Fraction Calculator

Add, subtract, multiply, or divide fractions and mixed numbers.

Fraction Calculation

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Result

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Understanding and Calculating Fractions

A fraction represents a part of a whole. Our calculator handles operations with proper fractions, improper fractions, and mixed numbers, providing both the simplified result and its decimal equivalent.

Key Concepts

  • Mixed Number: A whole number and a proper fraction combined (e.g., 1 ½).
  • Improper Fraction: A fraction where the numerator is greater than the denominator (e.g., 3/2).
  • Simplifying Fractions: To simplify, divide both the numerator and denominator by their greatest common divisor (GCD).

How to Perform Calculations

Before performing any operation, mixed numbers are converted to improper fractions using the formula: `((Whole × Denominator) + Numerator) / Denominator`.

1. Addition and Subtraction

To add or subtract fractions, they must have a common denominator.

Formula: `(a/b) + (c/d) = (ad + bc) / bd`

Example (1/2 + 1/4):First, find a common denominator (4). Convert 1/2 to 2/4. Then, `2/4 + 1/4 = 3/4`.

2. Multiplication

Multiply the numerators together and the denominators together.

Formula: `(a/b) × (c/d) = ac / bd`

Example (1/2 × 3/4): `(1 × 3) / (2 × 4) = 3/8`

3. Division

To divide, invert the second fraction (find its reciprocal) and then multiply.

Formula: `(a/b) ÷ (c/d) = (a/b) × (d/c) = ad / bc`

Example (1/2 ÷ 3/4): `(1/2) × (4/3) = 4/6`, which simplifies to `2/3`.