Solve Complex Expression: 12÷(1/3×(24÷(15×3))) Step-by-Step

According to the order of operations rules, we'll begin by solving the expression inside of the parentheses:

$(\frac{1}{3}\times(24:(15\times3))=$

Let's write the division problem as a fraction:

$\frac{1}{3}\times\frac{24}{15\times3}=$

Given that this is a fraction divided by a fraction, we'll proceed to combine everything into one fraction:

$\frac{1\times24}{3\times15\times3}=$

Break down 24 into a multiplication of:

$8\times3$

As seen below in the fraction's numerator:

$\frac{1\times8\times3}{3\times15\times3}=$

Proceed to reduce the 3 in both the numerator and denominator as follows:

$12:\frac{8}{15\times3}=$

Swap the numerator with the denominator, resulting in a multiplication problem where the denominator is 8:

$12\times\frac{15\times3}{8}=$

Combine the 12 with the fraction's numerator given that this is a simple multiplication operation:

$\frac{12\times15\times3}{8}=$

Proceed to break down the 12 in the numerator and the 8 in the denominator into multiplication problems:

$\frac{4\times3\times15\times3}{4\times2}=$

Reduce the 4 in both the numerator and denominator:

$\frac{3\times15\times3}{2}=$

Solve the expression in the numerator from left to right:

$3\times15\times3=45\times3=135$

We obtain the following fraction:

$\frac{135}{2}$

Break down the fraction into an addition of fractions:

$\frac{130}{2}+\frac{5}{2}=$

Proceed to solve both fractions:

$\frac{130}{2}=130:2=65$

$\frac{5}{2}=5:2=2.5$

We obtain the following expression:

$65+2.5=67.5$