Solve: 7÷(8×(10÷(3×12))) - Order of Operations Challenge

Let's look at the expression in parentheses and write it as a fraction:

$(8\times(10:(3\times12)))=8\times\frac{10}{3\times12}$

Now we'll get the expression:

$7:(8\times\frac{10}{3\times12})=$

Let's address the parentheses and combine the 8 with the multiplication in the numerator:

$7:(\frac{8\times10}{3\times12})=$

Let's break down the 8 and 12 into smaller multiplication problems:

$7:(\frac{4\times2\times10}{3\times4\times3})=$

Let's reduce between the 4 in the numerator and denominator and get:

$7:(\frac{2\times10}{3\times3})=$

Let's solve the multiplication problems in the parentheses and get:

$7:(\frac{20}{9})=$

Let's switch between the numerator and denominator so we can turn the expression into multiplication and add the 7 to the fraction's numerator:

$7\times\frac{9}{20}=\frac{7\times9}{20}=\frac{63}{20}$

Let's separate the fraction's numerator into an addition problem:

$\frac{60+3}{20}=$

Now let's separate it into an addition of fractions:

$\frac{60}{20}+\frac{3}{20}=3+\frac{3}{20}=$

Let's multiply the fraction by 5:

$3+\frac{3\times5}{20\times5}=3+\frac{15}{100}$

And we'll get the expression:

$3+0.15=3.15$