How to Add, Subtract, Multiply, and Divide Fractions (Step-by-Step)

Fractions have a reputation for being confusing, but the rules governing them are consistent and logical. Once you understand why each rule works — not just what to do — fraction arithmetic becomes straightforward. This guide covers all four operations with worked examples, explains mixed numbers and improper fractions, and shows how to simplify answers correctly.

Adding Fractions

Fractions must share a common denominator before you can add their numerators.

Different denominators: 1/4 + 1/6

Find the LCD. For 4 and 6: multiples of 4 are 4, 8, 12; multiples of 6 are 6, 12. LCD = 12.
Convert: 1/4 = 3/12 (multiply by 3); 1/6 = 2/12 (multiply by 2).
Add: 3/12 + 2/12 = 5/12.

Subtracting Fractions

Identical process to addition — find the LCD, convert, then subtract numerators.

Example: 3/4 − 2/5. LCD of 4 and 5 = 20. Convert: 3/4 = 15/20; 2/5 = 8/20. Subtract: 15/20 − 8/20 = 7/20.

Multiplying Fractions

No common denominator needed. Simply multiply numerators together and denominators together.

2/3 × 4/5 = (2×4) / (3×5) = 8/15.

Tip — cross-cancel: If a numerator and a denominator share a common factor, cancel before multiplying to keep numbers smaller. Example: 4/9 × 3/8 → cancel 4 and 8 (÷4), cancel 3 and 9 (÷3) → (1/3) × (1/2) = 1/6.

Dividing Fractions

Use "keep, change, flip": keep the first fraction, change ÷ to ×, flip the second fraction.

3/4 ÷ 2/5 → 3/4 × 5/2 = 15/8 = 1 and 7/8.

Mixed Numbers and Improper Fractions

Mixed to improper: multiply whole × denominator + numerator, keep denominator. 2 and 3/4 = (2×4+3)/4 = 11/4.

Improper to mixed: divide numerator by denominator. 11 ÷ 4 = 2 remainder 3, so 11/4 = 2 and 3/4.

Simplifying Fractions with GCD

Find the GCD of numerator and denominator, then divide both by it.

Example: 36/48. GCD(36, 48) = 12. Divide: 36/12 = 3; 48/12 = 4. Simplified: 3/4.

For quick verification of any of these operations, the fraction calculator shows the step-by-step work so you can see exactly where you are in the process.