Let's understand subtraction step by step. In basic subtraction like 5 minus 2 equals 3, we start at 5 on the number line and move left by 2 positions to reach 3. Subtraction means moving left on the number line. But what happens when we have 2 minus negative 1? This special case requires us to understand what it means to subtract a negative number.
Negative numbers are numbers less than zero, and they appear to the left of zero on the number line. We see negative numbers in everyday life: temperatures below freezing like negative 5 degrees Celsius, debt like negative 10 dollars, or basement floors like negative 1. On the number line, negative numbers occupy the left side of zero, while positive numbers are on the right. The number negative 1 is positioned exactly one unit to the left of zero. Understanding this position is crucial for our subtraction problem.
Here's the fundamental rule for subtracting negative numbers: subtracting a negative is the same as adding a positive. The general form is a minus negative b equals a plus b. Let's see this with examples. Five minus negative three becomes five plus three, which equals eight. Seven minus negative two becomes seven plus two, which equals nine. On the number line, instead of moving left as we normally do for subtraction, we move right because we're adding. Removing a negative creates a positive effect. This rule is the key to solving our original problem.
Now let's apply the double negative rule to solve 2 minus negative 1. Step 1: Apply the double negative rule. 2 minus negative 1 becomes 2 plus 1. Step 2: Perform the addition. 2 plus 1 equals 3. Therefore, 2 minus negative 1 equals 3. On the number line, we start at 2. Instead of moving left as we normally would for subtraction, we move right by 1 position because we're subtracting a negative number, which is the same as adding a positive. This brings us to 3, confirming our answer.
Let's reinforce our understanding with multiple visual methods. Method 1 uses integer chips: positive chips represent positive numbers, negative chips represent negative numbers. When we have 2 positive chips and remove 1 negative chip, removing the negative chip is equivalent to adding a positive chip, giving us 3 positive chips total. Method 2 uses the number line again: we see the direction change from moving left to moving right when subtracting a negative. Here's a real-world analogy: removing a debt is like gaining money. If you have 10 dollars and remove a 5 dollar debt, it's the same as gaining 5 dollars, giving you 15 dollars total. All these methods confirm that 2 minus negative 1 equals 3.