Fraction Calculator

Add, subtract, multiply, and divide fractions with automatic simplification. Get step-by-step solutions, decimal equivalents, and mixed number conversions.

Fraction Calculator

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Quick Examples

Fraction Operations

Addition/Subtraction: Find common denominator, then add/subtract numerators
Multiplication: Multiply numerators together and denominators together
Division: Multiply by the reciprocal of the second fraction
Simplification: Divide numerator and denominator by their GCD

How to Use the Fraction Calculator

  1. Select Operation: Choose addition (+), subtraction (-), multiplication (×), or division (÷)
  2. Enter First Fraction: Input the numerator and denominator of the first fraction
  3. Enter Second Fraction: Input the numerator and denominator of the second fraction
  4. View Results: See the simplified answer, mixed number form, and decimal equivalent
  5. Step-by-Step Solution: Review the detailed solution process for learning
  6. Quick Examples: Click on example problems to see common fraction calculations

Examples and Use Cases

Addition and Subtraction

1/2 + 1/3 = 5/6
Find common denominator (6), then add
3/4 - 1/8 = 5/8
Common denominator (8), then subtract
2/5 + 1/10 = 1/2
Simplifies to 1/2

Multiplication and Division

2/3 × 3/4 = 1/2
Multiply across, then simplify
5/6 ÷ 2/3 = 5/4 = 1¼
Multiply by reciprocal, convert to mixed
3/8 × 4/9 = 1/6
Simplify before or after multiplication

Understanding the Results

Result Formats

Simplified Fraction

Reduced to lowest terms by dividing numerator and denominator by their greatest common divisor (GCD).

Mixed Number

Improper fractions converted to whole number plus proper fraction (e.g., 5/4 = 1¼).

Decimal Equivalent

Fraction converted to decimal form for easy comparison and practical use.

Operation Rules

Addition/Subtraction

Find common denominator (LCM), convert fractions, then add/subtract numerators.

Multiplication

Multiply numerators together and denominators together: (a/b) × (c/d) = (a×c)/(b×d).

Division

Multiply by the reciprocal: (a/b) ÷ (c/d) = (a/b) × (d/c).

Frequently Asked Questions

How do I add fractions with different denominators?

Find the least common multiple (LCM) of the denominators, convert both fractions to equivalent fractions with that common denominator, then add the numerators.

What is the difference between proper and improper fractions?

Proper fractions have numerators smaller than denominators (like 3/4). Improper fractions have numerators larger than or equal to denominators (like 5/4), and can be converted to mixed numbers.

Why do I need to find a common denominator?

For addition and subtraction, fractions must have the same denominator to combine them meaningfully. It's like adding different units - you need a common unit first.

How does the calculator simplify fractions?

The calculator finds the greatest common divisor (GCD) of the numerator and denominator, then divides both by this number to get the simplest form.

Can I use negative numbers?

Yes! You can enter negative numerators or denominators. The calculator will handle the signs correctly and show the proper simplified result.

What if my answer is a whole number?

If the result simplifies to a whole number (denominator of 1), it will be displayed as just the whole number. Mixed numbers are shown when applicable.

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