Add, subtract, multiply, and divide fractions with step-by-step work. Supports mixed numbers, simplification, and instant decimal & percentage conversion.
Our fraction calculator is a powerful yet easy-to-use online tool designed to help students, teachers, engineers, and anyone working with fractions perform accurate arithmetic operations. Whether you need to add fractions, subtract fractions, multiply fractions, or divide fractions, this calculator handles it all with detailed step-by-step explanations.
Fractions are everywhere — from cooking recipes and construction measurements to financial calculations and academic problems. Working with fractions manually can be time-consuming and error-prone, especially when dealing with mixed numbers, unlike denominators, and complex operations. Our fraction problem solver eliminates guesswork by showing you exactly how each result is derived.
This free online fraction simplifier supports proper fractions, improper fractions, and mixed numbers (whole number + fraction). It automatically converts mixed numbers to improper fractions before performing the operation, then simplifies the result using the greatest common divisor (GCD). The output includes both improper and mixed number formats, plus the decimal equivalent and percentage.
Built entirely with vanilla JavaScript, this fraction math tool runs completely in your browser — no data is sent to any server, ensuring your privacy and delivering instant results. It's the perfect fraction homework helper for students learning fraction arithmetic and a reliable fraction converter for professionals who need quick, accurate calculations.
Fractions are one of the most fundamental concepts in mathematics, appearing in nearly every branch of the subject from basic arithmetic to advanced calculus. At its core, a fraction represents a division of a whole into equal parts. The numerator (top number) tells you how many parts you have, while the denominator (bottom number) tells you how many equal parts make up the whole. This elegant notation allows us to express quantities that fall between whole numbers with precision.
There are several types of fractions you will encounter. A proper fraction has a numerator smaller than the denominator, like 3/5 — its value is less than 1. An improper fraction has a numerator greater than or equal to the denominator, like 7/4 — its value is 1 or greater. A mixed number combines a whole number with a proper fraction, such as 1 3/4 (which is the same as 7/4). Understanding these forms and how to convert between them is essential for fraction arithmetic.
Adding and subtracting fractions requires a common denominator. This is because fractions represent parts of different-sized wholes, and you cannot combine them directly. The process involves finding the least common multiple (LCM) of the denominators, converting each fraction to an equivalent fraction with that denominator, then adding or subtracting the numerators. For example, to add 1/3 and 1/4, the LCM of 3 and 4 is 12, so 1/3 = 4/12 and 1/4 = 3/12, giving 7/12.
Multiplying fractions is simpler — just multiply straight across: numerators together and denominators together. This works because multiplying fractions is essentially finding a fraction of a fraction. For example, 1/2 of 3/4 is 1/2 × 3/4 = 3/8. Dividing fractions uses the reciprocal: to divide by a fraction, multiply by its reciprocal. This is often taught as "Keep, Change, Flip" — keep the first fraction, change division to multiplication, and flip the second fraction.
Simplifying fractions (reducing to lowest terms) is an important final step in any fraction calculation. A fraction is simplified when the numerator and denominator have no common factors other than 1. This is achieved by dividing both by their greatest common divisor (GCD), which can be found using the Euclidean algorithm. For instance, 12/18 simplifies to 2/3 because the GCD of 12 and 18 is 6.
Fractions are deeply connected to decimals and percentages. Any fraction can be converted to a decimal by dividing the numerator by the denominator. For example, 3/8 = 0.375. To convert a decimal to a percentage, multiply by 100: 0.375 = 37.5%. This three-way equivalence — fractions, decimals, and percentages — gives you flexibility in how you express and think about proportional relationships.
In the real world, fractions are everywhere. Recipes call for 2/3 cup of sugar. Carpenters measure 1/4 inch tolerances. Financial analysts calculate 3/8 of a percentage point in interest rates. Athletes track their statistics as fractions of games or attempts. Mastering fraction arithmetic is not just an academic exercise — it is a practical life skill that makes you more numerically literate and confident in everyday decision-making.
Our free fraction calculator is designed to support this learning journey. By showing every step of the calculation — from finding common denominators to performing the operation and simplifying the result — it serves as both a computation tool and a teaching aid. Whether you are a student checking your homework, a teacher preparing lesson materials, or a professional needing quick fraction arithmetic, this fraction solver online provides accurate results and clear explanations every time.