What is a fraction calculator?
A fraction calculator performs arithmetic with rational numbers while keeping the answer in exact fractional form. It accepts proper fractions, improper fractions, integers, finite decimals and mixed numbers.
Use the Math Calculators category to explore percentage, ratio and algebra tools.
How does the fraction calculator work?
Every entry is converted to an integer numerator and denominator. The selected operation is applied, then the numerator and denominator are divided by their greatest common divisor. This avoids the early decimal rounding that can occur with floating-point arithmetic.
Fraction formulas
How to use the fraction calculator
- Select add, subtract, multiply, divide or simplify.
- Enter the first fraction or mixed number.
- Enter a second value unless simplifying only one fraction.
- Select Calculate Fraction and review the exact fraction, mixed number, decimal and steps.
Affiliate disclosure: As an Amazon Associate I earn from qualifying purchases.
For optional supporting equipment or reference material, you can browse Arithmetic reference workbooks (paid link) on Amazon.com. Practice the relevant arithmetic with a suitable workbook. Worked exercises are optional; the calculator result and its steps do not depend on buying a book. No purchase is required to use this calculator.
Fraction examples
For 1/2 + 1/3, the common denominator is 6: 3/6 + 2/6 = 5/6. For 2/3 ÷ 4/5, multiply by the reciprocal: 2/3 × 5/4 = 10/12 = 5/6.
Rules and limitations
A denominator cannot be zero. Division by a zero-valued second fraction is also undefined. Decimal inputs must be finite ordinary decimals; repeating decimals should be entered directly as fractions when an exact value is required.
Worked example: Fraction
Enter the following values in the Fraction Calculator and calculate to reproduce this result.
- Operation: Add fractions
- First fraction: 1 1/2
- Second fraction: 3/4
Example result: 9/4. The exact result is 9/4. As a mixed number it is 2 1/4, and as a decimal it is 2.25.
Calculation used: 3/2 + 3/4 = 9/4
How to interpret this example
Convert the mixed number to an improper fraction, use a common denominator, then simplify. In this example, 3/2 + 3/4 = 6/4 + 3/4 = 9/4. The mixed and decimal displays represent the same value.
Frequently asked questions about fractions
Methodology and calculation scope
Inputs are parsed as rational numbers and normalized with the Euclidean greatest-common-divisor algorithm. Arithmetic uses exact BigInt integers before a decimal approximation is produced.