Integer Multiplication & Division

Understanding Negative Numbers

• Negative numbers mirror positive numbers on the number line.

  • Example: 2 (positive) and -2 (negative), 5 (positive) and -5 (negative).

Multiplying Negative Numbers

• Multiplying a positive number by -1 gives a negative number.

• Multiplying a negative number by -1 flips it back to positive.

  • Example:

    • -1 × -3 = 3 (returns to positive).

• Observing patterns in multiplying negatives:

  • Odd number of negatives = negative outcome.

  • Even number of negatives = positive outcome.

Rules for Multiplication

• Even number of negative factors: Result is positive.

  • Example: (-1) × (-1) = 1 (no effect on product).

• Odd number of negative factors: Result is negative.

  • Example: (-1) × 1 = -1.

Examples with Positive and Negative Multiplication

• Expression: 3 × 5 = 15

  • Variations:

    • 3 × -5 = -15 (1 negative)

    • -3 × 5 = -15 (1 negative)

    • -3 × -5 = 15 (2 negatives).

• Simplification Strategy: Ignore negative signs when multiplying/dividing, then determine sign based on number of negatives:

  • Even negatives = positive.

  • Odd negatives = negative.

Rules for Division of Integers

• Division follows the same negative rules:

  • Example:

    • 8 ÷ 2 = 4 (positive)

    • 8 ÷ -2 = -4 (1 negative)

    • -8 ÷ 2 = -4 (1 negative)

    • -8 ÷ -2 = 4 (2 negatives).

Final Takeaways

• Multiplication and division of integers with negative factors follows distinct rules based on even (positive result) or odd (negative result) factors.