Fraction Calculator – Add, Subtract and Simplify Fractions
Free online fraction calculator. Easily add, subtract, multiply, and divide fractions.
Fractions are one of the first abstract mathematical concepts that students encounter, and they remain relevant throughout advanced mathematics, science, and daily life. Whether you are scaling a recipe, dividing a bill, or working through algebraic equations, fractions appear everywhere. The fraction calculator performs addition, subtraction, multiplication, and division of fractions, while also simplifying results to their lowest terms. It handles mixed numbers, improper fractions, and complex expressions, providing step-by-step solutions that reinforce understanding rather than simply delivering an answer.
Key Takeaway
To add or subtract fractions, they must share a common denominator. Multiply the numerator and denominator of each fraction by whatever value is needed to achieve this common base. To multiply fractions, multiply numerators together and denominators together. To divide, multiply by the reciprocal of the divisor.
1. Adding and Subtracting Fractions
The most common source of errors in fraction arithmetic is addition and subtraction, because these operations require a common denominator. The denominator represents the size of each part, and you cannot combine parts of different sizes without first converting them to a uniform scale. To add 1/3 and 1/4, you must find the least common denominator (LCD), which is 12. Convert 1/3 to 4/12 and 1/4 to 3/12, then add the numerators: 4/12 + 3/12 = 7/12.
Subtraction follows the same principle. To subtract 1/4 from 2/3, convert to a common denominator of 12: 8/12 - 3/12 = 5/12. The calculator automatically finds the least common denominator and performs the conversion, showing each step so you can follow the logic.
2. Multiplying and Dividing Fractions
Multiplication is the simplest fraction operation: multiply the numerators together and the denominators together. For example, 2/3 x 4/5 = 8/15. No common denominator is needed. Division is performed by multiplying by the reciprocal of the divisor. To divide 2/3 by 4/5, flip 4/5 to get 5/4, then multiply: 2/3 x 5/4 = 10/12, which simplifies to 5/6.
Mixed numbers (combinations of whole numbers and fractions, like 2 3/4) must be converted to improper fractions before performing operations. The calculator handles this conversion automatically, performing 2 3/4 = 11/4 before proceeding with any calculation.
3. Simplifying Fractions
A fraction is in simplest form when the numerator and denominator share no common factors other than 1. To simplify, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. The fraction 12/18 simplifies to 2/3 because the GCD of 12 and 18 is 6. The calculator uses the Euclidean algorithm to find the GCD efficiently, even for large numbers. Simplification is not just aesthetic; it makes fractions easier to compare, combine, and use in further calculations. The fraction calculator presents all results in their simplest form by default.