How to Add, Subtract, Multiply and Divide Fractions — Step by Step

Fractions are one of the most feared topics in maths — but they follow simple, logical rules once you understand the pattern.

Adding fractions with different denominators

You can’t add fractions directly unless they share a denominator. The method:

1. Find the LCD (Least Common Denominator)
2. Convert both fractions to equivalent fractions with that LCD
3. Add the numerators, keep the denominator
4. Simplify if possible

Example: 2/3 + 1/4

LCD of 3 and 4 = 12
2/3 = 8/12 (multiply top and bottom by 4)
1/4 = 3/12 (multiply top and bottom by 3)
8/12 + 3/12 = 11/12 ✓

Subtracting fractions

Same process as addition — find LCD, convert, subtract numerators.

Example: 5/6 − 1/4 = 10/12 − 3/12 = 7/12

Multiplying fractions (the easiest operation)

Simply multiply numerators together and denominators together. No LCD needed!

a/b × c/d = (a×c) / (b×d)

Example: 3/4 × 2/5 = 6/20 = 3/10

Pro tip: Cross-cancel before multiplying to keep numbers small.

Dividing fractions (flip and multiply)

Keep the first fraction, flip the second, then multiply.

a/b ÷ c/d = a/b × d/c

Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1⁷⁄₈

Simplifying fractions

Divide both numerator and denominator by their GCD (Greatest Common Divisor).

Example: 18/24 → GCD is 6 → 18÷6 / 24÷6 = 3/4

Mixed numbers

A mixed number like 2³⁄₄ means 2 + 3/4. To convert to improper fraction: (2×4+3)/4 = 11/4.

Common mistakes to avoid

1. Adding denominators (wrong: 1/3 + 1/4 ≠ 2/7)
2. Forgetting to simplify the final answer
3. Not converting mixed numbers before operating

Try our Fraction Calculator for instant step-by-step solutions to any fraction problem.