Fraction Calculator

At its core, fraction arithmetic relies on fundamental algebraic rules. When performing operations like addition or subtraction, fractions must share a common denominator. If they do not, the calculator uses the least common multiple (LCM) of the denominators to convert them before computing.

Mixed numbers are first converted into improper fractions using the formula: n_mixed = w * d + n, where w is the whole number, d is the denominator, and n is the numerator. Once operated upon, the resulting numerator and denominator are reduced to their lowest terms by dividing both values by their greatest common divisor (GCD): n_reduced = n / gcd(n, d).

Let's walk through multiplying two fractions: 1/2 and 5/3.

Step 1: Multiply the numerators straight across. Numerator = 1 × 5 = 5.

Step 2: Multiply the denominators straight across. Denominator = 2 × 3 = 6.

Step 3: Combine the results to get the raw product: 5/6.

Step 4: Check for simplification. The greatest common divisor of 5 and 6 is 1, meaning 5/6 is already in its fully reduced form. If the result were an improper fraction like 7/5, the calculator would additionally convert it into the mixed number 1 2/5.

Always convert mixed numbers into improper fractions before performing multiplication or division to prevent arithmetic errors. When adding or subtracting, never add the denominators together; instead, focus entirely on finding a common denominator for the numerators. Finally, always double-check your final answer to ensure the fraction is reduced to its absolute lowest terms.