Solve Mixed Operations: 0.8 + 2/10 - (3/2 × 4/2) + 1/2

Complete the exercise:

$0.8+\frac{2}{10}-\frac{3}{2}\times\frac{4}{2}+\frac{1}{2}=$

To solve the exercise:

$0.8+\frac{2}{10}-\frac{3}{2}\times\frac{4}{2}+\frac{1}{2}=$

We will use the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right))

Step-by-step Solution:

• First, simplify the fractions and perform multiplication:

  $\frac{3}{2} \times \frac{4}{2}$

  Multiply the numerators and the denominators:

  $\frac{3 \times 4}{2 \times 2} = \frac{12}{4}$

  Simplify the fraction:

  $\frac{12}{4} = 3$

• Now, substitute back into the expression:

  $0.8 + \frac{2}{10} - 3 + \frac{1}{2}$

• Convert the decimals and fractions to have a common base for easy calculation:

  $0.8 = \frac{8}{10}$ and simplify $\frac{2}{10} = \frac{1}{5} = \frac{2}{10}$ as it is.

  The fraction $\frac{1}{2} = \frac{5}{10}$.

• Now simplify without changing the structure of the original question:

  $\frac{8}{10} + \frac{2}{10} - 3 + \frac{5}{10}$

• Add the fractions:

  $\frac{8}{10} + \frac{2}{10} + \frac{5}{10} = \frac{15}{10} = 1.5$

• Finally, subtract the whole number:

  $1.5 - 3$

  The result is:

  $1.5 - 3 = -1.5$

Thus, the final result is -1.5, indicating a typo or misrepresentation in the given correct answer statement 1.5-. However, following the provided order of operations correctly, the computed solution is $-1.5$.