Fraction Calculator
Add, subtract, multiply, or divide two fractions and view the simplified fraction, decimal equivalent, and mixed number when applicable.
This free online fraction calculator performs addition, subtraction, multiplication, and division with two fractions. It reduces the answer to simplest form and also displays its decimal equivalent and mixed-number representation when one applies.
How to Use the Fraction Calculator
Enter the integer numerator and nonzero integer denominator of the first fraction, select an operation, and enter the second fraction. Click Calculate Fraction to view the original expression and all available result formats.
How Are Fractions Simplified?
The calculator divides the result’s numerator and denominator by their greatest common divisor. For example, 8/12 has a greatest common divisor of 4, so it simplifies to 2/3.
How to Add Fractions
For a/b + c/d, cross-multiply and add the products: (a × d + c × b)/(b × d). The resulting numerator and denominator are then reduced by their greatest common divisor.
How to Subtract Fractions
For a/b − c/d, cross-multiply and subtract the second product from the first: (a × d − c × b)/(b × d). The final fraction is then simplified.
How to Multiply Fractions
Multiply the numerators together and multiply the denominators together: (a × c)/(b × d). Simplify the resulting fraction afterward.
How to Divide Fractions
Multiply the first fraction by the reciprocal of the second: a/b ÷ c/d = a/b × d/c. The second fraction cannot equal zero because division by zero is undefined.
Simplified Fraction, Decimal, and Mixed Number
The primary result is the reduced fraction or integer. The decimal representation is rounded to at most 10 decimal places. An improper fractional result is also displayed as a mixed number.
Negative Fractions
Negative numerators and denominators are supported. When the final denominator is negative, the sign is moved to the numerator before the fraction is simplified and formatted.
Zero Numerators and Denominators
A numerator may be zero, making the fraction equal to zero. A denominator may never be zero. When dividing, the second fraction must also have a nonzero numerator because it becomes the divisor.
Integer Inputs Only
Numerators and denominators must be integers. Decimal values should first be converted into equivalent fractions before using the calculator.
Private Browser-Based Calculation
All arithmetic runs locally in your browser. The fractions you enter do not need to be uploaded to or stored on the ORVITech server.
How Is the Result Calculated?
Addition: a/b + c/d = (a × d + c × b)/(b × d) Subtraction: a/b − c/d = (a × d − c × b)/(b × d) Multiplication: a/b × c/d = (a × c)/(b × d) Division: a/b ÷ c/d = (a × d)/(b × c)
Adding Fractions Example
For 1/2 + 1/3, cross-multiply to obtain (1 × 3 + 1 × 2)/(2 × 3) = 5/6. The fraction is already simplified, its decimal equivalent is approximately 0.8333333333, and no mixed number applies because the result is less than one.
Frequently Asked Questions
What operations can the fraction calculator perform?
It can add, subtract, multiply, and divide two fractions.
Does it simplify the result automatically?
Yes. The numerator and denominator are divided by their greatest common divisor.
Does the calculator show a decimal result?
Yes. It displays the decimal equivalent rounded to at most 10 decimal places.
Does it show mixed numbers?
Yes. When the simplified answer is an improper fraction, the calculator also displays its mixed-number form.
Can I enter negative fractions?
Yes. Numerators and denominators may be negative, and the final sign is normalized during simplification.
Can a numerator be zero?
Yes. A fraction with a zero numerator and nonzero denominator equals zero.
Can a denominator be zero?
No. A denominator of zero is invalid because division by zero is undefined.
Why can’t I divide by a fraction with numerator zero?
A fraction such as 0/5 equals zero. Dividing by that fraction would therefore be division by zero.
Can I enter decimal numerators or denominators?
No. This calculator requires integer numerators and denominators. Convert decimal values to fractions first.
How is a negative mixed number displayed?
The negative sign is placed on the whole-number portion, followed by the positive fractional remainder.
What does “not applicable” mean for the mixed number?
It means the result is already a proper fraction or integer and does not require a mixed-number representation.
Are repeating decimals rounded?
Yes. Decimal output is limited to at most 10 decimal places, while the simplified fractional result remains the primary representation.
Are my fractions stored?
No. The calculation occurs locally in your browser and the entered values are not stored on the ORVITech server.
Is the fraction calculator free?
Yes. You can use it without creating an account or installing an application.