Evaluate Mathematical Expression Step-by-Step

This solution explains how to evaluate the given mathematical expression using the standard order of operations, often remembered by the acronym PEMDAS or BODMAS.

Expression Overview

The expression we need to evaluate is:

$-12 - \{-8 \times (6-12) + 30 \div (-6)\}$

Order of Operations Rules

To ensure accuracy, we follow the order of operations:

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

Calculation Breakdown

Let's break down the calculation step-by-step:

1. Parentheses Calculation:

   First, we solve the innermost part: the expression within the parentheses $(6-12)$.

   $ (6 - 12) = -6 $

2. Multiplication within Braces:

   Next, we perform the multiplication part inside the curly braces: $-8 \times (6-12)$. Using the result from step 1, this becomes $-8 \times (-6)$.

   $ -8 \times (-6) = 48 $

3. Division within Braces:

   Then, we perform the division part inside the curly braces: $30 \div (-6)$.

   $ 30 \div (-6) = -5 $

4. Addition within Braces:

   Now, we add the results of the multiplication and division inside the braces: $48 + (-5)$.

   $ 48 + (-5) = 48 - 5 = 43 $

   The expression inside the curly braces simplifies to $43$.

5. Final Subtraction:

   Finally, we perform the main subtraction: $-12 - \{\dots\}$. Substituting the value we found for the braces:

   $ -12 - 43 $

   $ -12 - 43 = -55 $

Final Answer

The result of evaluating the expression $-12 - \{-8 \times (6-12) + 30 \div (-6)\}$ is $-55$.