Fraction calculator with steps
Add, subtract, multiply or divide two fractions and visualize each step of the calculation: finding a common denominator, performing the operation, then simplifying using the GCD. Ideal for checking a math exercise or understanding the method.
How it works
To add or subtract two fractions, you first need to bring them to the same denominator (the LCM of the two denominators), then add or subtract the numerators. To multiply, you multiply numerators together and denominators together. To divide, you multiply the first fraction by the reciprocal of the second. The result is then simplified by dividing numerator and denominator by their GCD.
Why bring fractions to the same denominator?
You can only add or subtract parts of the same size: 1/2 and 1/3 don't represent the same base unit. By converting them to 3/6 and 2/6, you get comparable sixths and the operation becomes a simple addition or subtraction of numerators.
How is the GCD used for simplification found?
The greatest common divisor (GCD) is calculated here using the Euclidean algorithm, which successively divides the two numbers until a remainder of zero is obtained. Dividing the numerator and denominator by this GCD gives the equivalent fraction in its simplest, lowest terms.
All calculations are performed locally in JavaScript in your browser: your fractions are never transmitted to a server.