Chapter 1.2, Problem 53PPE

To determine

To find: whether the expression can perform the operation at different orders and still get the correct answer.

Answer to Problem 53PPE

It can perform the operations in different order of the expression:

  ${\left(1+5\right)}^2-\left(18÷3\right)$ and still get the same answer.

Explanation of Solution

Given:

  ${\left(1+5\right)}^2-\left(18÷3\right)$ .

Concept used:

The operation is different but the both the term is in bracket and according to the $BODMAS$

rule:

First prior is bracket and the expression is independent of value inside the bracket.

First term can be solved earlier or second term it wouldn’t change the answer.

Calculation:

Consider the given expression ${\left(1+5\right)}^2-\left(18÷3\right)$:

To determine whether it get the correct or same answer if it is solved above expression in different operational order:

Firstly, solve the left had side parentheses such that $\left(1+5\right)$ of the expression:

  ${\left(1+5\right)}^2-\left(18÷3\right)$

Then it becomes:

  $\Rightarrow 6^2-\left(18÷3\right).$

Simplify the right-hand side parentheses such that:

  $\begin{array}{l}\Rightarrow 6^2-6.\\ \Rightarrow 30.\end{array}$

The value of the expression:

  ${\left(1+5\right)}^2-\left(18÷3\right)=30.$

Secondly, solve the right-hand side parentheses such that:

  $\begin{array}{l}{\left(1+5\right)}^2-6.\\ \Rightarrow 36-6.\\ \Rightarrow 30.\end{array}$

The value of expression ${\left(1+5\right)}^2-\left(18÷3\right)=30.$

The values are same in each order of operation.

Hence, it can perform the operations in different order of the expression:

  ${\left(1+5\right)}^2-\left(18÷3\right)$ and still get the same answer.