Question

Find the value of each expression

35.$\frac{12\left(52÷2^2\right)}{6}-\frac{2}{3}$

Short answer

Value of$\frac{12\left(52÷2^2\right)}{6}-\frac{2}{3}$ is $25\frac{1}{3}$

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 parenthesis and then simplify fraction as shown below

$\begin{array}{c}\frac{12\left(52÷2^2\right)}{6}-\frac{2}{3}=\frac{12\left(52÷4\right)}{6}-\frac{2}{3}\\ =\frac{12\left(13\right)}{6}-\frac{2}{3}\\ =\frac{156}{6}-\frac{2}{3}\\ =\frac{78}{3}-\frac{2}{3}\end{array}$

- Subtract 23 from 783

Now, to simplify further subtract the numbers to get

$\begin{array}{c}\frac{78}{3}-\frac{2}{3}=\frac{78-2}{3}\\ =\frac{76}{3}\\ =25\frac{1}{3}\end{array}$

Thus, value of$\frac{12\left(52÷2^2\right)}{6}-\frac{2}{3}$ is $25\frac{1}{3}$