Fraction Calculator
Perform any operation on fractions - add, subtract, multiply, divide, and simplify.
📊 What is a Fraction?
A fraction represents a part of a whole. It consists of two integers: the numerator (top number) which tells you how many parts you have, and the denominator (bottom number) which tells you how many equal parts the whole is divided into. For example, 3/4 means you have 3 out of 4 equal parts.
Fractions are one of the most fundamental concepts in mathematics and appear in everyday life constantly - from cooking recipes (1/2 cup of flour) to financial calculations (3/8 of a portfolio in equities) to engineering measurements. Understanding how to perform arithmetic operations on fractions is an essential skill.
A proper fraction has a numerator smaller than the denominator (e.g., 2/5). An improper fraction has a numerator equal to or greater than the denominator (e.g., 7/3). A mixed number combines a whole number with a proper fraction (e.g., 2 1/3). This calculator works with all types and automatically converts improper fractions to mixed numbers for readability.
Simplification is the process of reducing a fraction to its lowest terms by dividing both numerator and denominator by their greatest common divisor (GCD). For instance, 8/12 simplifies to 2/3 because GCD(8,12) = 4, and dividing both by 4 gives 2/3. A fully simplified fraction has no common factor between numerator and denominator other than 1 - it is in its lowest terms.
This calculator handles all four arithmetic operations - addition, subtraction, multiplication, and division - and automatically simplifies results to lowest terms, shows the mixed number form, and displays the decimal equivalent.
Fraction Formulas
📖 How to Use This Calculator
Steps to Calculate with Fractions
💡 Example Calculations
Example 1 - Adding Fractions
What is 2/3 + 3/8?
Example 2 - Dividing Fractions
What is 5/6 ÷ 2/3?
Example 3 - Multiplying Fractions
What is 7/8 × 4/5?
Frequently Asked Questions
🔗 Related Calculators
How do you add fractions with different denominators?
Find the least common denominator (LCD) of both fractions, convert each fraction to an equivalent fraction with that denominator, then add the numerators. For example, 1/3 + 1/4: the LCD is 12, so 1/3 becomes 4/12 and 1/4 becomes 3/12. Adding gives 7/12.
How do you multiply fractions?
Multiply the numerators together and the denominators together, then simplify. For example, 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2. You can also cross-simplify before multiplying to keep numbers smaller.
How do you divide fractions?
To divide by a fraction, multiply by its reciprocal (flip numerator and denominator). For example, 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8, which as a mixed number is 1 7/8.
What is a mixed number?
A mixed number combines a whole number and a proper fraction, such as 2 3/4. To convert an improper fraction to a mixed number, divide the numerator by the denominator - the quotient is the whole number and the remainder is the new numerator.
How do you simplify a fraction?
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that GCD. For example, 12/18: GCD(12,18) = 6, so 12/18 = 2/3. A fraction is fully simplified when the GCD of numerator and denominator is 1.
How do you convert an improper fraction to a mixed number?
To convert an improper fraction (where numerator is greater than denominator) to a mixed number: divide the numerator by the denominator. The quotient is the whole number part; the remainder becomes the new numerator over the original denominator. Example: 17/5. 17 divided by 5 = 3 remainder 2. So 17/5 = 3 and 2/5.
What is a proper fraction vs an improper fraction?
A proper fraction has a numerator smaller than the denominator (e.g. 3/4, value less than 1). An improper fraction has a numerator equal to or greater than the denominator (e.g. 7/4, value 1 or more). Improper fractions are mathematically valid and are often easier to work with in calculations. Mixed numbers (1 and 3/4) are just improper fractions written differently.
How do you subtract fractions with different denominators?
Find the least common denominator (LCD) of the two fractions. Convert each fraction to an equivalent fraction with the LCD. Then subtract the numerators and keep the denominator. Example: 3/4 minus 1/6. LCD = 12. Convert: 9/12 minus 2/12 = 7/12. Always simplify the result to lowest terms.