Fraction Calculator

When you enter two fractions and choose an operation, the calculator first identifies the numerators and denominators of each fraction, then applies the appropriate arithmetic rule. For addition and subtraction, it finds the least common denominator (LCD) — the smallest number that both denominators divide into evenly — converts each fraction to an equivalent form with that LCD, and then adds or subtracts the numerators. This approach avoids the common mistake of simply adding or subtracting numerators and denominators directly, which produces a mathematically incorrect result.

For multiplication, the process is more straightforward: the calculator multiplies the two numerators together to form the new numerator, and multiplies the two denominators together to form the new denominator. Division follows the 'keep, change, flip' rule — the first fraction is multiplied by the reciprocal of the second, turning a division problem into a multiplication problem. Both operations can benefit from cross-cancellation before multiplying, which reduces the size of intermediate numbers and makes simplification easier.

After computing the raw result, the calculator simplifies the fraction by finding the greatest common divisor (GCD) of the resulting numerator and denominator and dividing both by it. This guarantees the fraction is expressed in its lowest terms. If the numerator is larger than the denominator, the result is also converted into a mixed number, so you can see both the whole-number part and the proper fraction remainder at a glance.

A frequent source of errors for users working by hand is forgetting to simplify, or finding an incorrect LCD and then failing to adjust numerators proportionally. This calculator eliminates both pitfalls automatically. It also handles negative fractions correctly, preserving the sign through every step — something that trips up many manual calculations, especially during subtraction when a negative denominator or numerator is involved.