Complex Fraction Calculator

What counts as a "complex fraction" here

A complex fraction is a fraction whose numerator, denominator, or both are themselves fractions or mixed numbers — like (2+1/3) ÷ (1+1/2). The calculator's parser accepts four input shapes in each box: a plain integer (5, -3), a simple fraction (3/4), a mixed number written as addition (2+1/3, meaning 2 whole plus 1/3), or a mixed number written as subtraction (4-1/2, meaning 4 minus 1/2 — useful because some people prefer writing "3-1/2" for three-and-a-half over "3+1/2"). It evaluates each box to a single decimal, then divides.

Worked example

Enter "2+1/3" as the numerator and "1+1/2" as the denominator. The parser converts the numerator to 2 + (1/3) = 2.333333 and the denominator to 1 + (1/2) = 1.5. Dividing: 2.333333 / 1.5 = 1.555556. The calculator then reduces this to a fraction by searching denominators up to 10,000 for the closest match, landing on 14/9, which it displays as the mixed number 1 5/9 — matching the exact algebraic answer of (7/3) ÷ (3/2) = 14/9.

How the decimal-to-fraction step works

Because the tool works from a decimal internally (not exact fraction arithmetic), it reconstructs a fraction by testing denominators 1 through 10,000 and keeping whichever numerator/denominator pair comes closest to the decimal, then simplifies that pair using the greatest common divisor. This is reliable for fractions with reasonably small denominators but can occasionally show a very close approximation instead of the mathematically exact fraction for awkward decimals.

Constraints

The parser only understands the four formats above — no nested parentheses, no decimals typed directly into the numerator/denominator boxes, and a denominator that evaluates to zero is rejected with an explicit error rather than returning Infinity.