🧮 Fraction Calculator
Perform operations with fractions step-by-step. Visual representations help you understand the math behind the solution.
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Simplify Fraction
Fraction to Decimal
Understanding Fractions
A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number).
Types of Fractions
| Type | Description | Example |
|---|---|---|
| Proper Fraction | Numerator < Denominator | 3/4 |
| Improper Fraction | Numerator ≥ Denominator | 7/4 |
| Mixed Number | Whole number + fraction | 1 3/4 |
| Equivalent Fractions | Same value, different form | 1/2 = 2/4 |
Fraction Operations Rules
- Find a common denominator (LCM of denominators)
- Convert each fraction to equivalent fractions with the common denominator
- Add or subtract the numerators
- Keep the denominator the same
- Simplify if possible
Formula: a/b ± c/d = (ad ± bc) / bd
- Multiply the numerators together
- Multiply the denominators together
- Simplify the result
Formula: a/b × c/d = (a × c) / (b × d)
- Flip the second fraction (find its reciprocal)
- Multiply the first fraction by the reciprocal
- Simplify the result
Formula: a/b ÷ c/d = a/b × d/c = (a × d) / (b × c)
Worked Examples
Example 1: Adding Fractions with Different Denominators
Problem: 1/4 + 1/6 = ?
Solution:
- Find common denominator: LCM of 4 and 6 is 12
- Convert: 1/4 = 3/12 and 1/6 = 2/12
- Add: 3/12 + 2/12 = 5/12
Answer: 5/12
Example 2: Multiplying Mixed Numbers
Problem: 2 1/2 × 1 1/3 = ?
Solution:
- Convert to improper fractions: 2 1/2 = 5/2 and 1 1/3 = 4/3
- Multiply: (5 × 4) / (2 × 3) = 20/6
- Simplify: 20/6 = 10/3 = 3 1/3
Answer: 3 1/3
Example 3: Dividing by a Fraction
Problem: 3/4 ÷ 2/5 = ?
Solution:
- Flip the second fraction: 2/5 becomes 5/2
- Multiply: 3/4 × 5/2 = (3 × 5) / (4 × 2) = 15/8
- Convert: 15/8 = 1 7/8
Answer: 1 7/8 or 1.875
Common Fraction to Decimal Conversions
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.1 | 10% |
Last Updated: February 17, 2026
Disclaimer: This calculator provides mathematical calculations for educational purposes. Double-check important calculations.
Disclaimer: This calculator provides mathematical calculations for educational purposes. Double-check important calculations.