Solve 33÷(4×(50÷(3×2))): Order of Operations Challenge

Recall the order of operations: parentheses precede all other operations, multiplication and division (from left to right) follow and finally addition and subtraction (from left to right)

When there are parentheses within parentheses, we start with the innermost ones first.

$33:(4\times(50:(3\operatorname{\times}2)))=$

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 this until no more parentheses remain in the exercise.

$33:(4\times(50:(3\operatorname{\times}2)))=33:(4\times(50:(6)))=$

$33:(4\times(50:(6)))= 33:(4\times(50:6))=$

Express the value obtained for the inner parentheses as a fraction and proceed to reduce it.

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

$33:(4\times(50:6))=33:(4\times(\frac{50}{6}))=$
The largest number by which we can reduce the fraction is 2

$33:(4\times(\frac{50}{6}))=33:(4\times(\frac{50:2}{6:2}))=$

$33:(4\times(\frac{50:2}{6:2}))=33:(4\times(\frac{25}{3}))=$

$33:(4\times(\frac{25}{3}))=33:(\frac{4\times25}{3})=$

$33:(\frac{4\times25}{3})=33:(\frac{100}{3})=$

Remember that division by definition is in fact multiplication by the reciprocal

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

$33:(\frac{100}{3})=33\times(\frac{3}{100})=$

$33\times(\frac{3}{100})= (\frac{33\times3}{100})=$

$(\frac{33\times3}{100})= (\frac{99}{100})= \frac{99}{100}$

Converting from a fraction to a decimal number we obtain the following.

$\frac{99}{100}= 0.99$

Therefore the answer is option b - (0.99)