Understanding the Mathematical Expression

We are asked to solve the given mathematical expression: \(\frac{1}{2} \nbsp;[{-2(2 + 3)*20}/2]\).

This expression involves several operations: addition, multiplication, division, and working with fractions and negative numbers. To solve it correctly, we need to follow the order of operations, often remembered by acronyms like PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right) or BODMAS (Brackets, Orders, Division and Multiplication from left to right, Addition and Subtraction from left to right).

Let's break down the expression and solve it step-by-step.

Step-by-Step Solution to Solve the Expression

The expression is: \(\frac{1}{2} \times [{-2(2 + 3) \times 20} \div 2]\)

1. Solve the operation inside the innermost parentheses first:

   The innermost part is \((2 + 3)\).

   \((2 + 3) = 5\)

   Now the expression becomes: \(\frac{1}{2} \times [{-2 \times 5 \times 20} \div 2]\)

2. Perform the multiplications inside the square brackets [ ] from left to right:

   Next, we have \(-2 \times 5 \times 20\).

   First multiplication: \(-2 \times 5 = -10\)

   The expression inside the brackets is now \([-10 \times 20 \div 2]\).

   Second multiplication: \(-10 \times 20 = -200\)

   The expression inside the brackets is now \([-200 \div 2]\).

3. Perform the division inside the square brackets:

   Now we have \(-200 \div 2\).

   \(-200 \div 2 = -100\)

   The expression is now simplified to: \(\frac{1}{2} \times [-100]\)

4. Finally, perform the multiplication outside the brackets:

   We need to multiply \(\frac{1}{2}\) by \(-100\).

   \(\frac{1}{2} \times -100 = \frac{-100}{2}\)

   \(\frac{-100}{2} = -50\)

Final Result

The value of the expression \(\frac{1}{2} \nbsp;[{-2(2 + 3)*20}/2]\) is -50.