Everyday mathematics

Fraction Calculator

Add, subtract, multiply or divide two integer fractions. The rational result is reduced exactly using integer arithmetic; a decimal approximation is also displayed.

Explicit formulas and worked examples
Check your inputs, then calculate
Data is calculated in this browser only

Check the stated input format, calculation convention and limits before using the result.

Check the example inputs, then calculate. Your values stay in this browser.

Fractional numerators or denominators are rejected rather than truncated.

Calculation notes

Understand the Fraction Calculator

Fraction Calculator validates first numerator, first denominator, operation, second numerator, second denominator before applying the displayed equation. Fractional numerators or denominators are rejected rather than truncated.

Formula and logic

What is the formula for the Fraction Calculator?

Fraction Calculator: a/b + c/d = (ad + bc)/bd; reduced numerator = numerator / gcd(numerator, denominator). Input definitions: a = First numerator; b = First denominator; mode = Operation; c = Second numerator; d = Second denominator. Use the selected convention throughout the calculation.

Worked example

How can I reproduce the Fraction Calculator example?

Fraction Calculator baseline input: First numerator: 1; First denominator: 2; Operation: +; Second numerator: 1; Second denominator: 3. Output: Simplified fraction = 5/6; Decimal = 0.833333333333. Substitute these values into the displayed equation to reproduce the result.

How to read the result

How should I interpret the Fraction Calculator result?

Read simplified fraction with its stated unit and convention. The default example and the independent worked scenario use different inputs, so compare the assumptions before comparing the numbers.
Change one input at a time and use the equation to explain the result; do not mix unit, grade-scale, time-zone or rounding conventions across comparisons.

Limits and assumptions

What limits apply to the Fraction Calculator?

Fractional numerators or denominators are rejected rather than truncated.
Denominators and a divisor fraction must be nonzero; decimal output is approximate.

Content and calculation reviewed: 2026-10-11

Understand the calculation

How to use it and the math behind it

Read the complete explanation

Four steps to check your inputs and results

Add, subtract, multiply or divide two integer fractions. The rational result is reduced exactly using integer arithmetic; a decimal approximation is also displayed.
Enter First numerator, First denominator, Operation, Second numerator, Second denominator in the stated format. Baseline values are for reproduction.
Check the output unit and convention: Read simplified fraction with its stated unit and convention. The default example and the independent worked scenario use different inputs, so compare the assumptions before comparing the numbers.
Change one input and compare the result. Fractional numerators or denominators are rejected rather than truncated. Denominators and a divisor fraction must be nonzero; decimal output is approximate.