Directed Numbers
Adding Directed Numbers
🎯 The Idea – Movement on the Number Line
Addition can be thought of asmovement on the number line:
- Adding a positive number = move right ↗ ↗
- Adding a negative number = move left ↙ ↙
➕➕ Adding Two Positive Numbers
Rule: Add the values, result is positive
✏️ Example: \(3 + 5 = ?\)
\(3 + 5 = 8\) ✓
✏️ More examples:
\(7 + 4 = 11\)
\(10 + 25 = 35\)
\(1.5 + 2.5 = 4\)
➖➖ Adding Two Negative Numbers
Rule: Add the absolute values, result is negative
✏️ Example: \((-3) + (-5) = ?\)
\((-3) + (-5) = -8\) ✓
💡 Think of it: Two debts combine into a larger debt!
Debt of ₪3 + debt of ₪5 = debt of ₪8
✏️ More examples:
\((-7) + (-4) = -11\)
\((-10) + (-20) = -30\)
\((-1) + (-1) = -2\)
➕➖ Adding a Positive and a Negative Number
Rule: Subtract the absolute values; the sign belongs to the larger one
✏️ Example 1: \(7 + (-3) = ?\)
The larger absolute value is 7 (positive)
\(7 - 3 = 4\), and the result is positive
\(7 + (-3) = 4\) ✓
✏️ Example 2: \(3 + (-7) = ?\)
The larger absolute value is 7 (negative)
\(7 - 3 = 4\), and the result is negative
\(3 + (-7) = -4\) ✓
💡 Think of it: money vs debt!
I have ₪7 and a debt of ₪3 → I have ₪4 left
I have ₪3 and a debt of ₪7 → I am ₪4 in debt
📋 Rules Table for Addition
| Addition type | Operation | Result sign | Example |
|---|---|---|---|
| (+) + (+) | Add | + | \(3+5=8\) |
| (-) + (-) | Add | - | \((-3)+(-5)=-8\) |
| (+) + (−) or (−) + (+) | Subtract | of the larger | \(7+(-3)=4\) |
📝 Summary
Same sign: add and keep the sign
Different signs: subtract, take the sign of the larger
Addition = movement on the number line!