Question

Evaluate the expression.

$72÷[(11-7)\cdot 2]$

Short answer

The value of the expression is9.

Step-by-step solution

Step-1 – Order of operations

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.

Step-2 – Solve the expression inside grouping symbols

In order to evaluate the given expression, first evaluate the expression inside the parentheses. And then simplify the expression inside the bracket.

So, first subtract the numbers inside parenthesis and then multiply the resulting number with 2 to get

$\begin{array}{l}72÷[(11-7)\cdot 2]\\ =72÷[4\cdot 2]\\ =72÷\left[8\right]\\ =72÷8\end{array}$

Step-3 – Multiply and divide from left to right

Now to simplify further, divide the resulting numbers to get

$\begin{array}{l}72÷8\\ =9\end{array}$

Thus, the value of the expression is 9.