How to Use
- Enter the first fraction
Input the numerator and denominator of the first fraction.
- Select operation and enter second fraction
Choose addition, subtraction, multiplication, or division, then enter the second fraction.
- View result
Click Calculate to see the simplified result and its decimal equivalent.
What is a fraction?
A fraction expresses part of a whole as numerator/denominator. The denominator shows how many equal parts the whole is divided into, and the numerator shows how many of those parts you have. For example, 3/4 means 3 out of 4 equal parts of the whole.
Fractions let you represent quantities that don't divide evenly by 1 with perfect accuracy. A value that would repeat forever as a decimal, like 0.333..., can be handled cleanly as 1/3. That's why fractions are essential in cooking recipes, dividing lengths and time, probability, and school mathematics.
This calculator performs addition, subtraction, multiplication, and division of two fractions, automatically simplifies the result to lowest terms, and also shows the mixed number and decimal value.
Calculation formulas
The four arithmetic operations for two fractions a/b and c/d are as follows.
- Addition:
a/b + c/d = (ad + cb) / bd - Subtraction:
a/b - c/d = (ad - cb) / bd - Multiplication:
a/b × c/d = ac / bd - Division:
a/b ÷ c/d = ad / bc(multiply by the reciprocal of the second fraction)
Here b and d are the denominators, and a and c are the numerators. For example, 1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6. Finally, divide the numerator and denominator by their greatest common divisor (GCD) to simplify (e.g., 4/8 has a GCD of 4, giving 1/2).