Solving Integer Expressions: Step-by-Step Guide

We are asked to solve the mathematical expression: $(-4) \{19 – (-2) × (-8)\}$.

To solve this expression, we need to follow the order of operations, often remembered by acronyms like BODMAS or PEMDAS.

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

Applying Order of Operations to the Expression

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

The expression is: $(-4) \{19 – (-2) × (-8)\}$

1. Solve the operations inside the curly braces { }:

   Inside the braces, we have $19 – (-2) × (-8)$. According to the order of operations, multiplication comes before subtraction.

   First, calculate $(-2) × (-8)$. When multiplying two negative numbers, the result is positive.

   $\qquad (-2) × (-8) = 16$

   Now substitute this back into the expression inside the braces:

   $\qquad 19 – 16$

   Perform the subtraction:

   $\qquad 19 – 16 = 3$

   So, the value inside the curly braces is $3$. The expression simplifies to: $(-4) \{3\}$.

2. Perform the final multiplication:

   Now we have $(-4) × 3$. When multiplying a negative number by a positive number, the result is negative.

   $\qquad (-4) × 3 = -12$

Final Result of the Integer Expression

The value of the expression $(-4) \{19 – (-2) × (-8)\}$ is $-12$.

Revision Table: Order of Operations

Additional Information: Integer Operations

Understanding how to perform operations with integers (positive and negative whole numbers) is crucial for solving such problems.

• Multiplication of Integers:
  • Positive × Positive = Positive
  • Negative × Negative = Positive (as seen with $(-2) \times (-8)$)
  • Positive × Negative = Negative
  • Negative × Positive = Negative (as seen with $(-4) \times 3$)
• Subtraction of Integers:

  Subtracting a negative number is the same as adding a positive number. For example, $19 – (-16)$ is the same as $19 + 16 = 35$. In our problem, $19 – (-2) \times (-8)$ became $19 – 16$.

Practicing these rules helps in accurately solving mathematical expressions involving integers.