Solve 63÷(14×(38÷(3×2))): Complete Order of Operations Challenge

Let's recall the order of operations: calculate what's in parentheses, multiplication and division (from left to right), addition and subtraction (from left to right)

We emphasize that when there are parentheses within parentheses, we start with the innermost ones first.

$63:(14\times(38:(3\operatorname{\times}2)))=$

In this exercise, there are only multiplication and division operations and parentheses within parentheses.

Therefore, we will first perform the operation in the inner parentheses, and after calculating we can remove the inner parentheses. We'll continue doing this until there are no more parentheses in the exercise.

$63:(14\times(38:(3\operatorname{\times}2)))=63:(14\times(38:(6)))=$

$63:(14\times(38:(6)))=63:(14\times(38:6))=$

We will present the part of the exercise we got in the inner parentheses as a fraction and try to reduce the fraction

Reminder - How do we approach fraction reduction? Divide both numerator and denominator by the same number

$63:(14\times(38:6))=63:(14\times(\frac{38}{6}))=$
The largest number by which we can reduce the fraction is 2

$63:(14\times(\frac{38}{6}))=63:(14\times(\frac{38:2}{6:2}))=$

$63:(14\times(\frac{38:2}{6:2}))=63:(14\times(\frac{19}{3}))=$

$63:(14\times(\frac{19}{3}))=63:(\frac{14\times19}{3})=$

$63:(\frac{14\times19}{3})=63:(\frac{266}{3})=$

Remember that division by definition is actually multiplication by the reciprocal

$\frac{a}{\frac{1}{b}}=a\times b$

$63:(\frac{266}{3})=63\times(\frac{3}{266})=$

$63\times(\frac{3}{266})=(\frac{63\times3}{266})=\frac{63\times3}{266}=$

$\frac{63\times3}{266}=\frac{189}{266}=$

The largest number by which we can reduce the fraction is 7

$\frac{189}{266}=\frac{189:7}{266:7}=$

$\frac{189:7}{266:7}=\frac{27}{38}$

Therefore the answer is option c -

$\frac{27}{38}$