Question

Find the value of each expression

$\frac{1}{2}\left[9+5\left(-3\right)\right]$

Short answer

Value of $\frac{1}{2}\left[9+5\left(-3\right)\right]$ is $-3$

Step-by-step solution

- Order for simplification 

To evaluate any expression involving more than one operation, follow the below order of operations:

• First evaluate expressions inside grouping symbols like parentheses ( ) or brackets [ ].
• Evaluate the exponents.
• Perform Multiplication and division from left to right.
• Perform addition and subtraction from left to right.

- Simplify expression inside grouping symbol

To evaluate the value of the given expression, first simplify the expression inside the bracket as shown below

$\begin{array}{c}\frac{1}{2}\left[9+5\left(-3\right)\right]=\frac{1}{2}\left[9+\left(-15\right)\right]\\ =\frac{1}{2}\left(-6\right)\end{array}$

- Divide by 2

Now, to simplify further divide the numbers to get

$\begin{array}{c}\frac{1}{2}\left(-6\right)=\frac{-6}{2}\\ =-3\end{array}$

Thus, value of $\frac{1}{2}\left[9+5\left(-3\right)\right]$is $-3$