Complex fraction calculator

A complex fraction has a fraction in its numerator, its denominator or both, such as (3/4) / (5/6). The main fraction bar means divide, so simplifying one means dividing two fractions, and there are two standard methods.

Method 1, the reciprocal. Divide by multiplying by the bottom fraction turned upside down: 3/4 × 6/5 = 18/20, which reduces to 9/10.

Method 2, the least common denominator. Find the LCD of the small denominators, 12 for 4 and 6, and multiply the top and the bottom of the big fraction by it. 3/4 × 12 = 9 and 5/6 × 12 = 10, so the complex fraction becomes 9/10 in one step. Multiplying a numerator and a denominator by the same number does not change the value, and the LCD clears every inner fraction at once.

The LCD method is faster when the top or the bottom is a sum. To simplify (1/2 + 1/3) / (5/6), multiply every term by 6: (3 + 2) / 5 = 1. The reciprocal method gets there by adding first, 1/2 + 1/3 = 5/6, and then dividing 5/6 by 5/6.

Mixed numbers become improper fractions first: (2 1/2) / (1/4) is (5/2) / (1/4) = 5/2 × 4 = 10. Dividing by a fraction smaller than 1 makes the answer larger than the top.