Fraction Calculator

📖 How to Use This Fraction Calculator

Select operation - Choose Add, Subtract, Multiply, Divide, or Simplify.

Enter fractions - Input numerators, denominators, and optional whole numbers for mixed fractions.

Click the operation button - Get the result as a simplified fraction and decimal.

🔢 Understanding Fractions

A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number). Fractions can be proper (numerator < denominator), improper (numerator ≥ denominator), or mixed (whole number + fraction).

🧮 Fraction Operations Formulas

Addition: a/b + c/d = (ad + bc) / bd
Subtraction: a/b - c/d = (ad - bc) / bd
Multiplication: a/b × c/d = (a × c) / (b × d)
Division: a/b ÷ c/d = (a × d) / (b × c)
Simplification: Divide numerator and denominator by GCD

📊 Types of Fractions

Proper Fraction: Numerator < Denominator (e.g., 3/4)
Improper Fraction: Numerator ≥ Denominator (e.g., 5/3)
Mixed Number: Whole number + proper fraction (e.g., 1 2/3)
Equivalent Fractions: Different fractions representing same value (e.g., 1/2 = 2/4)

💡 How to Simplify Fractions

Find the Greatest Common Divisor (GCD) of numerator and denominator
Divide both numerator and denominator by the GCD
Example: 8/12 → GCD = 4 → 8÷4 / 12÷4 = 2/3
Our calculator automatically simplifies all results

❓ Frequently Asked Questions (FAQ)

How do I add fractions with different denominators?

Find the Least Common Denominator (LCD), convert both fractions, then add numerators. Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.

What is a mixed number?

A mixed number is a whole number plus a proper fraction (e.g., 2 1/2). To convert to improper fraction: multiply whole by denominator, add numerator, keep denominator.

How do I multiply fractions?

Multiply numerators together, denominators together, then simplify. Example: 2/3 × 4/5 = 8/15.

How do I divide fractions?

Multiply the first fraction by the reciprocal of the second fraction. Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

What is the difference between proper and improper fractions?

Proper fractions have numerator less than denominator (value < 1). Improper fractions have numerator greater than or equal to denominator (value ≥ 1).

Why do we need a common denominator for addition/subtraction?

You can only add or subtract fractions that represent the same-sized parts. Finding a common denominator ensures the fractions are expressed in equal units.

Fraction 1