Simplifying Complex Fractions Calculator

Enter Calculation

Numerator's numerator (a)

Numerator's denominator (b)

Denominator's numerator (c)

Denominator's denominator (d)

Results

Simplified Fraction

2 / 3

≈ 0.6667

Before reducing	4 / 6
Method	(a/b) ÷ (c/d) = (a·d) / (b·c)

What Is a Complex Fraction?

A complex fraction is a fraction whose numerator, denominator, or both are themselves fractions — for example \((a/b) / (c/d)\). Although they look intimidating, complex fractions simplify with one simple rule: dividing by a fraction is the same as multiplying by its reciprocal. This calculator does that for you and reduces the answer to lowest terms.

A complex fraction has a fraction stacked over another fraction.

How to Use This Calculator

Enter the four whole-number parts of your complex fraction. The numerator of the whole expression is the fraction \(a/b\) and the denominator is the fraction \(c/d\). Press calculate to see the simplified fraction and its decimal equivalent. The tool also shows the unreduced product so you can follow the work.

The Formula Explained

To divide \(a/b\) by \(c/d\), flip the bottom fraction and multiply:

$$\dfrac{a/b}{c/d} = \dfrac{a}{b} \times \dfrac{d}{c} = \dfrac{a \cdot d}{b \cdot c}$$

The result \(ad/bc\) is then reduced by dividing the top and bottom by their greatest common divisor (GCD):

$$\dfrac{ad}{bc} = \dfrac{ad \div g}{bc \div g}, \quad g = \gcd(ad, bc)$$

If the denominator comes out negative, the sign is moved to the numerator so the answer stays in standard form.

Dividing by \(c/d\) equals multiplying by its reciprocal \(d/c\), giving \((a\times d)/(b\times c)\).

Worked Example

Simplify \((2/3) / (4/5)\). Multiply across by the reciprocal:

$$\dfrac{2 \times 5}{3 \times 4} = \dfrac{10}{12}$$

The GCD of 10 and 12 is 2, so dividing gives \(5/6\), which equals about \(0.8333\). That is exactly what this calculator returns.

FAQ

Can I use negative numbers? Yes — enter a negative sign on any part and the result is normalized so the denominator is positive.

What if a part is zero? If \(a\), the result is 0. If \(c\) or \(d\) makes the bottom fraction zero, division is undefined and the calculator returns 0 as a safeguard.

Does it accept decimals? Inputs are treated as whole numbers (rounded), since complex fractions are defined with integer parts. Convert any decimals to fractions first for an exact result.