Add, subtract, multiply, or divide fractions — and convert between fractions and decimals instantly

To add or subtract fractions, both denominators must be the same. The simplest common denominator is the product of the two denominators (b × d), but the least common denominator (LCD) is more efficient. To find the LCD, list multiples of each denominator until you find the smallest one they share. For example, for 1/3 + 1/4, multiples of 3 are 3, 6, 9, 12 and multiples of 4 are 4, 8, 12 — so the LCD is 12. Then convert each fraction: 1/3 = 4/12 and 1/4 = 3/12. This calculator uses the product method (b × d) and then simplifies the result, which always gives the correct answer.

GCD stands for Greatest Common Divisor — the largest whole number that divides evenly into both the numerator and denominator. For example, the GCD of 12 and 18 is 6 because 6 is the largest number that divides into both. Dividing both parts of 12/18 by 6 gives the simplified fraction 2/3. The GCD is computed using the Euclidean algorithm, which repeatedly divides and takes remainders until the remainder is zero. Simplifying fractions makes them easier to understand, compare, and use in further calculations.

A mixed number like 2 3/4 can be converted to an improper fraction by multiplying the whole number by the denominator, adding the numerator, and keeping the same denominator. For 2 3/4: multiply 2 × 4 = 8, add the numerator 8 + 3 = 11, keep denominator 4, so 2 3/4 = 11/4. To go the other way, divide the numerator by the denominator: 11 ÷ 4 = 2 remainder 3, so 11/4 = 2 3/4. This calculator works with improper fractions directly, so convert your mixed numbers before entering them.