Adding and Subtracting Fractions Calculator

How Adding and Subtracting Fractions Works?

The calculator represents the two inputs as $\frac{a_1}{b_1}$ and $\frac{a_2}{b_2}$, where each denominator is required to be positive. Fractions can only be combined directly when they have a common denominator. The calculator finds the least common denominator using the least common multiple of the two denominators:

Each numerator is then scaled to match this denominator. For addition, the calculation is:

For subtraction, the second scaled numerator is subtracted instead:

The resulting numerator and denominator are reduced by their greatest common divisor, $g=\text{gcd}(n,d)$:

The outputs include the common denominator, simplified numerator and denominator, simplified fraction, decimal result, and a mixed-number form when the result is improper.

Practical Use Cases

Students: Students can check homework involving unlike denominators, such as $\frac{3}{4}+\frac{2}{3}$, and compare the simplified fraction, decimal equivalent, and mixed-number form with their handwritten work.

Teachers: Teachers can create worked examples and verify answer keys for addition and subtraction exercises, including problems with negative numerators and results that require complete reduction.

Parents and tutors: Parents and tutors can use the calculator to demonstrate why denominators must be made common before combining numerators, while using the intermediate common denominator to explain each step.

Engineers and technical professionals: Technical users can quickly combine exact fractional values during estimates, specifications, or algebraic checks without losing the exact result to an early decimal approximation.

DIY and woodworking users: DIY users can add or subtract fractional measurements represented as numbers, then use the simplified fraction or decimal result for checking a calculation.

Accuracy and Limitations

The calculator performs the fraction operation using integer numerators and positive integer denominators, then simplifies the result using a greatest-common-divisor reduction, so the fraction output is exact for valid entered integers. Numerators and denominators are limited to the supplied ranges: each numerator must be between -1,000,000 and 1,000,000, while each denominator must be between 1 and 1,000,000; zero or non-integer denominators are not supported. The decimal result is an equivalent numerical representation and may be displayed with finite precision, and the mixed-number output is provided only when the result is improper.

Quick Examples