Fraction Calculator

A fraction represents a numerator divided by a nonzero denominator. The numerator counts how many parts are present, while the denominator describes how many equal parts make one whole. This calculator performs the four basic arithmetic operations on two fractions and reduces the result to lowest terms. It uses integer arithmetic throughout, so familiar fraction inputs produce exact rational answers rather than rounded decimal approximations. Addition and subtraction require a common denominator. For a divided by b plus c divided by d, cross multiplication produces the numerator ad + bc over the denominator bd. Subtraction uses ad - bc over bd. The calculator may use a product denominator even when a smaller common denominator exists, because the final simplification removes every common factor and yields the same reduced answer. For example, one half plus one third becomes three sixths plus two sixths, which equals five sixths. Multiplication is direct: multiply the numerators together and multiply the denominators together. Two thirds times three fourths initially gives six twelfths, then reduction gives one half. Division uses the reciprocal of the second fraction. Dividing a divided by b by c divided by d is equivalent to multiplying a divided by b by d divided by c. The second numerator therefore cannot be zero during division because its reciprocal would have a zero denominator. Reduction uses the greatest common divisor of the result's numerator and denominator. Dividing both by that factor preserves the fraction's value while removing shared factors. A negative sign is normalized onto the numerator so the denominator remains positive. If the reduced denominator equals one, the calculator displays the result as an integer. Fractions are used in recipes, measurements, probability, ratios, geometry, finance, and algebra. Keeping answers as reduced fractions avoids the precision loss that can occur when repeating decimals are rounded. To check an answer, estimate each input as a decimal and confirm that the result has a reasonable size and sign. Also remember that denominators can never be zero, and division by a fraction equal to zero is undefined. With valid integer inputs, the calculator provides a concise exact answer suitable for homework checks and everyday arithmetic.