Mastering Fractions in GCSE Maths

Understanding Fractions

In GCSE Mathematics, fractions are one of the core topics covered under the Number domain. A fraction represents a part of a whole, expressed as a ratio of two integers - the numerator (top) and denominator (bottom). For example, 3⁄4 means 3 parts out of 4 equal parts.

Types of Fractions

• Proper fractions have a numerator smaller than the denominator, e.g. 1⁄2, 3⁄5.
• Improper fractions have a numerator greater than or equal to the denominator, e.g. 5⁄3, 7⁄7.
• Mixed numbers are a combination of a whole number and a proper fraction, e.g. 2 1⁄4, 5 3⁄8.

Converting Between Fractions

It is important to be able to convert between improper fractions, mixed numbers, and vice versa. For example, the improper fraction 7⁄3 is equivalent to the mixed number 2 1⁄3.

Worked Example

Convert 11⁄4 to a mixed number.

1. Divide the numerator by the denominator: 11 ÷ 4 = 2 remainder 3
2. The whole number part is 2 (the quotient)
3. The fractional part is 3⁄4 (the remainder over the divisor)
4. Therefore, 11⁄4 = 2 3⁄4

Fractions of Amounts

To find a fraction of an amount, multiply the amount by the fraction. For example, to find 3⁄5 of 25, calculate: 3⁄5 × 25 = 15.

Operating with Fractions

The four basic operations (addition, subtraction, multiplication, division) can be performed on fractions, with some rules to simplify:

• Addition/Subtraction: Find the LCD, convert fractions to equivalent fractions with the LCD as denominator, then add/subtract numerators.
• Multiplication: Multiply numerators, multiply denominators.
• Division: Invert the divisor fraction and multiply by the dividend fraction.

External Resources

• AQA GCSE Maths specification: https://www.aqa.org.uk/subjects/mathematics/gcse/mathematics-8300
• BBC Bitesize - Fractions: https://www.bbc.co.uk/bitesize/topics/zhdssrd