Solve 72÷(7×(24÷(4×2))): Complete Order of Operations Challenge

Whilst adhering to the order of operations: parentheses precede multiplication and division (from left to right) which in turn precede addition and subtraction (from left to right)

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

$72:(7\times(24:(4\operatorname{\times}2)))=$

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, and after calculating we are able to remove the inner parentheses. We'll continue doing this until no more parentheses remain in the exercise.

$72:(7\times(24:(4\operatorname{\times}2)))=72:(7\times(24:(8)))=$

$72:(7\times(24:(8)))=72:(7\times(24:8))=$

$72:(7\times(24:8))=72:(7\times(3))=$

$72:(7\times(3))=72:(7\times3)=$

$72:(7\times3)=72:(21)=$

Express the resulting numerical value obtained from the inner parentheses as a fraction and then proceed to reduce the fraction.

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

$72:(21)=72:21=\frac{72}{21}=$
The largest number by which we can reduce the fraction is 3

$\frac{72}{21}=\frac{72:3}{21:3}=$

$\frac{72:3}{21:3}=\frac{24}{7}=$

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

In order to determine 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 24 and the denominator is 7

7 goes into 24 three times with a remainder of 3

$\frac{24}{7}=3\text{ }\frac{3}{7}$

Therefore the answer is option a -

$3\text{ }\frac{3}{7}$