Fraction CalculatorFree online math calculator — instant results, no sign-up
Add, subtract, multiply and divide fractions.
About the Fraction Calculator
This calculator performs basic arithmetic—addition, subtraction, multiplication, and division—on two fractions. It converts the result into a simplified improper fraction, a decimal rounded to six decimal places, and a mixed number representation.
- First fraction
- The starting fraction entered as numerator/denominator (e.g., 3/4 or -2/5); the denominator cannot be zero.
- Operation
- The mathematical operation to execute: addition (+), subtraction (−), multiplication (×), or division (÷).
- Second fraction
- The operand fraction entered as numerator/denominator (e.g., 5/6); for division, the numerator cannot be zero.
Formula and method
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)
- a, bNumerator and denominator of the first fraction
- c, dNumerator and denominator of the second fraction
- p, qUnsimplified numerator and denominator of the combined result
The calculator parses each fraction into numerator and denominator pairs, then applies the cross-multiplication formula matching the selected operator. The unreduced fraction p/q is simplified by dividing by its greatest common divisor, converted to a decimal rounded to 6 digits, and formatted as an integer and reduced remainder fraction if the absolute numerator equals or exceeds the denominator.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- First fraction3/4
- Operation+
- Second fraction5/6
Results
- Result19/12
- Decimal1.583333
- Mixed number1 7/12
How to use the Fraction Calculator
- 1Parse the first fraction into numerator a and denominator b, and the second into c and d.
- 2Compute resulting numerator p and denominator q based on the chosen operator (+, −, ×, or ÷).
- 3Reduce p/q to simplest form by canceling out the greatest common divisor.
- 4Format the output as a reduced fraction, a 6-decimal floating-point number, and a mixed number.
Reading your result
The 'Result' row displays the simplified improper or proper fraction. 'Decimal' shows the exact or approximate floating-point value rounded to six decimal places. 'Mixed number' separates any whole integer component from the fractional remainder for values greater than or equal to 1 (or less than or equal to -1).
Limitations
The calculator operates on two fractions at a time and does not accept nested operations or parenthetical algebraic expressions. It does not accept mixed numbers directly as input without converting them to improper fractions first.
Common questions
How do I enter a whole number or a mixed number?+
To enter a whole number like 4, enter it as 4/1. To enter a mixed number like 2 1/3, convert it to an improper fraction first: (2 × 3 + 1)/3 = 7/3.
What happens if I divide by a fraction with a numerator of zero?+
Dividing by a fraction whose numerator is zero results in a division-by-zero error, as the divisor's numerator becomes the resulting denominator.
Why does the mixed number field match the result field for proper fractions?+
When the absolute value of the numerator is smaller than the denominator (less than 1), there is no whole number component, so the mixed number representation is simply the reduced proper fraction.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
Further reading
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Results are estimates for informational purposes and are not financial, medical or legal advice.