Complex Fraction Calculator: Simplify a Fraction of Fractions with Steps

How it works

(a/b) ÷ (c/d) = (a/b) × (d/c) = (a × d) ÷ (b × c), then reduce by the GCD · LCD method: multiply top and bottom by the least common denominator L of every small fraction, then divide the two results · mixed number w n/d = (w × d + n)/d

A complex fraction has a fraction in its numerator, its denominator or both, such as (1/2 + 1/3) over (3/4 − 1/6). The long fraction bar means "divide", so the standard way is to simplify the top and the bottom to single fractions, then multiply the top by the reciprocal of the bottom and reduce. The second textbook method multiplies the top and the bottom by the least common denominator of all the small fractions, which clears every inner fraction at once and leaves a simple fraction. The calculator shows both so you can check your homework either way. Type each part as a fraction (3/4), a mixed number with a space (2 1/2), an integer, a decimal (0.25 is read exactly as 1/4), or a short expression with + − × ÷ and brackets. All arithmetic is exact, with no rounding, and the answer is given in lowest terms, as a mixed number, as a decimal and, when the decimal repeats, with the repeating block in brackets. Variables (x, y) are not supported; for algebraic complex fractions, apply the same LCD steps by hand. The fraction calculator works on two simple fractions and one operation; the continued-fraction calculator expands a number into nested fractions. This page is for the reverse job: collapsing a stacked fraction into one.

Worked example

Simplify (1/2 + 1/3) over (3/4 − 1/6). Top: 1/2 + 1/3 = 3/6 + 2/6 = 5/6. Bottom: 3/4 − 1/6 = 9/12 − 2/12 = 7/12. Divide: 5/6 × 12/7 = 60/42 = 10/7 = 1 3/7 ≈ 1.428571, a repeating decimal 1.(428571). With the LCD method, the least common denominator of 2, 3, 4 and 6 is 12; 12 × (1/2 + 1/3) = 6 + 4 = 10 and 12 × (3/4 − 1/6) = 9 − 2 = 7, so the answer is 10/7 again.

Sources: CalculatorSoup: Simplifying complex fractions (LCD and division methods, 5 1/3 over −6/15) · OpenStax Prealgebra 2e, 4.3: Multiply and divide mixed numbers and complex fractions · CalculatorSoup: Complex fraction calculator

Frequently asked questions