## Percentages

__Basics:__» Per cent means out of 100, so 10% means "10 out of 100".

To work out the percentage OF something, replace the word OF with multiplication (×).

To get you introduced to percentages, we will go through** **3 different types of percentage questions that come up in GCSE Maths. Many more types of percentage questions are studied in our learning programme. Don’t worry, you probably already know most of it!

## Type 1: Find x% of y

**Question 1:**Find 15% of £8 - with a Calculator

Change 15% into a decimal and multiply.

15% converted to decimal equals 0.15

☝️ We will multiply 0.15 x £8 = £1.20**Question 2:**Find 125% of 300g - without a Calculator

You can use this very simple method instead if you don't have a calculator.

1 - Find 10% by dividing by 10

2 - Find 5% by dividing 10% by 2

3 - Use the above values to make 125%

So, 100% = 300g

10% = 300 ÷ 10 = 30g

5% = 30 ÷ 2 = 15g

So, 125% = 100% + (2 x 10%) + 5%

125% = 300 + (2 x 30) + 15 = 375g

☝️ 125% of 300g is 375g## Type 2: Express x as a % of y

Divide x by y, then multiply by 100

**Question 3:**Find 16p as a percentage of 60p - with a Calculator

**So, what you need to do is:**

Divide 16 by 60, then multiply by 100.

So, 16 ÷ 60 = 0.27

Multiply 0.27 x 100 = 26.67

☝️ 16 as a percentage of 60p is 26.67%**Question 4:**Organic fruit and veg business owner Lucy measured her premium Melon's width at the start and end of the month. At the beginning of the month, it was 98 cm wide, and at the end of the month, it was 1.45 m wide.

Please give us the width at the end of the month as a percentage of the start's width.

These are what we sometimes call "wordy" maths questions. They may give the impression that they are complicated. However, if you focus on the numbers, you will find these questions are straightforward.

1 - Make sure both amounts are in the same measurement units.

2 - After, divide 145 cm by 98 cm, then multiply by 100:

So, we have the calculations as:

1.45 m = 145 cm

(145 ÷ 98) × 100 = 147.96%

☝️ The width at the end of the month is 147.96% of the width at the start.## Type 3: New amount after a % increase or decrease

There are two different ways of finding the new amount after a percentage increase or decrease.**Method 1: Find the % then Add or Subtract**

Find the percentage of the **ORIGINAL AMOUNT. ADD** this on to (or **SUBTRACT** from) the **ORIGINAL VALUE**.

**Question 5:**A laptop has increased in price by 30%. The original cost was £400.

What is the new price of the laptop?

We need to breakdown the problem like this:

**1** - Find 30% of £400

**2** - It's an increase, so add on to the original:

So, to calculate

= 30% of £400

= 30% × £400

= 0.3 × 400 = £120

We add £400 + £120 = £520

**☝️ The**new price of the laptop is £520.

**Method 2: The Multiplier Method**

With this method, you simply **MULTIPLY** the **ORIGINAL VALUE** by the **MULTIPLIER** and by magic – you have the answer.

**REMEMBER**

% DECREASE has a multiplier LESS THAN 1.

% INCREASE has a multiplier GREATER THAN 1.

**Question 6:**A bicycle has reduced in price by 30% in the January New Year sales. It originally cost £420.

What is the new price of the bike?

1 - Find the **multiplier**

2 - Multiply the original value by the **multiplier**

= 30% decrease

= 1 - 0.30 = 0.7

= £420 × 0.7 = £294

**☝️ The new price of the bike is £**294

Hopefully, you found the above a breeze! Join us for more in-depth learning and a custom learning plan design around you!