Fraction Calculator

The Fraction Calculator handles the four core operations on fractions — addition, subtraction, multiplication, and division — and instantly returns both the simplified fraction and its decimal equivalent. It is designed for students learning fraction arithmetic, parents helping with homework, bakers scaling recipes, carpenters measuring wood, and anyone who wants a quick, reliable answer without breaking out a pencil.

To add or subtract fractions, you first need a common denominator. The standard approach is to multiply the two denominators together, rewrite each fraction with the new denominator, and then add or subtract the numerators. For example, 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6. Using a common denominator equal to the product of the two denominators always works, even if it is not the smallest possible. The calculator then simplifies the answer by dividing the numerator and denominator by their greatest common divisor (GCD).

Multiplying fractions is the simplest operation: multiply numerator by numerator and denominator by denominator. So 2/3 × 4/5 = 8/15. Division uses the "keep, change, flip" rule — keep the first fraction, change division to multiplication, and flip the second fraction (its reciprocal). So 2/3 ÷ 4/5 becomes 2/3 × 5/4 = 10/12, which simplifies to 5/6.

Every result is automatically reduced to its lowest terms using the Euclidean algorithm to find the GCD. The decimal output is rounded to six significant digits with trailing zeros removed for readability. Fractions with a denominator of zero are flagged as undefined. Whether you are checking your child's homework, converting between cups and tablespoons, or working through a math problem, the Fraction Calculator gives you an exact answer and shows the work so you can learn the method, not just memorize the result.

Beyond classroom arithmetic, fractions are the natural language of music, woodworking and recipe scaling. A 3/4 time signature in music describes three quarter-note beats per measure. A carpenter who needs to cut a board into three equal pieces from a 7-1/2-inch stock works in halves and quarters every day. A cook doubling a recipe with 2/3 cup of flour needs 4/3 = 1-1/3 cups. This calculator handles each scenario without forcing you to convert to decimals and back.

Improper fractions (numerator greater than denominator) and mixed numbers are equivalent representations. 7/4 is the same as 1-3/4, and many recipes and rulers prefer the mixed form for readability. The calculator returns the simplified improper fraction along with its decimal value, so you can convert in either direction as your context requires. For repeating decimals like 1/3 = 0.333…, the decimal form loses precision; the fraction form is exact.

The greatest common divisor (GCD) of two integers is the largest integer that divides both without remainder. The calculator finds it using the Euclidean algorithm, an iterative process that dates back to ancient Greece and is still used in modern cryptography. Dividing both numerator and denominator by the GCD reduces a fraction to its lowest terms, which is the conventional way to express any final answer.

When the result of a fraction operation is undefined (division by zero, for instance), the calculator flags it rather than silently returning a misleading value. Division by zero has no meaningful answer, and any tool that returns one is hiding a bug. Encountering this output is your cue to recheck your inputs — a zero denominator usually means you typed a wrong digit or forgot to enter a value.