Fraction Calculator
Result
Simplified Fraction
Decimal Result
Understanding Fraction Calculations
Fractions represent parts of a whole and are fundamental in mathematics. Our fraction calculator handles basic operations, simplification, and conversion to decimals with ease.
1. Basic Fraction Operations
The calculator performs four essential operations with fractions:
Addition (+)
Example: 1/2 + 1/4 = (1×4 + 1×2)/(2×4) = 6/8 = 3/4
Subtraction (-)
Example: 3/4 - 1/2 = (3×2 - 1×4)/(4×2) = 2/8 = 1/4
Multiplication (×)
Example: 2/3 × 3/5 = (2×3)/(3×5) = 6/15 = 2/5
Division (÷)
Example: 1/2 ÷ 3/4 = (1×4)/(2×3) = 4/6 = 2/3
2. Simplifying Fractions
A fraction is simplified when the numerator and denominator have no common divisors other than 1.
Example: Simplifying 8/12
GCD of 8 and 12 is 4
8 ÷ 4 = 2
12 ÷ 4 = 3
Simplified fraction: 2/3
3. Converting Fractions to Decimals
To convert a fraction to a decimal, simply divide the numerator by the denominator.
Example: Converting 3/4 to decimal
3 ÷ 4 = 0.75
Common Fraction Concepts
Proper vs. Improper Fractions
- Proper fractions: Numerator is less than denominator (e.g., 3/4)
- Improper fractions: Numerator is greater than or equal to denominator (e.g., 5/4)
- Mixed numbers: Combination of a whole number and a proper fraction (e.g., 1 1/4)
Equivalent Fractions
Fractions that represent the same value but have different numerators and denominators.
Example: 1/2 = 2/4 = 3/6 = 4/8
Reciprocal of a Fraction
The reciprocal is obtained by flipping the numerator and denominator.
Example: Reciprocal of 3/4 is 4/3
Practical Applications of Fractions
Cooking Measurements
Recipes often use fractions (e.g., 1/2 cup flour, 3/4 teaspoon salt). Being able to add or adjust these measurements is essential.
Construction and Woodworking
Measurements are frequently in fractions of an inch (e.g., cut a board to 5 3/8 inches).
Financial Calculations
Interest rates and financial ratios often involve fractions (e.g., 3/8% interest rate).
Frequently Asked Questions
Q: How do I add fractions with different denominators?
A: Find a common denominator (usually the least common multiple of the denominators), convert both fractions to equivalent fractions with that denominator, then add the numerators.
Q: What's the difference between simplifying and reducing a fraction?
A: They mean the same thing - making the fraction as simple as possible by dividing numerator and denominator by their greatest common divisor.
Q: How do I convert a mixed number to an improper fraction?
A: Multiply the whole number by the denominator, add the numerator, and place over the original denominator. Example: 2 1/3 = (2×3 + 1)/3 = 7/3
Q: Why can't the denominator be zero?
A: Division by zero is undefined in mathematics. A fraction represents division, so the denominator must never be zero.