Integers (Negative Numbers) • Topic 2 of 3

Comparing Integers

Comparing Integers Rules:

Rule	Example	Why?
Positive > Negative	5 > -3	Positive on right
Larger positive > Smaller positive	8 > 3	8 is further right
Smaller negative > Larger negative	-2 > -7	-2 is right of -7
Any negative < 0	-4 < 0	Negative left of zero

Number Line Shortcut:

More Negative ←                     → More Positive
        -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3
         
The farther LEFT, the SMALLER
The farther RIGHT, the LARGER

Comparing Trick:

For negatives, the number with the smaller absolute value is larger!
Example: -3 vs -7 → |−3|=3, |−7|=7 → 3 < 7 → -3 > -7

COMPARING INTEGERS ON NUMBER LINE:

    -8   -7   -6   -5   -4   -3   -2   -1    0    1    2    3
    
    <─────── Smaller ──────┼────── Larger ───────>
    
    Which is greater: -3 or -7?
    
    -8   -7   -6   -5   -4   -3   -2
                  ↑         ↑
                -7         -3
                
    -3 is to the RIGHT → -3 > -7


COMPARISON TABLE:

    Comparison      True?      Reason
    ─────────────────────────────────────
    5 > -2          YES        Positive > negative
    -4 < -1         YES        -4 is left of -1
    0 > -6          YES        Zero > any negative
    -8 < -12        NO         -8 is right of -12
    -3 > -10        YES        -3 is right of -10
    |−5| > |−2|     YES        |-5|=5, |-2|=2, 5>2


USING ABSOLUTE VALUE TO COMPARE NEGATIVES:

    Compare -6 and -3
    
    Step 1: Find absolute values
    |-6| = 6, |-3| = 3
    
    Step 2: Larger absolute value = more negative
    6 > 3, so -6 is more negative
    
    Step 3: More negative = smaller number
    -6 < -3

Solved Examples

Worked Example

Compare: -5 ___ -2 (use <, >, or =)

Solution

On number line: -5 is left of -2
Left = smaller
-5 < -2
Answer: <

Worked Example

Arrange in ascending order: -3, 4, -7, 0, 2

Solution

Smallest to largest (left to right on number line)
-7, -3, 0, 2, 4
Answer: -7, -3, 0, 2, 4

Worked Example

Which is larger: -12 or -9?

Solution

-9 is to the right of -12
Therefore -9 > -12
Answer: -9

Key Points

On number line: LEFT is SMALLER, RIGHT is LARGER
Positive > all negatives
Zero > all negatives, < all positives
For negatives: -1 is largest negative, -100 is smallest
Use absolute value to compare: smaller absolute value = larger number

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.The symbol $>$ means:

Explanation: Greater than.

Q2.Any positive integer is ___ any negative integer.

Explanation: Greater.

Q3.Compare: $-5$ and $-2$.

Explanation: $-5<-2$.

Q4.$0$ is ___ every negative integer.

Explanation: Greater.

Practice more MCQs → 📝 Assignment · 35 marks