Percentages Basics

Percentages are a frequent and important part of our everyday lives. Percentages crop up everywhere, for example here are some of the most common places you experience them; taxes, test scores, cooking measurements, sale prices, body mass index, and probably the one you’re most commonly used to looking at; your battery life percentage. With percentages being one of the most frequently used mathematical tools, it’s important to understand what they are, how to work them out, and when to use them.

What are percentages?

The word ‘percent’ means ‘out of 100’. So for example if 25 percent of the households have a pet dog that means that 25 out of 100 people will live in a house with a dog. We use the symbol ‘%’ to mean percent.

Finding percentages

A percentage is a fraction of 100. Let’s take 20% and explore it:

• 20% means 20 in each 100
• As a fraction you’d write this as 20/100
• As a decimal you’d write this as 0.2

How to find the percentage of a quantity:

Let’s look at some examples:

20% of £50:

• First, write 20% as a fraction: 20% = 20/100 = 2/10 = 1/5
• Now multiply the fraction by the quantity: 1/5 x 50 = £10

30% of £150

• 30% as a fraction = 30/100 = 3/10
• 3/10 x 150 = £45

Example Question:

Tom is buying some speakers. The original price was £118, but there is a 40% discount.

There are 2 types of questions you may get asked here, one would be “what price are the speakers with the discount taken off” or “how much will the discount be”. We are going to look at the first question because you have to work out “how much the discount will be” In order to find the answer anyway, so it’s good practise for both questions.

• 40% = 40/100 = 4/10 = 2/5
• 2/5 x 118 = £20

 

Income Tax

People pay tax on the income they earn. The basic rate of income tax is 20% (as of 2011).

VAT

Value Added Tax is added to the cost of most things you buy. It is charged at 20% (as of 2011).

Simple interest

With simple interest the amount of money borrowed remains fixed.

For example £300 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 £300

= (5/100) × 300

= £15

Interest over 3 years = 15 x 3 = £45

Interest = P × R × T

P (principal) is the amount borrowed.

R is the rate of interest per year.

T is the time in years.

 

Working out Percentage decrease:

Amanda buys a coat in a sale for £70. The original price for the coat was £95. What is the percentage decrease?

• 95 – 70 = £25
• (25/95) x 100 = 26% (rounded down)

And there we have it! What percentages are, how you work them out and when to use them. With a little practise percentages will become an easy and natural part of your maths revision, they are an important skill to have as you’ll see them crop up in around 10% of everything you do and read!