Addition & Subtraction as Movement

Addition: The Movement Rule

We can solve integer problems using the formula:

• Positive Movement: Move Right.
• Negative Movement: Move Left.

Example 1: $(+2) + (+3)$

1. Start at $+2$.
2. Add $+3$ (Move 3 steps Right).
3. Land on $+5$.

Example 2: $(+2) + (-5)$

1. Start at $+2$.
2. Add $-5$ (Move 5 steps Left).
3. Cross 0 and land on $-3$.

Subtraction: Distance Rule

Subtraction answers the question: “How much do I need to move to get from Start to Target?”

Example: $2 - 5$

• Target: $2$
• Wait! Let’s rephrase. Usually subtraction is $A - B$.
• Standard view: Start at $A$, take away $B$.
• Better View for Integers: Adding the Inverse.

The Golden Rule of Subtraction

To subtract a number, simply add its inverse.

1. Example: $5 - 2 = 5 + (-2) = 3$
2. Example: $2 - 5 = 2 + (-5) = -3$
3. Example: $5 - (-2)$
   • Inverse of $-2$ is $+2$.
   • So, $5 + (+2) = 7$.
   • Subtracting a negative is like adding a positive!