Fraction Calculator

Adding fractions with different denominators requires finding a common denominator first. The most efficient approach is to compute the Least Common Denominator (LCD), which is the smallest number that both denominators divide into evenly. To find the LCD, you can compute the Least Common Multiple (LCM) of the two denominators. Once you have the LCD, multiply each fraction's numerator and denominator by the factor needed to reach the LCD. With matching denominators, add the numerators together and keep the denominator. Finally, simplify the resulting fraction by dividing both the numerator and denominator by their Greatest Common Divisor (GCD). For example, to add 1/4 and 2/3, the LCD is 12. Rewrite as 3/12 and 8/12, then add to get 11/12. This calculator automates every step and shows the full working so you can follow along and learn the process.

The Greatest Common Divisor, also known as the Greatest Common Factor (GCF) or Highest Common Factor (HCF), is the largest positive integer that divides both numbers without leaving a remainder. When simplifying a fraction, you divide the numerator and the denominator by their GCD to reduce the fraction to its lowest terms. For example, the fraction 24/36 has a GCD of 12, so dividing both parts by 12 gives 2/3. The Euclidean algorithm is the most efficient way to compute the GCD: repeatedly replace the larger number with the remainder of dividing the larger by the smaller until the remainder is zero. This calculator uses the Euclidean algorithm internally and displays the GCD in the step-by-step solution so you can verify the simplification. Understanding GCD is fundamental to fraction work because it ensures your answers are always in their simplest, most readable form.

Converting a fraction to a decimal is straightforward: divide the numerator by the denominator. If the division terminates, you get an exact decimal (for instance, 3/8 = 0.375). If the division does not terminate, you get a repeating decimal (for instance, 1/3 = 0.333... with the 3 repeating infinitely). This calculator shows the decimal result rounded to a reasonable number of significant digits. Knowing how to convert fractions to decimals is essential for comparing values, performing calculations on a standard calculator, interpreting data in spreadsheets, and working with measurements in science and engineering contexts where decimal notation is the standard. The Fraction to Decimal tab in the conversion suite lets you perform this conversion independently from the main arithmetic calculator.

To convert a terminating decimal to a fraction, count the number of digits after the decimal point, then write the digits over a power of ten with that many zeros. For example, 0.625 has three decimal places, so it becomes 625/1000. Then simplify by dividing both the numerator and denominator by their GCD (125 in this case) to arrive at 5/8. For repeating decimals, algebraic techniques are used: if x = 0.666..., then 10x = 6.666..., and subtracting gives 9x = 6, so x = 6/9 = 2/3. This calculator handles terminating decimals accurately by using the power-of-ten method with automatic simplification. The Decimal to Fraction tab provides a dedicated interface for this conversion, making it easy to turn measurement readings, statistical results, or financial figures back into exact fractional form.

A mixed number consists of a whole number and a proper fraction, such as 3 2/5. To convert it to an improper fraction, multiply the whole number by the denominator and add the numerator, then place the result over the original denominator. For 3 2/5: (3 times 5) + 2 = 17, so the improper fraction is 17/5. To go the other direction, divide the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the new numerator over the same denominator. For 17/5: 17 divided by 5 is 3 remainder 2, giving 3 2/5. The Mixed Number tab in this calculator handles both conversions instantly. Improper fractions are useful for arithmetic operations because they are easier to multiply and divide, while mixed numbers are more intuitive for everyday measurements like cooking or construction.

Multiplying fractions is simpler than adding or subtracting because you do not need a common denominator. Simply multiply the numerators together to get the new numerator, multiply the denominators together to get the new denominator, and then simplify the result. For example, 2/3 times 4/5 equals 8/15. Division requires one extra step: flip the second fraction (take its reciprocal) and then multiply. So 2/3 divided by 4/5 becomes 2/3 times 5/4, which equals 10/12, and simplifies to 5/6. An important edge case to watch for is division by zero. If the second fraction's numerator is zero, the reciprocal would have zero in the denominator, which is undefined. This calculator checks for that condition and displays a clear error message rather than returning an incorrect result.

Yes, this fraction calculator is completely free, requires no account or signup, and has no usage limits. All calculations run entirely in your browser using JavaScript, which means nothing is uploaded to a server and your data remains completely private on your device. The tool works on desktops, laptops, tablets, and smartphones. You can bookmark this page for instant access whenever you need to solve fraction problems for school, tutoring, engineering, cooking conversions, or any other purpose. After the initial page load, the calculator even works offline since all the math happens locally without requiring an internet connection for subsequent calculations.