Fraction Calculator

Q: How do I enter mixed numbers?

Convert to an improper fraction first. For example, 2¾ = 11/4, enter it as frac(11;4). Or write it as 2 + frac(3;4).

Q: What is the GCD used for?

The Greatest Common Divisor (GCD) is used to reduce a fraction to its lowest terms. Dividing both numerator and denominator by GCD(n,d) gives the simplest equivalent fraction. You can compute the GCD of any two numbers with our GCD & LCM Calculator.

Q: What is the Least Common Denominator (LCD)?

The LCD is the smallest denominator that both fractions can be converted to before adding or subtracting. It is exactly equal to the Least Common Multiple (LCM) of the two denominators. For example, LCD(4, 6) = LCM(4, 6) = 12.

Perform addition, subtraction, multiplication and division on fractions. Press frac to insert a fraction, e.g. frac(1;2) + frac(3;4). Results are automatically reduced, with full step-by-step MathML explanations.

💡 Use frac(numerator ; denominator) to enter a fraction Supports: + − × ÷ and parentheses

Try: ½ + ¾ · ⅔ − ⅙ · ¾ × ⁸∕₉ · ⅚ ÷ ¹⁰∕₃ · (½+⅓)×⁶∕₅

How fraction arithmetic works

Adding and subtracting fractions

To add or subtract fractions, first find the Least Common Denominator (LCD). The LCD is equal to the Least Common Multiple (LCM) of the two denominators. Convert each fraction to that denominator, then add or subtract the numerators. Finally, reduce the result by dividing both numerator and denominator by their GCD.

Multiplying fractions

Multiply the numerators together and the denominators together: a/b × c/d = (a×c)/(b×d). Then reduce. You can also cross-reduce before multiplying to keep numbers smaller.

Dividing fractions

Dividing by a fraction is the same as multiplying by its reciprocal: a/b ÷ c/d = a/b × d/c. Then proceed as for multiplication.

Reducing to lowest terms

Divide both numerator and denominator by their Greatest Common Divisor (GCD). A fraction is in lowest terms when GCD(numerator, denominator) = 1. Use our GCD & LCM Calculator to find the GCD or LCM of any two integers directly.

Frequently asked questions

How do I add fractions with different denominators?

Find the LCD, convert both fractions, add the numerators, then reduce. Example: 1/2 + 1/3 → LCD = 6 → 3/6 + 2/6 = 5/6.

What is a proper vs improper fraction?

A proper fraction has |numerator| < denominator (e.g. 3/4). An improper fraction has |numerator| ≥ denominator (e.g. 7/4). Both are valid inputs in this calculator.

How do I enter mixed numbers?

Convert to an improper fraction first. For example, 2¾ = 11/4, enter it as frac(11;4). Or write it as 2 + frac(3;4).

What is the GCD used for?

The Greatest Common Divisor (GCD) is used to reduce a fraction to its lowest terms. Dividing both numerator and denominator by GCD(n,d) gives the simplest equivalent fraction. You can compute the GCD of any two numbers with our GCD & LCM Calculator.

What is the Least Common Denominator (LCD)?

The LCD is the smallest denominator that both fractions can be converted to before adding or subtracting. It is exactly equal to the Least Common Multiple (LCM) of the two denominators. For example, LCD(4, 6) = LCM(4, 6) = 12.