Chapter 1.2, Problem 56PPE

To determine

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

Answer to Problem 56PPE

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:

  $9+3-2+4=6$ .

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:

  $9+3-2+4=\mathrm{6....}\left(i\right)$

To make given statement true, parentheses will be added inserted to $9+3\text{ and }2+4$ and new statement will look like:

  $\left(9+3\right)-\left(2+4\right)=\mathrm{6....}\left(ii\right)$ .

Checking the truthfulness of new statement:

Left hand side of $\left(2\right)=\left(9+3\right)-\left(2+4\right)$ .

Simplifying the brackets, it becomes:

  $\Rightarrow 12-6=6.$

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