Evaluating the Integer Expression

The problem asks us to evaluate the following mathematical expression:

$(-9) - (-60) $ \div $ (-10) + (-3) $ \times $ 8$

To solve this correctly, we need to follow the order of operations, often remembered by the acronym PEMDAS/BODMAS:

• Parentheses (or Brackets)
• Exponents (or Orders)
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

Step-by-Step Solution

1. Perform Division: First, we handle the division part of the expression: $(-60) $ \div $ (-10)$.

   Dividing a negative number by a negative number results in a positive number.

   $ (-60) \div (-10) = 6 $

2. Perform Multiplication: Next, we handle the multiplication part: $(-3) $ \times $ 8$.

   Multiplying a negative number by a positive number results in a negative number.

   $ (-3) \times 8 = -24 $

3. Substitute results: Now, substitute these results back into the original expression:

   $ (-9) - (6) + (-24) $

4. Perform Subtraction: Evaluate the subtraction from left to right: $(-9) - 6$.

   Subtracting a positive number is the same as adding its negative counterpart.

   $ (-9) - 6 = -9 + (-6) = -15 $

5. Perform Addition: Finally, perform the addition: $-15 + (-24)$.

   Adding two negative numbers results in a more negative number.

   $ -15 + (-24) = -15 - 24 = -39 $

Final Answer Check

The calculation step-by-step leads to the result $-39$. This matches one of the options provided.

The expression evaluation follows the standard order of operations:

$ (-9) - (-60) \div (-10) + (-3) \times 8 $

$ = (-9) - (6) + (-24) $

$ = -9 - 6 - 24 $

$ = -15 - 24 $

$ = -39 $