🎯 Learning Objectives

By the end of this lesson, you should be able to:

• Identify different number systems (Natural numbers, Integers, Rational numbers).
• Represent numbers on a number line.
• Perform basic operations with directed numbers (positive and negative numbers).
• Apply directed numbers to real-life situations (e.g., temperature, bank balances).

1. What is a Number System?

A number system is a way of writing and expressing numbers. In mathematics, we group numbers into different "families" based on their properties.

• Natural Numbers (N): These are the counting numbers. 
  Example: 1, 2, 3, 4, 5...
• Integers (Z): This includes all natural numbers, their negative counterparts, and zero. 
  Example: ...-3, -2, -1, 0, 1, 2, 3...
• Rational Numbers (Q): Any number that can be written as a fraction (a/b), where 'b' is not zero. This includes whole numbers, fractions, and terminating decimals. 
  Example: ½, -4, 0.75

2. The Number Line

A number line is a straight line with numbers placed at equal intervals. It helps us visualize the relationship between positive and negative numbers.

• Numbers to the right of zero are positive (+).
• Numbers to the left of zero are negative (-).
• Zero (0) is neither positive nor negative; it is the neutral starting point.

Visualize this: Imagine a thermometer. 0°C is freezing. 5°C is warm (positive), and -5°C is below freezing (negative).

3. Directed Numbers in Real Life

Directed numbers (positive and negative) are used everywhere in Malawi and the world:

• Temperature: Mzuzu might be 15°C (positive), while a freezer is at -18°C (negative).
• Banking: Depositing MWK 5,000 is +5000. Withdrawing or owing MWK 2,000 is -2000.
• Elevation: Mount Mulanje is above sea level (+), while some lake beds are measured relative to sea level (0).

4. Rules for Operating Directed Numbers

Addition and Subtraction:

• Adding a negative is the same as subtracting: 5 + (-3) = 5 - 3 = 2
• Subtracting a negative is the same as adding: 5 - (-3) = 5 + 3 = 8 (Think: "minus a minus makes a plus")

Multiplication and Division:

• Positive × Positive = Positive (3 × 4 = 12)
• Negative × Negative = Positive (-3 × -4 = 12)
• Positive × Negative = Negative (3 × -4 = -12)

📌 Summary

Understanding number systems is the foundation of all mathematics. Always use a number line to help you visualize problems with negative numbers, and remember the golden rule: subtracting a negative number makes it more positive!