# Fraction Calculator > Free fraction calculator to add, subtract, multiply, and divide fractions. Simplify fractions, convert to decimals, and solve fraction problems step by step. **URL:** https://calculators.im/fraction-calculator **Category:** math **Last updated:** 2026-07-03 Add, subtract, multiply, and divide fractions with ease. Simplify fractions, convert to decimals or percentages, and see step-by-step solutions. Our free fraction calculator helps you solve any fraction problem with detailed step-by-step explanations. Whether you need to add fractions with different denominators, convert mixed numbers, or simplify complex fractions, this calculator shows you exactly how it's done. ## Formula ``` a/b ± c/d = (ad ± bc) / bd ``` **Variables:** - **a, c** — Numerators of the fractions - **b, d** — Denominators of the fractions - **±** — Addition or subtraction operation To add or subtract fractions, find a common denominator, adjust numerators accordingly, then combine. Multiply by multiplying numerators and denominators. Divide by multiplying by the reciprocal. ## Worked Example ### Example: Add 1/2 + 2/3 1/2 + 2/3 = 3/6 + 4/6 = 7/6 = 1 1/6 ≈ 1.167 ## How to Use the Fractions Calculator 1. **Choose Operation** — Select arithmetic, simplify, convert, or compare fractions. 2. **Enter Fractions** — Input numerators and denominators. Add whole numbers for mixed fractions. 3. **Calculate** — Click calculate to see results with step-by-step explanation. 4. **View Results** — See simplified fraction, decimal, percentage, and detailed steps. ## Pro Tips - Find the LCD (Least Common Denominator) for adding/subtracting - Multiply straight across: (a/b) × (c/d) = ac/bd - Divide by flipping the second fraction and multiplying - Always simplify your final answer by finding the GCD - Convert mixed numbers to improper fractions first - To convert to decimal, divide numerator by denominator ## Frequently Asked Questions ### How do I add fractions with different denominators? Find the Least Common Denominator (LCD) of both fractions, convert each fraction to have the LCD as its denominator, then add the numerators. For example: 1/2 + 1/3 → 3/6 + 2/6 = 5/6. The LCD of 2 and 3 is 6. ### How do I multiply fractions? Multiply the numerators together and multiply the denominators together. For example: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2. You can simplify before or after multiplying. ### How do I divide fractions? Flip the second fraction (take its reciprocal) and multiply. For example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6. Remember: Keep, Change, Flip. ### How do I simplify fractions? Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by it. For example: 12/18 → GCD is 6 → 12÷6/18÷6 = 2/3. ### How do I convert a fraction to a decimal? Divide the numerator by the denominator. For example: 3/4 = 3 ÷ 4 = 0.75. Some fractions create repeating decimals, like 1/3 = 0.333... ### How do I convert a decimal to a fraction? Write the decimal over a power of 10 based on decimal places, then simplify. For example: 0.75 = 75/100 = 3/4. For repeating decimals, use algebraic methods. ### What's the difference between mixed numbers and improper fractions? A mixed number has a whole part and fraction (2 1/3). An improper fraction has a numerator larger than the denominator (7/3). To convert: 2 1/3 = (2×3+1)/3 = 7/3. ### How do I convert a fraction to a percentage? Divide the numerator by the denominator, then multiply by 100. For example: 3/4 = 0.75 × 100 = 75%. Or use: (numerator/denominator) × 100%. ### How do I work with mixed numbers? Convert mixed numbers to improper fractions first, perform the operation, then convert back if needed. Example: 1 1/2 + 2 1/3 = 3/2 + 7/3 = 9/6 + 14/6 = 23/6 = 3 5/6. ### What is the LCD and how do I find it? LCD (Least Common Denominator) is the smallest number divisible by all denominators. Find it by listing multiples or using LCM. For 4 and 6: multiples of 4 (4,8,12...), multiples of 6 (6,12...) → LCD = 12. ## Deep Dive Calculate fractions with ease using our free online fraction calculator. Add, subtract, multiply, divide fractions, simplify, and convert between fractions, decimals, and percentages with step-by-step solutions. ### Adding and Subtracting Fractions To add or subtract fractions: - find the Least Common Denominator (LCD) - convert fractions to equivalent fractions with the LCD - then add or subtract numerators Our calculator handles this automatically and shows each step. ### Multiplying and Dividing Fractions **Multiply fractions** by multiplying numerators together and denominators together. **Divide** by flipping the second fraction and multiplying. Remember: **Keep, Change, Flip** for division. ### Simplifying Fractions **Simplify fractions** by finding the Greatest Common Divisor (GCD) of numerator and denominator, then dividing both by it. A fraction is fully simplified when **GCD equals 1**. ### Converting Fractions Our converter handles all these transformations: - Convert fractions to decimals by dividing. - Convert decimals to fractions by placing over powers of 10. - Learn how to calculate percentages by multiplying a fraction by 100. ### Mixed Numbers and Improper Fractions **Mixed numbers** combine whole numbers with fractions (2 1/2). **Improper fractions** have numerators larger than denominators (5/2). Convert between them easily with our calculator. ### Step-by-Step Solutions Every calculation shows **detailed steps** so you can learn the process. Perfect for students learning fraction arithmetic or anyone who wants to understand the math behind the answer. ### What Is a Fraction and How Does It Work? **A fraction** represents a part of a whole, written as two numbers separated by a bar: the **numerator** on top and the **denominator** on the bottom. The denominator tells you how many equal parts the whole is divided into, while the numerator tells you how many of those parts you are counting. For example, in 3/4 the whole is split into 4 equal parts and you are taking 3 of them. According to Encyclopaedia Britannica, fractions extend the natural numbers so that quantities between whole numbers can be expressed exactly. Any fraction with a denominator that is not zero represents a **rational number**, and equal fractions like 2/4 and 1/2 name the same value. ### How to Find the LCD and GCD for Fraction Math The **Greatest Common Divisor (GCD)** is the largest number that divides two integers evenly, and the **Least Common Denominator (LCD)** is the smallest number that both denominators divide into. To simplify 12/18, find GCD(12, 18) = 6, then divide to get 2/3. To add 1/4 + 1/6, find the LCD, which equals the least common multiple of 4 and 6: since LCM(4, 6) = 4 × 6 / GCD(4, 6) = 24 / 2 = 12, the LCD is 12. As Wolfram MathWorld explains, the GCD and LCM are linked by the identity a × b = GCD(a, b) × LCM(a, b), which our calculator uses to keep denominators as small as possible. ### How to Compare Two Fractions Correctly To compare two fractions quickly, **cross-multiply** — the same step you use to solve a proportion: multiply the numerator of each fraction by the denominator of the other, then compare the products. For 2/3 versus 3/4, multiply 2 × 4 = 8 and 3 × 3 = 9; because 8 is less than 9, 2/3 is smaller than 3/4. This works because both products share the same effective denominator, a technique Khan Academy teaches for ordering fractions. You can also convert each fraction to a decimal and compare: 2/3 ≈ 0.667 and 3/4 = 0.75, confirming 3/4 is larger. Our comparison mode shows the cross-multiplication and the decimal check side by side. ### Real-World Uses of Fraction Calculations Fractions appear constantly in daily life, which makes fast, accurate fraction math genuinely useful. - **Cooking** recipes call for 3/4 cup of flour or half of a 2/3-cup measure, so scaling a recipe up or down requires multiplying fractions. - **Woodworking and construction** rely on inch fractions like 5/8 and 7/16, where adding board thicknesses means finding a common denominator. - **Finance** uses fractions and their decimal equivalents for interest rates and stock quotes, and probability expresses chances as fractions such as 1/6 for rolling a specific number on a die. Encyclopaedia Britannica notes that fractional notation predates decimals by millennia, and it still gives exact answers where rounding a decimal would introduce error. ### Common Mistakes When Calculating Fractions - The most frequent fraction error is adding numerators and denominators directly, such as writing 1/2 + 1/3 = 2/5, which is wrong; you must first find the LCD, giving 3/6 + 2/6 = 5/6. - Another common slip is forgetting to flip only the second fraction when dividing, since a ÷ b uses the reciprocal of b, not of a. - Students also skip simplifying the final answer, leaving 6/12 instead of 1/2, or misconvert mixed numbers by adding instead of using (whole × denominator + numerator). Khan Academy stresses checking that a final fraction is fully reduced, meaning the GCD of numerator and denominator equals 1. Our step-by-step output flags each of these stages so mistakes are easy to catch. ## Related Calculators - [percentage-calculator](https://calculators.im/percentage-calculator) - [decimal-calculator](https://calculators.im/decimal-calculator) - [ratio-calculator](https://calculators.im/ratio-calculator) ## Authoritative Sources - [Wolfram MathWorld — Fraction](https://mathworld.wolfram.com/Fraction.html) — Formal definition of fractions and rational numbers - [Wolfram MathWorld — Greatest Common Divisor](https://mathworld.wolfram.com/GreatestCommonDivisor.html) — GCD definition and its relationship to the LCM - [Khan Academy — Fraction Arithmetic](https://www.khanacademy.org/math/arithmetic/fraction-arithmetic) — Step-by-step lessons on adding, comparing, and simplifying fractions - [Encyclopaedia Britannica — Fraction (mathematics)](https://www.britannica.com/science/fraction-mathematics) — History and conceptual overview of fractions - [NIST Digital Library of Mathematical Functions](https://dlmf.nist.gov/) — Authoritative reference on mathematical functions and rational quantities --- *Source: https://calculators.im/fraction-calculator — calculators.im, 299+ free online calculators.*