How do you simplify $3\left( {7 + 4 - 2} \right) \div 9 - 7$ using the order of operations ?

Hint: In the given question, we are required to simplify an arithmetic expression given to us in the problem. So, we add and subtract the like terms so as to simplify the arithmetic expression. We can use arithmetic rules and properties in order to simplify the given arithmetic expression.

Complete step by step solution:
We would use the BODMAS rule in order to simplify the arithmetic expression $3\left( {7 + 4 - 2} \right) \div 9 - 7$. BODMAS is an acronym for the sequence in which the mathematical operations are to be done. In BODMAS, B stands for brackets, O stands for of, D stands for division, M stands for multiplication, A stands addition, S stands subtraction.
So, $3\left( {7 + 4 - 2} \right) \div 9 - 7$
So, we open up the brackets first and carry out the operations going by sequence set by the acronym BODMAS. So, simplifying the bracket first, we get,
$ \Rightarrow 3 \times 9 \div 9 - 7$
Simplifying the expression further, we get,
$ \Rightarrow 3 \times 1 - 7$
Carrying out multiplication next according to the order set by the acronym BODMAS.
$ \Rightarrow 3 - 7$
Simplifying the expression further, we get,
$ \Rightarrow - 4$

Hence, the expression $3\left( {7 + 4 - 2} \right) \div 9 - 7$ can be simplified as $ - 4$ using the BODMAS rule.

Note: The given problem deals with algebraic expression. There is no fixed way of simplifying a given algebraic expression. Care should be taken while doing the calculation steps. Algebraic identities and rules may also be used as and when required as they help simplify complex and tedious tasks. Nowadays, another acronym PEMDAS is also coming into use for describing the sequence of arithmetic operations.