Solve 35 ÷ (3 × (4 ÷ (3 × 8))): Complete Order of Operations

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

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

$35:(3\times(4:(3\operatorname{\times}8)))=$

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.

$35:(3\times(4:(3\operatorname{\times}8)))= 35:(3\times(4:(24)))=$

$35:(3\times(4:(24))) = 35:(3\times(4:24))=$

Express the value obtained in the inner parentheses as a fraction and precede to reduce it.

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

$35:(3\times(4:24))=35:(3\times(\frac{4}{24}))=$
$35:(3\times(\frac{4}{24}))=35:((\frac{3\times4}{24}))=$
$35:((\frac{3\times4}{24}))=35:(\frac{12}{24})=$

The largest number by which we can reduce the fraction is 12

$35:(\frac{12}{24})= 35:(\frac{1}{2})=$

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

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

This means that in this case, instead of dividing by one-half, we can multiply by two, which is the reciprocal of one-half

$35:(\frac{1}{2})=35\times(\frac{2}{1})=35\times(2)=$

$35\times(2)=35\times2=$

$35\times2=70$

Therefore the answer is option A - (70)