# Using Percentages

## Using Percentages

#### Amounts as Percentages

To express an amount as a percentage, write it as a fraction of the total amount and multiply it by 100. Here's an example!

There are 14 boys and 11 girls in a class.

What percentage of the class are boys?

Total in the class = 25 so the fraction of boys is 14/25.

So the percentage of boys in the class is 56%.

#### Finding Percentages

To find a percentage of a quantity, turn the percentage into a decimal (divide by 100) and multiply the quantity by this. Here's an example:

Find 55% of 230km.

#### Increasing and Decreasing

The simple way to increase (or decrease) a quantity by a percentage is to find the percentage of the quantity that you want to increase (or decrease) it by and add it on (or take it off).

For example:

Increase £56 by 25%.

25% of £56 is £14

56 + 14 = 70 so the answer is £70.

Quick way!

You can actually do it in one step instead of two!

Here's how.

1. Work out what percentage you will have after your increase or decrease.

2. Change it to a decimal (divide by 100).

3. Multiply!

Have a look at this example:

Decrease 900kg by 35%.

After taking away 35% there will be 65% left.

65% as a decimal is 0.65 so 0.65 x 900 = 585

#### Compound Interest

Let's say you have £10 in the bank at 10% interest per annum (that means per year!).

So at the end of one year you will get £1 interest giving you a balance of £11.

At the end of the second year you now get 10% of £11 i.e. £1.10 so you are getting interest on your interest (if you see what we mean!). This is called Compound Interest.

So if you want to find out how a sum of money has grown due to interest added over a number of years, here's what you do:

1. Add the interest rate on to 100% to get your new percentage.

2. Change it to a decimal. This is now the number you multiply by at the end of each year.

Example:

A man has £50 in his bank account at the start of the year. The interest rate is 5.3% per annum. If he leaves his money there, how much will the balance be at the end of 3 years?

If you add 5.3% on you will have 105.3%.

As a decimal this is 1.053. So we simply multiply the £50 by this number 3 times as there are 3 years. In other words we are multiplying by (1.053)3.

50 x (1.053)3 = 58.37879385

Now remember money has two decimal places so the answer is £58.38.