Solve 13:(9×(4:(18×5))) Using Order of Operations

$13:(9\times(4:(18\times5)))=$

Let's first address the expression in parentheses and convert it to a fraction:

$(9\times(4:(18\times5)))=(9\times\frac{4}{18\times5})$

Now we'll get the expression:

$13:(9\times\frac{4}{18\times5})=$

We'll add the 9 to the numerator of the fraction in the multiplication expression, and we'll separate the 18 into a smaller multiplication expression:

$13:(\frac{9\times4}{2\times9\times5})=$

Let's reduce the 9 in both numerator and denominator:

$13:(\frac{4}{2\times5})=$

Let's factor the numerator into a multiplication expression:

$13:(\frac{2\times2}{2\times5})=$

Let's reduce the 2 in both numerator and denominator:

$13:(\frac{2}{5})=$

We'll write the fraction in inverse form so we can convert the expression to a multiplication expression:

$13\times\frac{5}{2}=\frac{13\times5}{2}=\frac{65}{2}$

Let's factor the numerator into an addition expression:

$\frac{65}{2}=\frac{60+5}{2}$

Let's separate it into an addition of fractions:

$\frac{60}{2}+\frac{5}{2}=30+2.5=32.5$