Percentages are a fundamental concept in maths, representing parts of a whole as fractions of 100. This makes them incredibly useful for a wide range of applications, from finance to everyday calculations. In this section, we delve into the basics of percentage calculations, focusing on techniques for computing the percentage of quantities and expressing quantities as percentages.

**Understanding Percentages**

A percentage is essentially a fraction with a denominator of 100, denoted by the symbol "%". This simple concept is pivotal in comparing proportions and understanding changes in quantities.

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**Calculating the Percentage of a Quantity**

To find what one quantity is as a percentage of another, we use the formula:

$\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100$**Example 1: Finding a Percentage of a Quantity**

**Question:** What is 25% of 200?

**Solution:**

Therefore, 25% of 200 is 50.

**Expressing a Quantity as a Percentage of Another**

This involves rearranging the formula above to solve for the percentage:

$\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100$**Example 2: Expressing One Quantity as a Percentage of Another**

**Question:** If 50 is what percentage of 200?

**Solution:**

Hence, 50 is 25% of 200.

**Converting Decimals and Fractions to Percentages**

Decimals and fractions can be easily converted to percentages by understanding their relationship to the whole.

**Converting Decimals to Percentages**

Multiply the decimal by 100 to find the equivalent percentage.

**Example 3:** Convert 0.75 to a percentage.

**Solution:**

**Converting Fractions to Percentages**

Divide the numerator by the denominator, then multiply by 100.

**Example 4:** Convert $\frac{3}{5}$ to a percentage.

**Solution:**

**Applying Percentage Calculations in Real-Life Scenarios**

Percentages are incredibly useful in a variety of contexts, including financial calculations and data analysis.

**Example 5: Calculating a Discount**

**Question:** A £120 item is on sale for 20% off. What is the sale price?

**Solution:**

First, calculate the discount amount:

$\text{Discount} = \left( \frac{20}{100} \right) \times 120 = 24$Then, subtract the discount from the original price:

$\text{Sale Price} = 120 - 24 = 96$Thus, the sale price is £96.

**Example 6: Determining Interest Earned**

**Question:** How much interest does £1000 earn in a year at an annual interest rate of 5%?

**Solution:**

Therefore, £1000 will earn £50 in interest over one year.