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

Whilst adhering to the the order of operations: calculate the operations within the parentheses, multiplication and division (from left to right), addition and subtraction (from left to right)

Note that there are parentheses within parentheses, hence we will 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, after which we can remove the inner parentheses. We'll continue doing so until no more parentheses remain.

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

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

The resulting numerical value obtained from the inner parentheses can be expressed as a fraction. Proceed to reduce the fraction.

Reminder - How do we approach fraction reduction? Divide both the 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 -

$\frac{27}{38}$