Question

simplify this numerical expression using the order of operations.\\( 5.75 - \frac{1}{2} (20 div 2.5) div 2 + 6 \\)\
order of operations:\

1. evaluate within parentheses.\
2. evaluate exponents.\
3. multiply and divide from left to right.\
4. add and subtract from left to right.\

what is the value of the expression?

Explanation:

Step1: Evaluate within parentheses

First, calculate the expression inside the parentheses: \(20\div2.5 = 8\)
So the expression becomes \(5.75-\frac{1}{2}\times8\div2 + 6\)

Step2: Multiply and divide from left to right

Next, perform the multiplication and division operations from left to right. First, calculate \(\frac{1}{2}\times8\):
\(\frac{1}{2}\times8 = 4\)
Now the expression is \(5.75 - 4\div2+6\)
Then, calculate \(4\div2\):
\(4\div2 = 2\)
Now the expression is \(5.75 - 2+6\)

Step3: Add and subtract from left to right

Finally, perform the addition and subtraction operations from left to right. First, calculate \(5.75 - 2\):
\(5.75 - 2 = 3.75\)
Then, calculate \(3.75+6\):
\(3.75 + 6 = 9.75\)

Answer:

\(9.75\)