Solve the Nested Fraction Division: 4/5 ÷ (2/3 ÷ (4 ÷ 3/2))

$\frac{4}{5}:(\frac{2}{3}:(4:\frac{3}{2}))=\text{?}$

We convert the exercise with the innermost parentheses into a multiplication exercise, inverting the numerator and the denominator:

$\frac{4}{5}:(\frac{2}{3}:(4\times\frac{2}{3}))=$

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

$\frac{4}{5}:(\frac{2}{3}:(\frac{4\times2}{3}))=$

Again, we convert the exercise with the innermost parentheses into a multiplication exercise, inverting the numerator and the denominator:

$\frac{4}{5}:(\frac{2}{3}\times\frac{3}{4\times2}))=$

We convert the multiplication exercise between fractions into a single exercise, and we obtain:

$\frac{4}{5}:(\frac{2\times3}{3\times4\times2})=$

We simplify the 2 and the 3 in the numerator and denominator, and we obtain:

$\frac{4}{5}:(\frac{1}{4})=$

We convert the exercise with the secondary parentheses into a multiplication exercise, inverting the numerator and the denominator:

$\frac{4}{5}\times\frac{4}{1}=\frac{4\times4}{5\times1}=\frac{16}{5}$

We convert the numerator of the fraction into a sum exercise:

$\frac{15+1}{5}=$

We separate into a sum exercise between fractions:

$\frac{15}{5}+\frac{1}{5}=$

We obtain:

$3+\frac{1}{5}=3\frac{1}{5}$