Fraction Calculator

To add fractions, they must have the same denominator. Find the least common multiple (LCM) of the denominators, expand both fractions to that denominator, then add the numerators. Example: 1/4 + 2/3 = 3/12 + 8/12 = 11/12.

When multiplying fractions, simply multiply numerator by numerator and denominator by denominator. Example: 2/3 × 3/5 = 6/15 = 2/5 (simplified). A common denominator is not needed.

Simplifying means dividing numerator and denominator by their greatest common divisor (GCD). The fraction keeps its value but becomes simpler. Example: 12/18 ÷ 6 = 2/3. The GCD of 12 and 18 is 6.

Divide the numerator by the denominator. Example: 3/4 = 3 ÷ 4 = 0.75. Some fractions result in repeating decimals, e.g., 1/3 = 0.333... (repeating 3).

A mixed number consists of a whole number and a proper fraction, e.g., 2 3/4. It arises when the numerator is larger than the denominator (improper fraction): 11/4 = 2 3/4, because 11 ÷ 4 = 2 remainder 3.

To divide by a fraction, multiply by its reciprocal (numerator and denominator are swapped). Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

The GCD is the largest number that divides both numerator and denominator without remainder. It's used to simplify fractions. For 24 and 36, the GCD is 12, because 24 = 2×12 and 36 = 3×12.

The LCM of two numbers is the smallest positive number divisible by both. It's used as the common denominator when adding and subtracting fractions. For 4 and 6, the LCM is 12.

Bring both fractions to the same denominator (LCM) and compare the numerators. The fraction with the larger numerator is greater. Alternatively, convert both to decimals and compare directly.

In Germany, fraction arithmetic is typically introduced in 5th and 6th grade. Simple fractions and the concept of sharing are covered in elementary school, while formal fraction arithmetic with all operations follows in secondary school.