Mastering Fractions for 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.

Converting Between Fractions and Mixed Numbers

Mixed numbers combine a whole number part and a fractional part. To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. Then combine these values as the new numerator over the original denominator.

Worked Example

Problem: Convert 25⁄6 to an improper fraction.

Solution:

1. Multiply the whole number (2) by the denominator (6): 2 × 6 = 12
2. Add the numerator (5) to this product: 12 + 5 = 17
3. The improper fraction is 17⁄6

Finding Fractions of Amounts

To find a fraction of an amount, multiply the amount by the fraction. For example, to find 3⁄5 of 20, calculate: 3⁄5 × 20 = 12.

Fraction Operations

When adding or subtracting fractions, a common denominator is needed. Find the LCM of the denominators and convert the fractions.

Problem: Evaluate 1⁄2 + 1⁄3

1. LCM of 2 and 3 is 6, so convert to common denominator: 3⁄6 + 2⁄6
2. Now add: 3⁄6 + 2⁄6 = 5⁄6

To multiply fractions, multiply the numerators and multiply the denominators.

To divide fractions, multiply the first fraction by the reciprocal of the second.

Simplifying and Equivalence

Equivalent fractions represent the same value. To simplify a fraction, divide both the numerator and denominator by common factors.

Problem: Simplify 12⁄20

Solution:

1. Both 12 and 20 are divisible by 4, so divide through: 12⁄20 = 3⁄5