The Fraction Calculator adds, subtracts, multiplies, and divides fractions — automatically simplifying the result to lowest terms and showing the decimal equivalent. No manual common denominator finding needed.

Fraction Calculator

Add, subtract, multiply, and divide fractions with simplified results.

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Result

How to Use This Calculator

  1. Enter the numerator and denominator of both fractions.
  2. Select the operation: Add (+), Subtract (−), Multiply (×), or Divide (÷).
  3. Click Calculate.

Example: 2/3 + 1/4 → click Add → result is 11/12 (with decimal 0.916…)

Fraction Operations Reference

Adding/Subtracting: Find a common denominator (multiply both denominators), adjust the numerators, then add or subtract. Simplify by dividing by the GCD.

Multiplying: Multiply numerator × numerator and denominator × denominator. Simplify.

Dividing: Multiply by the reciprocal of the second fraction (flip numerator and denominator), then multiply. Simplify.

What Does “Simplifying to Lowest Terms” Mean?

A fraction is in lowest terms (simplest form) when the numerator and denominator share no common factors other than 1. For example, 6/8 simplifies to 3/4 because both 6 and 8 are divisible by 2 (the GCD). The calculator does this automatically using the Euclidean algorithm.

Frequently Asked Questions

Can I enter mixed numbers?

Convert mixed numbers to improper fractions first: multiply the whole number by the denominator and add the numerator. For example, 2¾ = (2×4+3)/4 = 11/4.

Why do I see “simplified from X/Y”?

The calculator shows the unsimplified intermediate result for transparency, then the final simplified form.

How it works

The calculator converts fractions to a common denominator for addition and subtraction: result = (n1×d2 ± n2×d1) / (d1×d2). For multiplication: (n1×n2) / (d1×d2). For division: (n1×d2) / (d1×n2). The result is simplified by dividing both numerator and denominator by their GCD, found using the Euclidean algorithm.

Formula

Add: (n1×d2 + n2×d1)/(d1×d2). Subtract: (n1×d2 − n2×d1)/(d1×d2). Multiply: (n1×n2)/(d1×d2). Divide: (n1×d2)/(d1×n2). Simplify by GCD.