### What are Percentages?

Percentage means ** out of 100**.

Percentages are written using the symbol **%**.

**10%** means **10 out of 100**.

**15%** means **15 out of 100**.

**80%** means **80 out of 100**.

Percentages are useful because they allow us to easily **compare** things.

For example exam scores are often given as a **percentage**. If Charlie scored 84 out of 100 on one exam and 102 out of 120 on another, it is hard to **compare** his scores and say which exam he did **better** on. But if I **change** his scores to **percentages** I can see that he got 84% in his first exam and 85% in the second, so he did better in his second exam.

How did I change his scores to percentages?

Well the first one was easy, Charlie scored 84 out of 100. Remember **percentages are out of 100**, so 84 out of 100 is **84%**.

On the second exam his score was 102 out of 120. To **change this to a percentage** we have to change 102 out of 120 in to the form:

? out of 100.

In a similar way to changing fractions we need to find a way to **change** 120 in to 100 by using division and multiplication:

120 ÷ 6 = 20

20 x 5 = 100

Now must apply the same steps to 102:

102 ÷ 6 = 17

17 x 5 = 85

So 102 out of 120 is **85%**.

### Finding Percentages of Numbers

To find the percentage of a number we can follow two simple steps:

- We divide the percentage by 100 to change it to a decimal. The quick way to do this is just by moving the decimal point – see the lesson that covers dividing by 100 if you don’t understand this.
- We times the decimal by the number we are trying to find a percentage of.

Let’s work through an example question:

Example

**Question**: What is 40% of 20?

First we **divide the percentage by 100** to form a decimal:

40 ÷ 100 = 0.4

Then we **multiply the decimal by the number** we want to find a percentage of:

0.4 x 20 = 8

(A good way to do this last step is to say that 4 x 20 = 80, so 0.4 x 20 = 8. See the lesson on multiplication if you don’t understand this).

So 40% of 20 = 8

Another way to tackle this type of question, especially when there are easy numbers involved is to say, well 40% is the same as 4 tenths. One tenth of 20 (20 ÷ 10) = 2, so 4 tenths is 4 x 2 = 8.

### Example Questions

Example

Question: ‘Spaceships R Us’ are having a sale and all their spaceships have 20% off their original price. What was the original price of a spaceship now on sale for £400?

This type of question can be a bit tricky to get your head round. You need to think that the original price is 100% and the sale price is a percentage of the original cost.

If 20% has been taken off the original price to get the sale price of £400 then this means £400 is 80% of the original price.

If £400 is 80% then we need to find 100% as this will be the original price.

To do this we must first work out a way to get from 80% to 100%.

I can see two easy ways to do this. Either we divide 80% by 8 to get 10% and then times by 10 to get 100%. Or we divide 80% by 4 to get 20% and then times by 5 to get 100%. Either way will work, i’ll use the first method:

400 ÷ 8 = £50

(So £50 is 10% of the original price. Now we times by 10 to get 100% of the price:)

50 x 10 = £500

### Visual Questions

You might be asked to show percentages **visually** by shading a certain percentage of a picture.

Example

Question: Fill in 30% of the squares in this grid:

If we count the grid squares there are 10 so we just need to find 30% of 10 and fill in that many squares:

First convert the percentage to a decimal:

30 ÷ 100 = 0.3

Then times the decimal by the number we are finding the percentage of:

0.3 x 10 = 3

Another way to work it out would be to think, 10% of 10 is 1, so 30% must be 3

So we shade in 3 squares: