Fraction Calculator
Fraction Calculator
Enter Fractions
Result
Quick Reference
Related Tools
What is a Fraction Calculator?
A fraction calculator is an essential mathematical tool that helps you perform arithmetic operations with fractions quickly and accurately. Our free online fraction calculator allows you to add, subtract, multiply, and divide fractions with different denominators, automatically simplifying results to their lowest terms.
Fractions can be challenging to work with manually, especially when dealing with different denominators. This calculator handles all the complexity for you, finding common denominators, performing the calculations, and reducing the result to its simplest form.
Whether you're a student learning fractions, a professional working with measurements, or anyone who needs to work with fractional values, this tool makes fraction arithmetic simple and error-free.
How Fraction Operations Work
Adding & Subtracting Fractions
To add or subtract fractions, you need a common denominator:
a/b + c/d = (ad + bc) / bd
Example: 1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6
Multiplying Fractions
Multiply numerators together and denominators together:
a/b × c/d = ac / bd
Example: 2/3 × 3/4 = 6/12 = 1/2
Dividing Fractions
Multiply by the reciprocal of the second fraction:
a/b ÷ c/d = a/b × d/c = ad / bc
Example: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2
Simplifying Fractions
Divide both numerator and denominator by their Greatest Common Divisor (GCD):
Example: 12/18 → GCD is 6 → 12÷6 / 18÷6 = 2/3
Calculator Features
Fraction Arithmetic
- Add fractions with different denominators
- Subtract fractions accurately
- Multiply fractions together
- Divide fractions (multiply by reciprocal)
- Automatic simplification to lowest terms
Additional Features
- Simplify any fraction instantly
- Convert decimals to fractions
- Convert fractions to decimals
- Display results as mixed numbers
- Copy results to clipboard
Frequently Asked Questions
How do I add fractions with different denominators?
Our calculator automatically finds the common denominator for you. Simply enter your fractions, select the addition operation, and click Calculate. The calculator will find the least common multiple of the denominators, convert both fractions, add them, and simplify the result.
What does it mean to simplify a fraction?
Simplifying a fraction means reducing it to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD). For example, 6/8 simplified becomes 3/4 because both 6 and 8 can be divided by 2. Our calculator always shows results in their simplest form.
Can I use negative fractions?
Yes, you can enter negative numbers in either the numerator or denominator. The calculator handles negative fractions correctly and will display the result with the appropriate sign.
What is a mixed number?
A mixed number combines a whole number with a proper fraction. For example, 7/4 can be written as the mixed number 1 3/4 (one and three-fourths). Our calculator shows both forms when applicable, making it easier to understand the result in context.
Common Uses for Fraction Calculations
Cooking & Recipes
- Scaling recipes up or down
- Adding ingredient measurements
- Converting between measurement units
Construction & DIY
- Measuring lumber and materials
- Calculating dimensions
- Working with inch fractions
Education
- Learning fraction arithmetic
- Checking homework answers
- Understanding fraction concepts
Music
- Working with time signatures
- Calculating note durations
- Understanding rhythm fractions