# Using Percentages

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## Using 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%.

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.**

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

The answer is **585kg.**

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?

**Answer:**

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.**