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Fraction Calculator Add, subtract, multiply, and divide fractions with automatic simplification.

Fraction Calculator illustration
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Fraction Calculator

Add, subtract, multiply, and divide fractions with automatic simplification.

1

Select Operation

Choose whether to add, subtract, multiply, or divide your two fractions.

2

Enter Fractions

Input the numerator and denominator for each fraction in the provided fields.

3

Get Simplified Result

View the answer as a simplified fraction, the unsimplified form, and its decimal equivalent.

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What Is Fraction Calculator?

A fraction calculator performs arithmetic operations on fractions — addition, subtraction, multiplication, and division — and automatically simplifies the result to its lowest terms. When you add or subtract fractions, the calculator finds a common denominator, performs the operation on the numerators, and then reduces the resulting fraction by dividing both numerator and denominator by their greatest common divisor (GCD). For multiplication, it multiplies numerators and denominators directly, then simplifies. For division, it multiplies the first fraction by the reciprocal of the second. The tool also displays the decimal equivalent of every result, making it easy to convert between fraction and decimal representations. This calculator is invaluable for students learning fraction arithmetic, professionals working with measurements in fractions (common in construction and cooking), and anyone who needs precise fractional calculations. Unlike decimal approximations, fractions preserve exact values — one-third is exactly 1/3, not the endlessly repeating 0.333...

Why Use Fraction Calculator?

  • Automatically simplifies fractions to lowest terms using GCD
  • Shows both simplified and unsimplified results for learning
  • Converts to decimal equivalent for easy interpretation
  • Handles negative fractions and improper fractions correctly
  • Instant results with no manual common-denominator work

Common Use Cases

Math Homework

Quickly check fraction arithmetic answers or understand the step-by-step process of simplification.

Cooking & Recipes

Scale recipe measurements that use fractions, like adding 2/3 cup to 3/4 cup of an ingredient.

Construction & Woodworking

Add and subtract fractional measurements common in building plans and materials.

Music Theory

Work with time signatures and note durations expressed as fractions.

Technical Guide

Fraction arithmetic follows specific rules depending on the operation. For addition and subtraction, fractions must share a common denominator: a/b ± c/d = (a×d ± c×b) / (b×d). This cross-multiplication approach always works but may produce a fraction that isn't in lowest terms, so the result is simplified by dividing both parts by their GCD. The GCD is found using the Euclidean algorithm: repeatedly replacing the larger number with the remainder of dividing the larger by the smaller until the remainder is zero. For multiplication: (a/b) × (c/d) = (a×c) / (b×d). For division: (a/b) ÷ (c/d) = (a/b) × (d/c) = (a×d) / (b×c), which requires that c ≠ 0. Sign handling follows standard rules: negative signs are normalized to the numerator, and a fraction with a negative denominator is flipped. This calculator preserves mathematical precision by working with integers rather than floating-point numbers, avoiding rounding errors that plague decimal-based calculations.

Tips & Best Practices

  • 1
    To check your work, convert both fractions to decimals and verify the result
  • 2
    When multiplying, you can cross-cancel before multiplying to keep numbers smaller
  • 3
    Remember: dividing by a fraction is the same as multiplying by its reciprocal
  • 4
    An improper fraction (numerator > denominator) is perfectly valid — no need to convert to mixed number
  • 5
    Zero in the denominator is undefined; the calculator will show an error

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Frequently Asked Questions

Q How do you add fractions with different denominators?
Find a common denominator by cross-multiplying: a/b + c/d = (a×d + c×b) / (b×d), then simplify the result by dividing both numerator and denominator by their GCD.
Q What does it mean to simplify a fraction?
Simplifying (or reducing) a fraction means dividing both the numerator and denominator by their greatest common divisor (GCD) until they share no common factors other than 1.
Q Can this calculator handle negative fractions?
Yes, negative fractions are fully supported. The sign is always normalized to the numerator in the result.
Q Why does 1/3 show as 0.33333... in decimal?
Some fractions produce repeating decimals because their denominators have prime factors other than 2 and 5. The fraction 1/3 = 0.333... repeating infinitely.
Q What is a reciprocal?
The reciprocal of a fraction a/b is b/a (flip numerator and denominator). Multiplying a fraction by its reciprocal always gives 1.
Q Can I enter improper fractions?
Yes. Improper fractions where the numerator is larger than the denominator (like 7/3) are valid inputs and the result will also be shown as a fraction.

About This Tool

Fraction Calculator is a free online tool by FreeToolkit.ai. All processing happens directly in your browser — your data never leaves your device. No registration or installation required.