🔢 Fraction Calculator

Fraction Calculator

Add, subtract, multiply, and divide fractions instantly. Simplify results, convert to mixed numbers, and see step-by-step solutions. Perfect for students, teachers, and everyday math.

4
Operations
✓
Instant Simplify
↔️
Mixed Numbers
📊
Decimal Conversion

🔢 Fraction Calculator

+ Add
- Subtract
× Multiply
÷ Divide

Result

12
= 0.5

Step-by-Step Solution

Step 1: Find common denominator
Step 2: Perform operation
Step 3: Simplify result

📊 Additional Results

Simplified

1/2

Decimal

0.5

Percentage

50%

Reciprocal

2/1

Understanding Fractions: A Complete Guide

A fraction represents a part of a whole. It is written as a/b, where a is the numerator (how many parts) and b is the denominator (total number of equal parts). Fractions are everywhere: cooking (3/4 cup flour), shopping (1/2 off sale), measurements (1/2 inch), and percentages (3/4 = 75%).

Types of fractions:

  • Proper fraction: Numerator < Denominator (e.g., 1/2, 3/4)
  • Improper fraction: Numerator ≥ Denominator (e.g., 5/3, 7/4)
  • Mixed number: Whole number + proper fraction (e.g., 1⅓, 2½)
  • Equivalent fractions: Different numbers representing same value (e.g., 1/2 = 2/4 = 4/8)

This calculator handles all fraction operations: addition, subtraction, multiplication, division, and simplification. It also converts between improper fractions and mixed numbers automatically.

📘 How to Use This Fraction Calculator

  1. Enter the numerator and denominator for Fraction 1
  2. Select the operation (+, -, ×, ÷)
  3. Enter the numerator and denominator for Fraction 2
  4. Click "Calculate" to see the result
  5. View the simplified fraction, mixed number, and decimal conversion
  6. Review the step-by-step solution to understand the math

💡 Pro Tip:

Denominators cannot be zero. The calculator automatically simplifies fractions to lowest terms and converts improper fractions to mixed numbers.

📊 Real-World Example: Recipe Scaling

Problem: A cookie recipe calls for 2/3 cup sugar. You want to make half the recipe. How much sugar do you need?

Calculation: 2/3 × 1/2 = ?

Multiply numerators: 2 × 1 = 2

Multiply denominators: 3 × 2 = 6

Result: 2/6 = 1/3 cup sugar

Using this calculator, you instantly get the answer: 1/3 cup. No more guessing!

📊 How to Add, Subtract, Multiply & Divide Fractions

➕ Addition

1. Find common denominator
2. Add numerators
3. Simplify

Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6

➖ Subtraction

1. Find common denominator
2. Subtract numerators
3. Simplify

Example: 3/4 - 1/2 = 3/4 - 2/4 = 1/4

✖ Multiplication

1. Multiply numerators
2. Multiply denominators
3. Simplify

Example: 2/3 × 3/4 = 6/12 = 1/2

➗ Division

1. Multiply by reciprocal
2. Multiply numerators/denominators
3. Simplify

Example: 1/2 ÷ 2/3 = 1/2 × 3/2 = 3/4

🔄 Simplifying Fractions: Finding the GCD

To simplify a fraction, divide both numerator and denominator by their Greatest Common Divisor (GCD). Example: Simplify 8/12 → GCD of 8 and 12 is 4 → 8÷4 = 2, 12÷4 = 3 → 2/3. Our calculator automatically simplifies all results to lowest terms!

6/8 → 3/4
9/12 → 3/4
10/25 → 2/5
14/21 → 2/3

🔄 Converting Between Mixed Numbers & Improper Fractions

Mixed → Improper

(Whole × Denominator + Numerator) / Denominator

Example: 2⅓ = (2×3+1)/3 = 7/3

Improper → Mixed

Divide numerator by denominator → whole + remainder/denominator

Example: 7/3 = 2 remainder 1 → 2⅓

⚠️ 5 Common Fraction Mistakes to Avoid

  • Adding denominators — Never add denominators! Only add numerators after finding common denominator.
  • Forgetting to flip when dividing — Division = multiply by reciprocal. Forgetting this gives wrong answer.
  • Not simplifying completely — Always reduce fractions to lowest terms.
  • Confusing mixed numbers with multiplication — 2⅓ means 2 + 1/3, NOT 2 × 1/3.
  • Zero denominator — Denominator can never be zero (division by zero is undefined).

💡 Verification Tip: Always check if your answer makes sense. If you multiply two proper fractions, the result should be smaller than both!

❓ Frequently Asked Questions (Fraction Calculator)

1. 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.

2. How do I multiply fractions?

Multiply the numerators together and denominators together. Then simplify. Example: 2/3 × 3/4 = 6/12 = 1/2.

3. How do I divide fractions?

Multiply the first fraction by the reciprocal of the second. Example: 1/2 ÷ 2/3 = 1/2 × 3/2 = 3/4.

4. What is the reciprocal of a fraction?

Swap numerator and denominator. Reciprocal of 2/3 is 3/2. Reciprocal of 5 is 1/5.

5. How do I convert a fraction to a decimal?

Divide numerator by denominator. Example: 3/4 = 3 ÷ 4 = 0.75.

6. How do I convert a decimal to a fraction?

Write decimal over 1, multiply numerator and denominator by 10 for each decimal place, then simplify. Example: 0.75 = 75/100 = 3/4.

7. What is the least common denominator (LCD)?

The smallest number that both denominators divide into evenly. For 1/2 and 1/3, LCD = 6.

8. Is my data stored or shared?

Never. All calculations happen locally in your browser. ToolHub does not track, store, or transmit any data — complete privacy guaranteed.

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⚠️ Disclaimer: This fraction calculator provides accurate mathematical results for educational purposes. Always verify critical calculations independently.

🔒 100% private — no data storage. ToolHub does not collect or share your calculations.