Chapter 1.2, Problem 57PPE

To determine

To find: using grouping symbols to make the given equation true.

Answer to Problem 57PPE

The new statement $\left(ii\right)$ obtained by adding parentheses in statement $\left(i\right)$ has now become a true statement.

Explanation of Solution

Given:

  $16-4÷2+3=9$ .

Concept used:

There are basically three types of grouping symbol which are parentheses, brackets and braces which are used to group numbers or variables.

Bracket of division multiplication addition and subtraction $\left(BODMAS\right)$ .

Abiding the rules of $\left(BODMAS\right)$ Subtraction cannot be done before addition therefore the grouping symbol is necessary to derived the exact solution.

Calculation:

According to the given expression:

  $16-4÷2+3=\mathrm{9....}\left(i\right)$

To make given statement true, parentheses will be added inserted to $16-4$ and new statement will look like:

  $\left(16-4\right)÷2+3=\mathrm{9....}\left(ii\right)$ .

Checking the truthfulness of new statement:

Left hand side of $\left(2\right)=\left(16-4\right)÷\left(2+3\right)$ .

Simplifying the brackets, it becomes:

  $\Rightarrow 12÷2+\mathrm{3..}$

Simplifying the division, it becomes:

  $\begin{array}{l}\Rightarrow 6+3.\\ \Rightarrow 9.\end{array}$

Hence, new statement $\left(ii\right)$ obtained by adding parentheses in statement $\left(i\right)$ has now become a true statement.