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

According to the order of operations rules, we'll first solve the expression in parentheses:

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

Let's write the division problem as a fraction:

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

Since this is a fraction divided by a fraction, we'll combine everything into one fraction:

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

Let's break down 24 into a multiplication of:

$8\times3$

And we'll get in the fraction's numerator:

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

We'll reduce the 3 in both numerator and denominator and get the expression:

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

We'll swap between numerator and denominator, so we get a multiplication problem where the denominator is 8:

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

We'll combine the 12 with the fraction's numerator since this is just a multiplication operation:

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

Let's break down the 12 in the numerator and the 8 in the denominator into multiplication problems:

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

We'll reduce the 4 in both numerator and denominator:

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

Let's solve the expression in the numerator from left to right:

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

We'll get the fraction:

$\frac{135}{2}$

Let's break down the fraction into an addition of fractions:

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

Let's solve both fractions:

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

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

Now we'll get the expression:

$65+2.5=67.5$