Fraction Calculator

All four fraction operations with simplified results, mixed numbers, and decimals.

Enter Fractions

Operation

+

Simplified Result

17/12

Mixed number: 1 5/12

Decimal: 1.416667

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What is the Fraction Calculator?

Fractions represent parts of a whole, and operating on them follows precise rules that are easy to mix up: addition and subtraction need a common denominator, multiplication works straight across, and division means multiplying by the reciprocal.

This calculator performs all four operations on any two fractions and always reduces the answer to lowest terms using the greatest common divisor (GCD). It also shows the result as a mixed number and a decimal, so it doubles as a fraction-to-decimal converter.

Fraction Calculator Formula & How It Works

a/b + c/d = (ad + bc)/bd | a/b × c/d = ac/bd | a/b ÷ c/d = ad/bc
  • Add/subtract: cross-multiply over the common denominator bd
  • Multiply: multiply numerators and denominators straight across
  • Divide: flip the second fraction and multiply
  • Simplify: divide both parts by GCD

After any operation, the result is simplified by dividing the numerator and denominator by their greatest common divisor. For instance 6/8 reduces to 3/4 because GCD(6,8) = 2. An improper result like 7/2 is also shown as the mixed number 3 1/2.

Worked Examples

Add: 2/3 + 3/4

(2×4 + 3×3) / (3×4) = 17/12 = 1 5/12 ≈ 1.4167.

Divide: 5/6 ÷ 2/3

5/6 × 3/2 = 15/12, simplified to 5/4 = 1 1/4 = 1.25.

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Fraction Calculator FAQs

How do you add fractions with different denominators?

Convert both to a common denominator first: multiply each numerator by the other fraction's denominator, add the results, and place over the product of the denominators. Then simplify.

How do you simplify a fraction?

Divide both the numerator and denominator by their greatest common divisor (GCD). For 18/24, the GCD is 6, so it simplifies to 3/4.

Why do you flip the fraction when dividing?

Dividing by a number is the same as multiplying by its reciprocal. Dividing by 2/3 means asking how many two-thirds fit — which equals multiplying by 3/2.

What is a mixed number?

A mixed number combines a whole number and a proper fraction — 7/2 written as 3 1/2. It is the same value in a more readable form.

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