What Is a Fraction?
A fraction describes part of a whole or a ratio between two quantities. The top number is the numerator, and the bottom number is the denominator. The denominator shows how many equal parts make one whole, while the numerator shows how many of those parts are used.
Types of Fractions
- Proper fraction: the numerator is smaller than the denominator, such as 3/5.
- Improper fraction: the numerator is equal to or larger than the denominator, such as 9/4.
- Mixed number: a whole number and a fraction written together, such as 2 1/3.
- Equivalent fractions: different fractions that have the same value, such as 1/2 and 2/4.
- Unit fraction: a fraction with 1 as the numerator, such as 1/8.
How to Use the Fraction Calculator
Enter the whole number if needed, then fill in the numerator and denominator. Choose add, subtract, multiply, or divide, then select Calculate. The result is reduced automatically when possible.
How to Add Fractions
Fractions can be added directly when they share a denominator. If the denominators are different, convert both fractions to a common denominator first, add the numerators, and simplify the answer.
How to Subtract Fractions
Subtraction follows the same denominator rule as addition. Use a common denominator, subtract the second numerator from the first, and reduce the result to its lowest terms.
How to Multiply Fractions
Multiply the numerators together and multiply the denominators together. After that, simplify the fraction if the numerator and denominator have a common factor.
How to Divide Fractions
To divide by a fraction, multiply by its reciprocal. This means flipping the second fraction, then multiplying across the numerators and denominators.
How to Simplify Fractions
A fraction is simplified when the numerator and denominator no longer share a common factor greater than 1. Dividing both numbers by their greatest common divisor gives the fraction in lowest terms.
Worked Example
For 2/3 + 1/4, use 12 as a common denominator: 2/3 becomes 8/12 and 1/4 becomes 3/12. The sum is 11/12. For division, 3/5 divided by 2/7 becomes 3/5 x 7/2 = 21/10, or 2 1/10.
Limits
A denominator cannot be zero. Decimal inputs are handled by the separate decimal conversion tools; use exact fractions where possible when you need an exact rather than rounded result.