Evaluate numerical expressions involving integers

Key Notes:

1. Understanding Integers

• Integers are whole numbers that can be positive, negative, or zero.
• Examples: -5, -2, 0, 3, 8.

2. Numerical Expressions

• A numerical expression is a mathematical phrase that can include numbers, operation symbols (+, -, *, /), and parentheses, but no variables.
• Examples: 4 + 6, 3 * (-2), (8 – 5) * 3.

3. Order of Operations (PEMDAS)

• Parentheses: Simplify expressions inside parentheses first.
• Exponents: Evaluate exponents (powers or square roots).
• Multiplication and Division: From left to right.
• Addition and Subtraction: From left to right.

4. Adding and Subtracting Integers

• Same signs: Add the absolute values and keep the sign.
  Example: (-5) + (-3) = -8.
• Different signs: Subtract the smaller absolute value from the larger absolute value and keep the sign of the larger number.
  Example: 7 + (-4) = 3.
• When subtracting, add the opposite of the second integer.
  Example: 5 – (-3) = 5 + 3 = 8.

5. Multiplying and Dividing Integers

• Same signs: The product or quotient is positive.
  Example: (-4) * (-3) = 12, 6 ÷ 2 = 3.
• Different signs: The product or quotient is negative.
  Example: (-5) * 2 = -10, 9 ÷ (-3) = -3.

6. Evaluating Expressions with Parentheses

• Always simplify the part inside parentheses first.
• Example: Evaluate (3 + 2) * (-4).
  First, solve inside parentheses: 3 + 2 = 5.
  Then multiply: 5 * (-4) = -20.

7. Examples of Evaluating Numerical Expressions

• Example 1: Evaluate 5 + (-3) * 2.
  Step 1: Multiply: (-3) * 2 = -6.
  Step 2: Add: 5 + (-6) = -1.
• Example 2: Evaluate (-6) – (-2) + 3.
  Step 1: Subtract the negative: (-6) – (-2) = (-6) + 2 = -4.
  Step 2: Add 3: -4 + 3 = -1.