GCSE Maths: Working with Fractions

Understanding Fractions

Fractions are a way of representing parts of a whole. A fraction is written in the form a/b, where a is the numerator and b is the denominator. The numerator represents the number of equal parts, while the denominator represents how many of those equal parts make up the whole.

Types of Fractions

• Proper Fractions: When the numerator is less than the denominator (a/b where a < b), e.g., 1/2, 3/5
• Improper Fractions: When the numerator is greater than or equal to the denominator (a/b where a ≥ b), e.g., 5/3, 7/7
• Mixed Numbers: A combination of a whole number and a proper fraction, e.g., 21/4, 53/8

Converting Between Fractions and Mixed Numbers

To convert an improper fraction to a mixed number, divide the numerator by the denominator and express the result as a whole number plus a proper fraction.

Example

Convert 17/4 to a mixed number.

Solution:

• 17 ÷ 4 = 4 remainder 1
• Therefore, 17/4 = 41/4

To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and write this sum over the denominator.

Example

Convert 31/2 to an improper fraction.

Solution:

• 3 × 2 = 6
• 6 + 1 = 7
• Therefore, 31/2 = 7/2

Operations with Fractions

To add or subtract fractions, they must have a common denominator. If the denominators are different, find the least common multiple (LCM) of the denominators and convert the fractions to equivalent fractions with the same denominator.

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

To divide fractions, invert the divisor (second fraction) and multiply.

Helpful Resources

• BBC Bitesize: Fractions
• AQA GCSE Maths Resources