Math Calculators
Fraction Calculator
Add, subtract, multiply, and divide fractions with reduced and decimal results.
Enter the values and review the result.
Calculation assumptions
- *Denominators cannot be zero.
- *Division by a fraction means multiplying by its reciprocal.
- *Results are simplified to lowest terms when possible.
- *Inputs must be whole-number numerators and denominators; mixed-number entry is not supported.
Enter your values and press Calculate.
Results and breakdowns will appear here after a valid calculation.
How the fraction operations work
Fractions represent parts of a whole. To add or subtract them, use a common denominator. To multiply, multiply numerator by numerator and denominator by denominator. To divide, multiply by the reciprocal of the second fraction.
The result is reduced by dividing its numerator and denominator by their greatest common divisor. A negative sign is normalized to the numerator.
Worked fraction examples
Addition with different denominators
For 1/2 + 1/3, use denominator 6: 3/6 + 2/6 = 5/6. The decimal approximation is 0.8333.
Multiplication and reduction
For 3/4 x 2/3, multiply to get 6/12, then reduce by the common factor 6 to get 1/2.
Division by a fraction
For 2/3 / 4/5, multiply 2/3 by the reciprocal 5/4 to get 10/12, which reduces to 5/6.
Scope and limitations
- Enter integer numerators and denominators. Convert mixed numbers to improper fractions first.
- The fraction result is exact for supported integer inputs; the decimal is rounded to four places.
- A denominator cannot be zero, and division by a zero fraction is undefined.
Common mistakes
- Do not use zero as a denominator.
- When dividing, the second fraction cannot be zero.
- For addition and subtraction, remember that denominators must be aligned before combining.
- A negative denominator is normalized into the numerator in the simplified result.
Transparency note
Accuracy and limitations
Calzivo tools are built for practical estimates, conversions, and checks. Some tools use standard formulas or simplified assumptions, and results can be affected by input accuracy, rounding, units, local rules, or changing official requirements.
Results depend on the values you enter and any simplified assumptions used by the tool. Verify important results before making decisions or submitting official information.
Reference check
Sources and references
These references provide background context for the topic. They do not replace official advice or documents for personal decisions.
- Add and Subtract Fractions
OpenStax, Elementary Algebra 2e
- Multiply and Divide Fractions
OpenStax, Prealgebra 2e
How to Use This Tool
Use these steps to enter the right inputs and interpret the result correctly.
Enter the numerator and denominator for the first fraction.
Select the mathematical operation.
Enter the numerator and denominator for the second fraction.
Review the simplified fraction first and use the four-decimal result as a secondary approximation.
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Related Guides
Background reading and explanations related to Fraction Calculator.
Percentage Calculator Guide: What It Solves and How It Works
Learn how a percentage calculator works and what problems it solves.
Average Calculator Guide: Mean, Median, Mode, and Range
Learn how average calculators find mean, median, mode, range, sum, and count with examples.
Fraction Calculator Guide: Add, Subtract, Multiply, and Divide
Learn fraction operations, common denominators, reciprocals, simplification, and decimal checks.
Frequently Asked Questions
Common questions about Fraction Calculator and how to read the result.
Does it simplify the fraction?
Yes, the calculator automatically reduces the result to its simplest form.
Can a denominator be zero?
No. Division by zero is undefined, so denominators must not be zero.
How do I divide fractions?
Multiply the first fraction by the reciprocal of the second fraction.
Can I use negative fractions?
Yes. Negative numerators or denominators are supported, and the sign is normalized in the result.
Why does addition need a common denominator?
Fractions must represent the same size parts before they can be added or subtracted directly.
Does it show a decimal?
Yes. The calculator shows the simplified fraction and a decimal approximation.