Fraction Calculator
Add, subtract, multiply, and divide fractions or mixed numbers with complete step-by-step GCD reduction and decimal conversions.
Step-by-Step Working
Term 1: 1/2 · Term 2: 3/4
Common denominator LCM(2, 4) = 4. Scale numerators: (1 × 2) + (3 × 1) = 2 + 3 = 5/4
GCD(5/4) = 1. Dividing top and bottom gives 5/4.
Rules of Fraction Arithmetic & Simplification
Adding & Subtracting (Common Denominators)
Fractions can only be directly added or subtracted when they share the same bottom number (denominator).
Find the Least Common Multiple (LCM) of both denominators, scale each numerator proportionally, combine the numerators, and reduce.
Multiplying & Dividing (Keep-Change-Flip)
For multiplication, multiply straight across: (a/b) × (c/d) = (a×c) / (b×d).
For division, use reciprocal multiplication: Keep the first fraction, change division to multiplication, and flip the second fraction: (a/b) ÷ (c/d) = (a/b) × (d/c).
Greatest Common Divisor (GCD)
A fraction is in simplest form when the numerator and denominator share no common factors other than 1.
Using Euclid's algorithm, compute GCD(numerator, denominator) and divide both sides by this factor to reach irreducible lowest terms.