Fraction Calculator
Add, subtract, multiply, and divide fractions. Simplify fractions, convert between fractions and decimals, and work with mixed numbers. Perfect for students and professionals.
Operation
Enter numerator and denominator (e.g., 3/4 for three-fourths).
Enter numerator and denominator for the second fraction.
Enter fractions above to perform calculations
Table of Contents
What are Fractions?
A fraction represents a part of a whole. It consists of two numbers separated by a slash:
numerator / denominator
The numerator (top number) represents how many parts you have, and the denominator (bottom number) represents how many equal parts the whole is divided into.
Example: 3/4 means you have 3 parts out of 4 equal parts.
Fractions are essential in mathematics and appear in many real-world situations:
- Cooking recipes (1/2 cup, 3/4 teaspoon)
- Measurements (1/4 inch, 2/3 meter)
- Probability and statistics
- Financial calculations (interest rates, ratios)
- Engineering and construction
How it Works
Our fraction calculator performs accurate fraction arithmetic using mathematical algorithms:
- Parsing: Converts input values into fraction format
- Calculation: Performs the selected operation (add, subtract, multiply, divide)
- Simplification: Finds the greatest common divisor (GCD) to simplify the result
- Conversion: Converts to decimal and mixed number formats
All calculations use exact arithmetic, ensuring precise results without rounding errors. The calculator automatically simplifies fractions to their lowest terms.
Fraction Operations
Addition
To add fractions, find a common denominator, then add the numerators:
a/b + c/d = (ad + bc) / bd
Example: 1/4 + 1/3 = (1×3 + 1×4) / (4×3) = 7/12
Subtraction
To subtract fractions, find a common denominator, then subtract the numerators:
a/b - c/d = (ad - bc) / bd
Example: 1/2 - 1/3 = (1×3 - 1×2) / (2×3) = 1/6
Multiplication
To multiply fractions, multiply numerators and denominators:
a/b × c/d = (a×c) / (b×d)
Example: 2/3 × 3/4 = (2×3) / (3×4) = 6/12 = 1/2
Division
To divide fractions, multiply by the reciprocal:
a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)
Example: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2
Simplification
To simplify a fraction, divide both numerator and denominator by their greatest common divisor (GCD):
Example: 8/12 = 2/3 (both divided by GCD of 4)
Examples
Example 1: Adding Fractions
Problem: 1/3 + 1/4
Solution: Find common denominator (12), then add: (4 + 3) / 12 = 7/12
Example 2: Multiplying Fractions
Problem: 2/5 × 3/7
Solution: Multiply numerators and denominators: (2×3) / (5×7) = 6/35
Example 3: Simplifying Fractions
Problem: Simplify 18/24
Solution: GCD of 18 and 24 is 6, so: 18/24 = 3/4
Example 4: Converting Decimal to Fraction
Problem: Convert 0.75 to a fraction
Solution: 0.75 = 75/100 = 3/4 (simplified)
Common Use Cases
- Education: Students learning fraction arithmetic and simplifying fractions
- Cooking: Adjusting recipe measurements and scaling ingredients
- Construction: Calculating measurements and material quantities
- Finance: Calculating interest rates, ratios, and percentages
- Engineering: Working with precise measurements and ratios
- Statistics: Calculating probabilities and proportions
- Everyday Math: Solving fraction problems in daily life
Frequently Asked Questions
To add fractions with different denominators, first find a common denominator (the least common multiple of the denominators), then convert both fractions to have that denominator, and finally add the numerators. The calculator does this automatically.
A simplified fraction (also called a fraction in lowest terms) is a fraction where the numerator and denominator have no common factors other than 1. For example, 8/12 simplifies to 2/3 because both 8 and 12 can be divided by 4.
Yes, the calculator supports negative fractions. Simply enter a negative number for the numerator. For example, -3/4 represents negative three-fourths.
A mixed number is a combination of a whole number and a fraction, such as 2 1/3 (two and one-third). The calculator automatically converts improper fractions (where the numerator is greater than the denominator) to mixed numbers when appropriate.
The calculator uses exact arithmetic, so all calculations are mathematically precise with no rounding errors. Fractions are always simplified to their lowest terms, and decimal conversions are exact.
Yes! Use the "To Fraction" operation and enter a decimal number. The calculator will convert it to the simplest fraction representation. For example, 0.75 converts to 3/4.