Fraction Calculator & Simplifier
Add, subtract, multiply, and divide fractions with simplified results.
Calculator
Results
Result (simplest fraction)
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Mixed number
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Decimal
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Percent
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Steps
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What is a fraction?
A fraction represents a part of a whole and is written as \( \frac{a}{b} \), where \(a\) is the numerator and \(b\) is the denominator. In Italian, “fraction” in the mathematical sense is “frazione”.
In English, fraction can also mean “a very small part” (Italian: “una piccola parte”, “minima parte”). This page focuses on the mathematical tool.
Basic fraction operations
Add/Subtract: \( \frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd} \)
Multiply: \( \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd} \)
Divide: \( \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc} \)
How to simplify a fraction
- Find the greatest common divisor (GCD) of numerator and denominator.
- Divide both by the GCD.
- Ensure denominator is positive.
FAQ
Can it parse “2 1/2”?
Yes. It’s converted to \(\frac{5}{2}\) internally.
What about decimals?
Decimals are converted to fractions by counting decimal places. For example 0.125 → 125/1000 → 1/8.
Formula (LaTeX) + variables + units
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Add/Subtract: \( \frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd} \) Multiply: \( \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd} \) Divide: \( \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc} \)
- No variables provided in audit spec.
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.