Solve 2×(200÷(35×3)): Order of Operations Challenge

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

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

$2\operatorname{\times}(200:(35\operatorname{\times}3))=$

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.

$2\times(200:(35\times3))=2\times(200:(105))=$

$2\times(200:(105))= 2\times(200:105) =$

Express the value obtained 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

$2\times(200:105)=2\times(\frac{200}{105})=$
The largest number by which we can reduce the fraction is 5

$2\times(\frac{200}{105})= 2\times(\frac{200:5}{105:5})=$

$2\times(\frac{200:5}{105:5})= 2\times(\frac{40}{21})=$

$(\frac{ 2\times40}{21})= (\frac{ 80}{21})=\frac{ 80}{21}$

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

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

For the denominator – we don't change anything.

In this exercise, the numerator is 80 and the denominator is 21

21 goes into 80 three times with a remainder of 17

$\frac{ 80}{21}=3\text{ }\frac{17}{21}$

Therefore the answer is option a -

$3\text{ }\frac{17}{21}$