Fraction Calculator

How does the calculator work with fractions?

The tool runs on exact integer arithmetic, never on rounded decimals. It computes the raw result of your operation, then reduces it with the greatest common divisor (GCD), so 42/56 always comes back as 3/4 rather than 0.75 with hidden rounding. The decimal value rides along for reference and stays out of the math itself.

The four operations

How do I add two fractions step by step?

Adding 1/2 and 1/3 by hand needs a common denominator. Multiply each numerator by the other denominator: 1 × 3 = 3 and 1 × 2 = 2, then put the sum over the product of the denominators: (3 + 2) ÷ 6 = 5/6. The calculator does exactly that, then checks whether the result reduces. Here 5 and 6 share no factor, so 5/6 is final.

How do I simplify a fraction with the GCD?

Simplifying divides the numerator and the denominator by their greatest common divisor. For 42/56, the GCD of 42 and 56 is 14, so 42/56 = 3/4. To use the tool as a plain fraction simplifier, divide your fraction by 1/1: you get back the same fraction, fully reduced. The sign always rides on the numerator, so 1/-2 shows as -1/2.

What are the mixed number and decimal forms?

When the result is an improper fraction like 7/6, the calculator also shows the mixed number 1 1/6: one whole plus 1/6. That is the form recipes and measurements use, 1 1/2 cups rather than 3/2 cups. The decimal lands last, rounded to at most 6 places for display only, so 5/6 shows as 0.833333 while the stored math stays exact.

Where do fractions come up day to day?

Fractions turn up wherever measurements resist round numbers. Doubling a recipe that calls for 3/4 cup of sugar means 3/4 × 2/1 = 3/2, so 1 1/2 cups. Halving a 5/8 inch board allowance gives 5/16. Splitting two thirds of a pizza between four people is 2/3 ÷ 4/1 = 1/6 each. Typing these straight in beats converting to decimals and back.

What are the limits and error cases?

Numerators and denominators take whole numbers from -9999 to 9999, plenty for schoolwork, cooking and carpentry. A denominator of zero is rejected with a clear message, and so is dividing by a fraction equal to zero, since both are undefined.