Mastering Fractions in GCSE Maths

Understanding Fractions

A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number). For example, in the fraction 3⁄4, the numerator is 3 and the denominator is 4, representing three equal parts out of four equal parts of a whole.

Types of Fractions

• Proper Fractions: Numerator is less than the denominator, e.g. 1⁄2, 3⁄5
• Improper Fractions: Numerator is greater than or equal to the denominator, e.g. 5⁄3, 7⁄4
• Mixed Numbers: A whole number combined with a proper fraction, e.g. 21⁄3, 45⁄6

Converting Between Fractions

It's important to be able to convert between improper fractions and mixed numbers:

Example: Convert 7⁄3 to a mixed number

1. Divide the numerator by the denominator: 7 ÷ 3 = 2 (with a remainder of 1)
2. The whole number part is 2
3. The fractional part is the remainder over the denominator: 1⁄3
4. Therefore, 7⁄3 = 21⁄3

Operations with Fractions

To operate with fractions, find the least common denominator (LCD) and convert both fractions to equivalent fractions with the LCD as the denominator. Then perform the desired operation with the new numerators.

Example: 1⁄3 + 1⁄6

1. LCD = 6
2. Convert fractions: 1⁄3 = 2⁄6, 1⁄6 = 1⁄6
3. 2⁄6 + 1⁄6 = 3⁄6 = 1⁄2

For more fractions resources and examples, visit the BBC Bitesize on Fractions and the official AQA GCSE Mathematics Specification on Fractions.