Math & Engineering
Fraction Calculator
Perform basic arithmetic operations with fractions including addition, subtraction, multiplication, and division.
Reviewed by the calculator.uk.com Team · Last reviewed 4 August 2026 · Our methodology
Enter two fractions and select an operation to see results
Related to Fraction Calculator
The fraction calculator performs basic arithmetic operations (addition, subtraction, multiplication, and division) with fractions. It follows standard mathematical rules for each operation and provides both the original result and a simplified version using the greatest common divisor (GCD) method.
Addition and Subtraction
To add or subtract fractions, the calculator first finds a common denominator by multiplying the denominators. Then it adjusts the numerators accordingly and performs the operation. For example, to add 1/2 + 1/3, it converts to 3/6 + 2/6 = 5/6.
Multiplication
For multiplication, the calculator multiplies the numerators together and the denominators together. For example, 1/2 × 1/3 = 1/6.
Division
Division is performed by multiplying the first fraction by the reciprocal of the second fraction. For example, 1/2 ÷ 1/3 = 1/2 × 3/1 = 3/2.
The calculator provides three different representations of the result to help you understand and use the fraction in the most appropriate form for your needs.
Original Result
This is the direct result of the fraction operation before any simplification. It shows you the exact calculation outcome.
Simplified Fraction
This is the fraction reduced to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD). This form is typically preferred in mathematical notation.
Decimal Form
The decimal representation shows the fraction as a decimal number, rounded to 4 decimal places. This is useful for practical applications or when you need to compare fraction values.
1. Why can't I enter zero as a denominator?
Division by zero is undefined in mathematics. A fraction with a denominator of zero would represent an undefined value, which is why the calculator prevents this input.
2. What happens if I enter negative numbers?
The calculator handles negative numbers according to standard mathematical rules. The sign can be in either the numerator or denominator, and the calculator will determine the correct sign in the result.
3. How does the calculator simplify fractions?
The calculator uses the greatest common divisor (GCD) algorithm to find the largest number that divides evenly into both the numerator and denominator. It then divides both numbers by the GCD to produce the simplified fraction.
4. Why are some decimal results rounded?
Decimal results are rounded to 4 decimal places for clarity and practical use. Some fractions result in repeating decimals (like 1/3 = 0.3333...), which cannot be represented exactly in decimal form.
5. What is the scientific source for this calculator?
Simplifying the result relies on the Euclidean algorithm, the repeated-remainder method for finding a greatest common divisor that appears in Book VII of Euclid's Elements and is still the standard technique taught for reducing fractions today. Addition and subtraction cross-multiply the denominators rather than hunting for a least common multiple, which is mathematically valid but can leave a larger intermediate fraction before the GCD step reduces it. Division by the reciprocal and direct numerator-times-numerator multiplication for the other operations are the ordinary rules of fraction arithmetic found in any algebra textbook.