Positive and Negative Integers

1. Understanding Positive and Negative Numbers

• Positive Numbers:

  • Represent quantities greater than zero.

  • Often written without a sign (e.g., 5) or with a plus sign (e.g., +5).

  • Examples:

    • Temperature above zero degrees Celsius (e.g., +20°C)

    • Money earned or gained

    • Heights above sea level

• Negative Numbers:

  • Represent quantities less than zero.

  • Always written with a minus sign (e.g., -3).

  • Examples:

    • Temperature below zero degrees Celsius (e.g., -10°C)

    • Money owed or lost

    • Depths below sea level

2. The Number Line

• A visual representation of numbers, extending infinitely in both positive and negative directions.

• Zero is the central point.

• Numbers to the right of zero are positive, and those to the left are negative.

• The further a number is from zero, the greater its magnitude (absolute value).

3. Operations with Positive and Negative Numbers

• Addition:

  • Same signs: Add the magnitudes and keep the sign.

    • Example: -3 + (-2) = -5

  • Different signs: Subtract the smaller magnitude from the larger and keep the sign of the number with the larger magnitude.

    • Example: 5 + (-2) = 3

• Subtraction:

  • Change subtraction to addition of the opposite.

    • Example: 5 - (-2) = 5 + 2 = 7

• Multiplication and Division:

  • Same signs: Result is positive.

    • Example: (-2) * (-3) = 6

  • Different signs: Result is negative.

    • Example: 5 * (-2) = -10

4. Order of Operations (PEMDAS/BODMAS)

• A set of rules to ensure consistent evaluation of expressions.

• P/B - Parentheses/Brackets: Perform operations within parentheses first.

• E/O - Exponents/Orders: Evaluate exponents (powers).

• M/D - Multiplication and Division: Perform from left to right.

• A/S - Addition and Subtraction: Perform from left to right.

Example:

1. 2 * (3 + 4) - 5

2. 2 * (7) - 5

3. 2 * 7 - 5

4. 14 - 5

5. 9