directed numbers

Directed Numbers

• Directed numbers consist of magnitude and direction: positive or negative.
• Positive numbers are greater than zero; negative numbers are less than zero.
• Zero is considered neutral.

Addition of Directed Numbers

• Example: Starting at 3, adding 5 results in 8.
• Subtracting 10 from 8 means moving in the negative direction to arrive at -2.
• Adding a negative: -2 + (-4) moves left resulting in -6 (same as subtraction).

Subtraction of Negative Numbers

• Example: -6 - (-11) involves moving positively due to subtracting a negative; results in 5.
• General rule: Subtracting a negative equals adding a positive.

Real-world Application

• Financial example: Starting with $100, adding $200 leads to $300. Spending $500 results in $-200 debt.
• Further spending $400 leads to $-600. Earning $800 gets back to $200 positive.

Multiplication and Division of Directed Numbers

• Product or quotient of two positive numbers is positive.
• Example: Tripling debt of -200 gives -600.
• Halving debt (-200) results in -100.
• A negative number multiplied or divided by a positive yields a negative.
• A negative multiplied or divided by another negative yields a positive.
• Confusion often arises in the latter case; requires further exploration.