Chapter 1.2, Problem 8GP

To determine

The value of the expression $3\left[\left(20-7\right)+1\right]$

Answer to Problem 8GP

  $42$

Explanation of Solution

Given information:

The expression, $3\left[\left(20-7\right)+1\right]$

Concept used:

For Order of Operation, we will use PEMDAS rule.

Symbols are representing:

P − parenthesis, E − exponent, M − multiplication,

D − division, A − addition and S − subtraction.

• If grouping symbols such as parenthesis are present, simplify expressions within those first, starting with the innermost set.
• Evaluate exponential expressions or absolute values in order from left to right.
• Multiply or divide in order from left to right.
• Add or subtract in order from left to right.

If there is no grouping symbols or no exponents, we multiply or divide and then add or subtract in the order from left to right.

Calculation:

To simplify the expression $3\left[\left(20-7\right)+1\right]$ , first simplify the inner parenthesis inside the bracket and then simplify further by multiplying the number outside with the resulting number as shown below

  $\begin{array}{c}3\left[\left(20-7\right)+1\right]=3\left[\left(13\right)+1\right]\\ =3\left[13+1\right]\\ =3\left[14\right]\\ =42\end{array}$

Thus, the value of the given expression is 42.