Integers (Negative Numbers) • Topic 1 of 3

Placing Integers on a Number Line

What are Integers?

Integers are whole numbers and their opposites. They include:

  • Positive integers: 1, 2, 3, 4... (to the right of zero)
  • Zero: 0 (neither positive nor negative)
  • Negative integers: -1, -2, -3, -4... (to the left of zero)

The Number Line:

<----|----|----|----|----|----|----|----|----|----|---->
    -5   -4   -3   -2   -1    0    1    2    3    4    5
    
Negative ←                      → Positive

Absolute Value:

  • Distance from zero (always positive)
  • Written as |−5| = 5
  • |3| = 3
INTEGER NUMBER LINE - ANNOTATED:

 Negative Numbers Positive Numbers
 ↓ ↓
 <----●----●----●----●----●----●----●----●----●----●---->
 -5 -4 -3 -2 -1 0 1 2 3 4 5
 
 ←── Getting Smaller ──┼── Getting Larger ──→


PLACING INTEGERS ON NUMBER LINE:

 Where is -3?
 
 <----|----|----|----|----|----|----|---->
 -4 -3 -2 -1 0 1 2
 ↑
 -3 is here!


ABSOLUTE VALUE VISUAL:

 | -4 | = 4 | 4 | = 4
 
 <----|----|----|----|----|----|----|---->
 -4 -3 -2 -1 0 1 2 3 4
 ↑ ↑
 Distance = 4 Distance = 4


REAL-LIFE EXAMPLES OF NEGATIVES:

 Temperature: -5°C (below freezing)
 Elevation: -100 m (below sea level)
 Money: -20 (debt/owed)
 Football: -7 yards (loss)
 Time: -3 hours (3 hours ago)
Solved Examples
1
Worked Example

Draw a number line from -5 to 5 and place -2, 0, 3, -4.

Solution

``` <----|----|----|----|----|----|----|----|----|----|---->

-5 -4 -3 -2 -1 0 1 2 3 4 5 ↑ ↑ ↑ ↑

-4 -2 0 3 ```

2
Worked Example

Which is greater: -5 or -8?

Solution
  • On a number line, numbers increase to the right
  • -5 is to the right of -8
  • Therefore -5 > -8
  • Answer: -5
3
Worked Example

Find |−7| and |3|

Solution
  • |−7| = 7 (distance from 0 is 7 units)
  • |3| = 3 (distance from 0 is 3 units)
  • Answer: 7 and 3

Key Points

  • Integers = ..., -3, -2, -1, 0, 1, 2, 3, ...
  • Left of zero = negative, Right of zero = positive
  • Larger numbers are to the RIGHT
  • Absolute value = distance from zero (always positive)
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.Negative integers lie ___ of zero.
Explanation: Left of zero.
Q2.Positive integers lie ___ of zero.
Explanation: Right of zero.
Q3.Zero is:
Explanation: Neither.
Q4.The opposite of $5$ is:
Explanation: $-5$.
Practice more MCQs → 📝 Assignment · 35 marks