Fraction Calculator — Add, Subtract, Multiply and Divide with Steps
This fraction calculator performs the four basic operations — addition, subtraction, multiplication, and division — on any pair of fractions, including mixed numbers like 2 1/3. Every result comes with a step-by-step solution: finding the common denominator, converting mixed numbers to improper fractions, and simplifying the final answer to lowest terms using the greatest common divisor.
Fractions appear everywhere: recipes, measurements in inches, probability problems, and school math from elementary grades through algebra. Working through the steps by hand is the best way to learn, and the calculator's detailed solutions let you check each stage of your own work instead of just copying an answer. Results are shown both as a simplified fraction and as a decimal.
How it works
Addition: a/b + c/d = (a×d + c×b) / (b×d); Subtraction: a/b − c/d = (a×d − c×b) / (b×d); Multiplication: a/b × c/d = (a×c) / (b×d); Division: a/b ÷ c/d = (a×d) / (b×c). Simplify by dividing numerator and denominator by their GCD.
Use cases
- Checking homework on fraction operations with a full step-by-step solution
- Adding fractional measurements such as 3/4 inch + 5/8 inch in woodworking
- Scaling recipe quantities like 2/3 cup up or down
- Converting between mixed numbers, improper fractions, and decimals
- Simplifying fractions to lowest terms before comparing them
- Solving probability and ratio exercises that require exact fractional answers
Frequently asked questions
How do you add fractions with different denominators?
Rewrite both fractions over a common denominator, then add the numerators. The quickest common denominator is the product b×d, giving a/b + c/d = (a×d + c×b) / (b×d), though using the least common multiple keeps the numbers smaller. For example, 1/4 + 1/6 = (6 + 4)/24 = 10/24, which simplifies to 5/12. The calculator shows each of these steps in order.
How do you divide one fraction by another?
Multiply the first fraction by the reciprocal (the flipped version) of the second: a/b ÷ c/d = a/b × d/c = (a×d)/(b×c). For example, 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6. This works because dividing by a number is the same as multiplying by its inverse, and it turns every fraction division into a simple multiplication.
How do you simplify a fraction to lowest terms?
Divide the numerator and the denominator by their greatest common divisor (GCD). For 18/24, the GCD of 18 and 24 is 6, so the simplified fraction is 3/4. A fraction is in lowest terms when the GCD of its numerator and denominator is 1. The calculator computes the GCD with the Euclidean algorithm and simplifies every result automatically.
What is a mixed number and how is it converted to an improper fraction?
A mixed number combines a whole part and a fraction, such as 2 1/3. To convert it, multiply the whole part by the denominator and add the numerator: 2 1/3 = (2×3 + 1)/3 = 7/3. Improper fractions are easier to operate on, which is why the calculator converts mixed numbers first and then converts the result back at the end when appropriate.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator: 3/4 = 3 ÷ 4 = 0.75. Some fractions produce repeating decimals, such as 1/3 = 0.333…, which is why the exact fractional form is often preferred in math class. The calculator displays both representations so you can use whichever fits your problem.