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Fraction Calculator (With Step-by-Step Solutions)
Fractions represent parts of a whole consisting of a numerator (top number) and a denominator (bottom number). Performing arithmetic operations on fractions requires finding least common denominators for addition and subtraction, or inverting fractions for division. This tool solves complex fraction equations with complete step-by-step simplification.
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How to Use This Tool Step-by-Step
- Select fraction operation (+, -, ×, or ÷).
- Input Numerator and Denominator for Fraction 1 and Fraction 2 (or mixed numbers).
- Click Calculate to get the reduced fraction, mixed number, and decimal equivalent.
📐 Fraction Operation Rules
• 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/b) × (d/c) = (a × d) / (b × c)
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Worked Fraction Division Example
Solve 3/4 ÷ 2/5:
1. Invert second fraction (reciprocal): 2/5 becomes 5/2
2. Multiply numerators and denominators: (3 × 5) / (4 × 2) = 15/8
3. Convert to mixed number: 15 ÷ 8 = 1 with remainder 7 -> 1 7/8.
📊 Reference Benchmarks & Classification Data
| Fraction Type | Definition | Example | Decimal Equivalent |
|---|---|---|---|
| Proper Fraction | Numerator < Denominator | 3/4 | 0.75 |
| Improper Fraction | Numerator >= Denominator | 7/4 | 1.75 |
| Mixed Number | Whole number + proper fraction | 1 3/4 | 1.75 |
| Unit Fraction | Numerator is always 1 | 1/5 | 0.20 |
❓ Frequently Asked Questions (FAQ)
How do you find the Least Common Denominator (LCD)?
List the multiples of each denominator until you find the smallest multiple shared by both numbers. For example, for 4 and 6, multiples of 4 are 4, 8, 12… and multiples of 6 are 6, 12… The LCD is 12.
Why do we flip the second fraction when dividing?
Dividing by a fraction is the inverse operation of multiplication. Multiplying by the reciprocal distributes the divisor proportionally across the dividend.