### GCSE Maths

Numbers
Algebra
Geometry and Measures
Probability
Statistics

# Percentages

A percentage is a part of one hundred. When we say 30 out of 100, it is written as 30%, which is the same as .

If we want to find x% of a number, we use the formula: . For example, to find % of a number, we do the number. Let’s look at some examples:

1. Find 10% of 120:

2. What percentage of £360 is £54?

3. What percentage of £12 is 18 pence?

1. 10% of .

2. We calculate 3. We should convert the figures into the same unit. We can either say £12 = 1200 pence or 18 pence = £0.18. We’ll use £12 = 1200p. %

So, 18 pence is 1.5% of £12.

## Converting Fractions, Decimals, and Percentages

Converting between fractions, decimals, and percentages is an important skill to have when working with percentages. Let’s look at how we can carry out these conversions:

### Fraction to Percentage

To convert a fraction to a percentage, multiply the fraction by 100%. For example:

Convert to a percentage. %

### Decimal to Percentage

To convert a decimal to a percentage, multiply the decimal by 100%. For example:

Convert 0.25 to a percentage. %

### Percentage to Fraction

To convert a percentage to a fraction, divide the percentage by % and simplify the fraction if necessary. For example:

Convert 75% to a fraction. ### Percentage to Decimal

To convert a percentage to a decimal, divide the percentage by %. For example:

Convert 25% to a decimal. ### Examples

1. Find % of £200:

2. Calculate % of £2100:

3. 0.2% of a population were over 70 years old. If the population of the country was 13.1 million, how many were over 70 years old?

1. % .

2. % .

3. % of .

## Real-life Applications of Percentages

### Discounts

When shopping, you might encounter discounts represented as percentages. To find the discounted price, subtract the discount percentage from 100%, then multiply the result by the original price. For example:

A dress is on sale with a 30% discount. If the original price is £50, what is the discounted price?

Discounted price =  ### Tax Rates

Tax rates are often represented as percentages. To calculate the total amount to pay, including tax, multiply the original price by . For example:

A book costs £15, and the tax rate is 5%. What is the total price, including tax?

Total price ### Population Growth

Population growth is often represented as a percentage increase per year. To find the future population after a given number of years, use the formula:

Future population Let’s look at an example:

A town has a population of 5,000, and the population is growing at 2% per year. What will be the population after three years?

Future population After three years, the population will be approximately 5,306.

### Examples

1. In a sale, all prices have been decreased by 15%. Find the new price of a toy which costs £20.

2. Prices of cars in a showroom have increased by 25%. David bought his new car for £30,000. What was the price of David’s car before the prices increased?

3. During a sale, all prices have decreased by 15%. Find the original price of a toy which now costs £17.

4. In 2020, Jane had an annual income of £60,000, and income tax was deducted from her income at a rate of 25%. What was the amount of money Jane received after the income tax deduction?

1. % of £20 .

So the new price of the toy is £20 – £3 = £17.

2. Here £30,000 represents %, because the price is % higher. So, of the original price Original price 3. Since prices have gone down by %, this means that the £17 represents % ( ). of the original price = £17

Original price .

4. To calculate the amount of money Jane received after the income tax deduction, we can use the following formula:

Income after tax = Income before tax – (Income before tax × Tax rate)

Plugging in the values, we have:

Income after tax = Income after tax = Income after tax = Therefore, Jane received after the income tax deduction.