Question
How do we add and subtract integers (positive and negative numbers) using number line rules?
Solution — Step by Step
The number line has zero in the middle. Positive numbers go right, negative numbers go left.
Moving right = adding a positive number Moving left = adding a negative number (or subtracting a positive)
Think of it as walking: facing right is positive direction, facing left is negative direction.
Same signs — add the values, keep the common sign:
- (both positive, move right twice)
- (both negative, move left twice)
Different signs — subtract the smaller value from the larger, take the sign of the larger:
- (7 is bigger, so positive)
- (7 is bigger, so negative)
Subtraction of integers is the same as adding the opposite (additive inverse):
So:
This single rule handles every subtraction case.
graph TD
A[Integer Operation] --> B{Addition or Subtraction?}
B -->|Subtraction| C[Convert: a - b becomes a + opposite of b]
C --> D[Now treat as addition]
B -->|Addition| D
D --> E{Same signs?}
E -->|Yes| F[Add values, keep common sign]
E -->|No| G[Subtract smaller from larger, take sign of larger]Why This Works
The number line gives us a physical picture of what negative numbers mean. When we subtract a negative, we are removing a “debt” — which is the same as gaining. That is why . We removed a debt of 5 from a debt of 3, ending up with a gain of 2.
The rule “subtraction = adding the opposite” works because every integer has an additive inverse: the number that brings you back to zero.
Alternative Method
Use the “chip model” from NCERT: imagine red chips as negative and blue chips as positive. Equal numbers of red and blue cancel each other (make zero pairs). What remains after cancellation gives the answer and its sign.
For example, : you have 5 red and 3 blue chips. Three pairs cancel, leaving 2 red chips = .
Common Mistake
The most common Class 6 mistake: students write by just adding all the numbers with a negative sign. Remember, subtracting a negative flips it to addition: . Always convert subtraction to addition first, then apply the sign rules.