Solve 94÷(2×(70÷(5×8))): Complete Order of Operations Challenge

Solve the following problem:

$94:(2\times(70:(5\times8)))=$

Adhering to the order of operations: Begin with the operations inside of the parentheses proceed to the multiplication and division (from left to right) and finally address the addition and subtraction (from left to right)

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

$94:(2\times(70:(5\operatorname{\times}8)))=$

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

Therefore, we will begin by addressing the operation in the inner parentheses first. After calculating this we can proceed to remove the inner parentheses. Continue doing this until no more parentheses remain.

$94:(2\times(70:(5\operatorname{\times}8)))=94:(2\times(70:(40)))=$

$94:(2\times(70:(40)))=94:(2\times(70:40))=$

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

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

$94:(2\times(70:40))=94:(2\times(\frac{70}{40}))=$
The largest number by which we can reduce the fraction is 10

$94:(2\times(\frac{70}{40}))= 94:(2\times(\frac{70:10}{40:10}))=$

$94:(2\times(\frac{70:10}{40:10}))= 94:(2\times(\frac{7}{4}))=$

$94:(2\times(\frac{7}{4}))= 94:(\frac{2\times7}{4})=$

$94:(\frac{2\times7}{4})= 94:(\frac{14}{4})=$

Remember that division by definition is in fact equivalent to multiplication by the reciprocal:

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

$94:(\frac{14}{4})=94\times(\frac{4}{14})=$

$94\times(\frac{4}{14})=(\frac{94\times4}{14})=$

$(\frac{94\times4}{14})=(\frac{94\times4}{14})=(\frac{376}{14})=$

$(\frac{376}{14})=\frac{376}{14}=$

Reminder - How do we convert an improper fraction to a mixed number?

In order to find the numerator - check how many times the denominator goes into the numerator and add the remainder to the numerator.

For the denominator – don't change anything.

In this exercise, the numerator is 376 and the denominator is 14

14 goes into 376 26 times with a remainder of 12

$\frac{376}{14}=26\text{ }\frac{12}{14}=$

Let's reduce the fraction and divide by 2

$26\text{ }\frac{12}{14}=26\text{ }\frac{12:2}{14:2}=$

$26\text{ }\frac{12:2}{14:2}=26\text{ }\frac{6}{7}$

Therefore the answer is option b -

$26\text{ }\frac{6}{7}$