Fraction Calculator
Add, subtract, multiply, or divide two fractions and get the answer in lowest terms, as a mixed number, and as a decimal, with clear steps.
- Use a common denominator 6: 5/6.
- Divide numerator and denominator by their GCD 1: 5/6.
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All calculations run locally in your browser. Your entered values are not sent to an external service.
How to Use the Fraction Calculator
Choose an operation, enter the numerator and denominator of each fraction, and select Calculate. The tool reduces the answer to lowest terms and also shows it as a decimal and, when possible, as a mixed number.
- Pick Add, Subtract, Multiply, or Divide.
- Enter whole-number numerators and denominators for both fractions.
- Select Calculate and review the reduced result and steps.
Numerators can be negative to represent negative fractions. A denominator cannot be zero, and division requires the second fraction to have a nonzero numerator. To turn a decimal such as 0.75 into a fraction, use the Decimal to Fraction Calculator. To reduce one fraction with Euclidean GCD steps, use the Simplify Fraction Calculator.
How Fraction Operations Work
Addition and subtraction use a common denominator. Multiplying the denominators always gives one, then the numerators are combined over that shared denominator and the result is reduced.
Multiplication multiplies numerators together and denominators together. Dividing by a fraction multiplies by its reciprocal: a/b ÷ c/d = a/b × d/c.
Every result is reduced by dividing the numerator and denominator by their greatest common divisor, and the sign is kept on the numerator.
Fraction Calculator Examples
Addition
1/2 + 1/3 uses the common denominator 6: 3/6 + 2/6 = 5/6.
Subtraction
3/4 − 1/6 uses the common denominator 12: 9/12 − 2/12 = 7/12.
Multiplication
2/3 × 3/5 = 6/15, which reduces to 2/5.
Division
3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8, which is the mixed number 1 7/8.
Simplifying and Mixed Numbers
A fraction is in lowest terms when the numerator and denominator share no common factor other than 1. For 6/15, the greatest common divisor is 3, so dividing both parts by 3 gives 2/5. The Simplify Fraction Calculator shows those Euclidean remainder steps for one fraction or mixed number.
An improper fraction, where the numerator is at least as large as the denominator, can be written as a mixed number. For 15/8, 8 goes into 15 once with remainder 7, giving 1 7/8. The calculator reports the mixed form whenever the fraction is improper.
Common Fraction Mistakes
Adding denominators
Do not add denominators. 1/2 + 1/3 is not 2/5. Convert to a common denominator first.
Forgetting to reduce
6/15 is correct but not simplified. Divide both parts by the greatest common divisor to get 2/5.
Flipping the wrong fraction when dividing
To divide, take the reciprocal of the second fraction, not the first.
Dropping a negative sign
Keep the sign with the numerator and carry it through every step.
Using zero as a denominator
A denominator of zero is undefined. Division also fails if the second numerator is zero.
Fraction Calculator FAQs
How do I add two fractions?
Convert both fractions to a common denominator, add the numerators, and reduce the result to lowest terms.
How do I divide fractions?
Multiply the first fraction by the reciprocal of the second: a/b ÷ c/d = a/b × d/c.
What is a mixed number?
A mixed number combines a whole number and a proper fraction, such as 1 7/8 for the improper fraction 15/8.
How is a fraction reduced to lowest terms?
Divide the numerator and denominator by their greatest common divisor. The Simplify Fraction Calculator shows the Euclidean steps for a single fraction.
Can I use negative fractions?
Yes. Enter a negative numerator. The calculator keeps the sign on the numerator of the answer.
Are my values sent to a server?
No. The calculation runs locally in your browser.
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Reviewed by Prof. Dr. Khalil Mudassar (PhD) · Last updated: [mc_modified_date]
Sources
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Disclaimer
This calculator is intended for general educational and practical use. Review important results before relying on them in professional work.