What is a complex fraction?
A complex fraction is a fraction whose numerator, denominator, or both are themselves fractions. This calculator handles the common case of one fraction divided by another: (a/b) ÷ (c/d). It returns the result simplified to lowest terms along with the equivalent decimal value.
How to use it
Enter the numerator and denominator of the top fraction (a and b), then the numerator and denominator of the bottom fraction (c and d). Click calculate to see the reduced fraction and its decimal. Negative numbers are allowed; the calculator keeps the denominator positive and moves any sign to the numerator.
The formula explained
Dividing by a fraction is the same as multiplying by its reciprocal. So (a/b) ÷ (c/d) becomes (a/b) × (d/c), which equals (a×d) / (b×c). The calculator then divides the new numerator and denominator by their greatest common divisor (GCD) to express the answer in lowest terms.
$$\frac{a/b}{c/d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}$$The reduction to lowest terms uses the greatest common divisor \(g\):
$$\frac{n}{d} = \frac{n \div g}{d \div g}, \quad g = \gcd(n, d)$$
Worked example
Suppose you want to compute \((1/2) \div (3/4)\). Multiply across by the reciprocal: numerator = \(1 \times 4 = 4\), denominator = \(2 \times 3 = 6\). So the raw fraction is \(4/6\). The GCD of \(4\) and \(6\) is \(2\), so the reduced answer is 2/3 ≈ 0.6667.
$$\frac{1/2}{3/4} = \frac{1 \times 4}{2 \times 3} = \frac{4}{6} = \frac{2}{3} \approx 0.6667$$FAQ
What if c is zero? Division by zero is undefined. If the bottom fraction equals zero (c = 0), or b·c = 0, the result is not a valid number, so make sure c and d are non-zero.
Can I use whole numbers? Yes — a whole number n is just n/1. Enter b or d as 1 to treat that part as an integer.
Does it accept negative values? Yes. The sign is normalized so the displayed denominator is always positive.
