - £60 = £20.
To calculate the percentage decrease, divide the actual decrease by the original price and multiply by 100.
20 ÷ 80 x 100 = 25%.