Integers (Negative Numbers) • Topic 3 of 3

Adding & Subtracting Small Integers

Adding Integers Using Number Line:

Adding a positive = move RIGHT
Adding a negative = move LEFT

Rules for Adding Integers:

First Number	Operation	Second Number	Result
Positive	+	Positive	Positive (add)
Positive	+	Negative	Subtract, sign of larger
Negative	+	Positive	Subtract, sign of larger
Negative	+	Negative	Negative (add absolute values)

Subtracting Integers:

Rule: Subtracting a number = adding its opposite

a - b = a + (-b)
a - (-b) = a + b

Examples:

5 - 3 = 5 + (-3) = 2
5 - (-3) = 5 + 3 = 8
-5 - 3 = -5 + (-3) = -8
-5 - (-3) = -5 + 3 = -2

ADDING INTEGERS ON NUMBER LINE:

    Example 1: 3 + (-5) = -2
    
    Start at 3, move LEFT 5 spaces
    
    <----|----|----|----|----|----|----|---->
        -3   -2   -1    0    1    2    3    4
              ↑    ↑    ↑    ↑    ↑
        End  -2   -1    0    1    2   Start 3
        (←5 steps)


    Example 2: -2 + 4 = 2
    
    Start at -2, move RIGHT 4 spaces
    
    <----|----|----|----|----|----|----|---->
        -3   -2   -1    0    1    2    3    4
              ↑    ↑    ↑    ↑
            Start  -1    0    1   End 2
            (-2)   (←4 steps →)


SUBTRACTION AS ADDING OPPOSITE:

    Subtraction problem:  5 - 8 = ?
    
    Step 1: Change to addition: 5 + (-8)
    Step 2: Start at 5, move left 8: 5 → 4 → 3 → 2 → 1 → 0 → -1 → -2 → -3
    Answer: -3
    
    
    Subtraction problem: -3 - (-7) = ?
    
    Step 1: Change to addition: -3 + 7
    Step 2: Start at -3, move right 7: -3 → -2 → -1 → 0 → 1 → 2 → 3 → 4
    Answer: 4

Solved Examples

Worked Example

Add: 5 + (-3)

Solution

Start at 5, move left 3
5 → 4 → 3 → 2
Answer: 2

Worked Example

Add: -4 + (-2)

Solution

Start at -4, move left 2
-4 → -5 → -6
Answer: -6

Worked Example

Subtract: 8 - 12

Solution

8 - 12 = 8 + (-12)
Start at 8, move left 12
8 → 7 → 6 → 5 → 4 → 3 → 2 → 1 → 0 → -1 → -2 → -3 → -4
Answer: -4

Worked Example

Subtract: -6 - (-4)

Solution

-6 - (-4) = -6 + 4
Start at -6, move right 4
-6 → -5 → -4 → -3 → -2
Answer: -2

Worked Example

Simplify: 3 + (-7) + 2

Solution

First: 3 + (-7) = -4
Then: -4 + 2 = -2
Answer: -2

Key Points

Adding positive = move right
Adding negative = move left
Subtraction = add the opposite (keep-change-change)
Same signs: add and keep sign
Different signs: subtract and keep sign of larger absolute value
Practice with small numbers first

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.$(-3)+(-4)=$

Explanation: Same sign: add, keep sign.

Q2.$5+(-2)=$

Explanation: $5-2=3$.

Q3.$(-6)-(-2)=$

Explanation: $-6+2=-4$.

Q4.Subtracting a negative is the same as:

Explanation: Adding.

Practice more MCQs → 📝 Assignment · 35 marks