Add, subtract, multiply, and divide fractions or mixed numbers. Every result is fully simplified with step-by-step working.
A fraction represents a part of a whole. The top number (numerator) tells you how many parts you have; the bottom number (denominator) tells you how many equal parts the whole is divided into.
To add or subtract fractions, you must first find a common denominator — the lowest common multiple (LCM) of both denominators. Convert each fraction so both share that denominator, then add or subtract the numerators. Finally, simplify the result by dividing numerator and denominator by their greatest common factor (GCF).
Multiply the numerators together, then multiply the denominators together. Simplify the result. Example: ²⁄₃ × ³⁄₄ = ⁶⁄₁₂ = ½.
To divide by a fraction, multiply by its reciprocal (flip numerator and denominator). Example: ²⁄₃ ÷ ⁴⁄₅ = ²⁄₃ × ⁵⁄₄ = ¹⁰⁄₁₂ = ⁵⁄₆.
A mixed number combines a whole number and a proper fraction, like 2½. To calculate with mixed numbers, convert them to improper fractions first: multiply the whole number by the denominator and add the numerator (so 2½ becomes ⁵⁄₂). This calculator handles that conversion automatically.
Simplifying (or reducing) a fraction means dividing both numerator and denominator by their greatest common factor until no common factor greater than 1 remains. For example, ¹²⁄₁₈ simplifies to ²⁄₃ because the GCF of 12 and 18 is 6.
The LCD is the smallest number that is a multiple of both denominators. For ½ + ⅓, the LCD is 6 — so ½ becomes ³⁄₆ and ⅓ becomes ²⁄₆, giving ⁵⁄₆. Finding the LCD is the key step in adding and subtracting fractions.