### GCSE Maths

Numbers
Algebra
Geometry and Measures
Probability
Statistics

# Fractions and Decimals

## Fractions

A fraction is a way of representing a part of a whole and is written as , where is the numerator (the top part) and is the denominator (the bottom part).

Some examples of fractions are .

### Types of Fractions

• Proper fractions: When the numerator is smaller than the denominator. For example: .
• Improper fractions: When the numerator is larger than the denominator. For example: .

#### Mixed Numbers

Improper fractions can be converted into mixed numbers, which consist of a whole number and a proper fraction.

Examples:

• can also be written as .
• can also be written as .
• can also be written as .

### Equivalent Fractions

Fractions can have the same value if we multiply or divide both the numerator and the denominator by the same number. However, it is common practice to present fractions in their simplest form.

For example, and are all equivalent fractions, but is the simplest form.

## Decimals

Decimals are another way of representing fractions, particularly those with denominators that are powers of 10. To convert a fraction to a decimal, divide the numerator by the denominator.

Examples:

• • • Both fractions and decimals allow us to express values with greater precision and are essential for many mathematical calculations.