Addition and Subtraction on a Number Line

A number line is a straight horizontal line with equally spaced marks (ticks) representing numbers.

• Zero (0) is placed at the center.

• Positive numbers are on the right; negative numbers are on the left.

• Moving one step to the right means adding 1, and moving one step to the left means subtracting 1.

1. Positive + Positive

• Step 1: Start at 0 on the number line.
• Step 2: Move 2 units to the right because +2 is positive.
• Step 3: Now, from +2, move 3 more units to the right for +3.
• Result: You reach +5.

So, +2 + (+3) = 5

2. Positive + Negative

• Step 1: Start at 0 on the number line.
• Step 2: Move 3 units to the right because +3 is positive.
• Step 3: From +3, move 4 units to the left for -4 (since it's negative).
• Result: You reach -1.

So, (+3) + (−4) = −1

3. Negative + Positive

• Step 1: Start at 0 on the number line.
• Step 2: Move 4 units to the left for −4 (negative).
• Step 3: From −4, move 3 more units to the right for +3.
• Result: You reach −1.

So, (−4) + (+3) = −1

4. Negative + Negative

• Step 1: Start at 0 on the number line.
• Step 2: Move 2 units to the left for -2 (negative).
• Step 3: From -2, move 4 units to the right for -4.
• Result: You reach −6.

So, (−2) + (−4) = −6

Example:
1. Using a number line, evaluate (+ 6) − (+ 2). 

1. Mark the numbers +6 and +2 on the number line.
2. Count the steps from +2 to +6. You need to move 4 steps to the right.

Result: (+6) − (+2) = +4

2. Using a number line, evaluate (+5) − (−3)

1. Mark +5 and -3 on the number line.
2. Start at -3 and move 8 steps to the right to reach +5.

Result: (+5) − (−3) = +8

3. Using a number line, find the integer which is :3 less than 4
start from 4 and then move 3 units to the left of 4 to get 1.

• Addition: The sign tells you the direction.

• Subtraction: Count the gap between numbers.

• Positive: Always to the right.

• Negative: Always to the left.

• Zero: The center point of everything.