Fraction Calculator

How to Use the Fraction Calculator

This fraction calculator lets you perform arithmetic on two fractions with immediate results. Enter the numerator and denominator of the first fraction, pick an operation (addition, subtraction, multiplication, or division), then enter the second fraction. The calculator instantly shows the answer as a fully simplified fraction and its decimal equivalent. There is no need to press a calculate button or reload the page; results update in real time as you type.

Fractions are fundamental to cooking, construction, sewing, and many other real-world tasks. Whether you are doubling a recipe that calls for 3/4 cup of flour, splitting a board into equal segments, or solving homework problems, this tool handles the tedious arithmetic so you can focus on what matters. It automatically finds the greatest common divisor to simplify the result, saving you an extra step.

Rules for Fraction Arithmetic

The rules for fraction arithmetic are straightforward once you learn them. For addition and subtraction, both fractions must share a common denominator. Find the least common denominator (LCD), rewrite each fraction with that denominator, then add or subtract the numerators. For multiplication, simply multiply the numerators together and the denominators together. For division, multiply the first fraction by the reciprocal (flipped version) of the second fraction.

Simplifying Fractions

A fraction is in its simplest form when the numerator and denominator have no common factor other than 1. To simplify, find the greatest common divisor (GCD) of both numbers and divide each by it. For instance, 18/24 has a GCD of 6, so dividing both by 6 gives 3/4. This calculator simplifies every result automatically, so you always get the cleanest possible answer.

Converting Between Fractions and Decimals

To convert a fraction to a decimal, divide the numerator by the denominator. For example, 3/8 = 0.375. Some fractions produce repeating decimals, like 1/3 = 0.3333... To convert a decimal back to a fraction, place the decimal digits over the appropriate power of ten and simplify. For example, 0.75 = 75/100 = 3/4. The decimal result shown by this calculator is rounded to a reasonable number of decimal places for practical use.

Frequently Asked Questions

How do you add fractions with different denominators?

To add fractions with different denominators, first find the least common denominator (LCD). Convert each fraction so both share the LCD, then add the numerators and keep the common denominator. For example, 1/3 + 1/4: the LCD is 12, so 4/12 + 3/12 = 7/12.

How do you multiply fractions?

Multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. For example, 2/3 x 4/5 = (2x4)/(3x5) = 8/15. Simplify the result if possible.

How do you divide fractions?

To divide by a fraction, multiply by its reciprocal. Flip the second fraction (swap numerator and denominator) and then multiply. For example, 3/4 divided by 2/5 becomes 3/4 x 5/2 = 15/8 = 1 7/8.

How do you simplify a fraction?

Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. For example, 12/18: the GCD is 6, so 12/18 simplifies to 2/3. A fraction is fully simplified when the numerator and denominator share no common factors other than 1.

What is an improper fraction versus a mixed number?

An improper fraction has a numerator larger than its denominator, such as 7/4. A mixed number combines a whole number with a proper fraction, such as 1 3/4. Both represent the same value: 7/4 = 1 3/4.