Subtracting negative integers on number line
Subtracting negative integers on a number line is a Grade 8 visual model (Yoshiwara Core Math) for understanding why subtracting a negative equals adding a positive. On a number line, subtraction normally moves left, but subtracting a negative reverses direction — you move right. For example, 3 − (−4) = 3 + 4 = 7: start at 3, move 4 units right. This connects the visual model to the algebraic rule a − (−b) = a + b. Understanding this builds conceptual fluency before applying the rule abstractly in algebra.
Key Concepts
Property Subtracting a negative number gives the same result as adding a positive number. For both operations, we move to the right on the number line.
Examples The problem $4 ( 9)$ becomes an addition problem. We solve $4 + (+9)$ to get $13$. For $ 10 ( 3)$, we change it to $ 10 + (+3)$, which gives us an answer of $ 7$. Subtracting a negative from a negative, as in $ 6 ( 11)$, is the same as $ 6 + 11$, which equals $5$.
Explanation Imagine someone cancels a debt you owe. Taking away that negative debt increases your net worth! Similarly, subtracting a negative number is like adding a positive one, causing you to move right on the number line.
Common Questions
What does subtracting a negative number equal?
Subtracting a negative equals adding a positive. For example, 5 − (−3) = 5 + 3 = 8.
How do you show 3 − (−4) on a number line?
Start at 3. Subtracting −4 means moving right 4 units: 3 → 7. Answer is 7.
Why does subtracting a negative move right on the number line?
Subtraction moves left normally, but subtracting a negative reverses that direction. Two negatives cancel, giving rightward (positive) movement.
How is −2 − (−5) calculated?
Rewrite as −2 + 5. On the number line, move right 5 from −2 to reach 3.
What is the algebraic rule for subtracting a negative?
a − (−b) = a + b. Subtracting a negative always converts to adding the positive.