Solve Complex Nested Fraction: 12/(7·(4/(3·(12/(3·2)))) Step-by-Step

First, we start with the innermost parentheses, we rewrite the exercise in fraction form:

$12/(7\cdot(4/(3\cdot(\frac{12}{3\times2})))=$

We associate the 3 in the innermost parenthesis with the multiplication exercise in the numerator and convert the division exerciseinto a multiplication exercise in the next parenthesis:

$12/(7\cdot(4\times(\frac{3\times2}{3\times12}))=$

We add the 4 to the multiplication exercise in the numerator of the fraction:

$12/(7\cdot(\frac{4\times3\times2}{3\times12})=$

We add the 7 to the multiplication exercise in the numerator of the fraction:

$12/(\frac{7\times4\times3\times2}{3\times12})=$

We convert the exercise into a multiplication by inverting the fraction between numerator and denominator:

$12\times\frac{3\times12}{7\times4\times3\times2}=$

We add the 12 to the multiplication exercise in the numerator of the fraction:

$\frac{12\times3\times12}{7\times4\times3\times2}=$

We simplify the 3 in the numerator and denominator, and break down the 12 in the numerator for a simpler multiplication exercise:

$\frac{4\times3\times2\times6}{7\times4\times2}=$

We simplify to 4 and 2 in the numerator and denominator:

$\frac{3\times6}{7}=\frac{18}{7}$

We break down the fraction into a sum exercise:

$\frac{14+4}{7}=\frac{14}{7}+\frac{4}{7}=2+\frac{4}{7}=2\frac{4}{7}$