Ordering of Integers

Ordering integers means arranging numbers based on their size. A number line is a useful tool for visually comparing and ordering integers.

• Numbers on the right side of a number line are greater than numbers on the left side.
• Numbers on the left side of a number line are smaller than those on the right.
  
• 5 is to the right of 2, meaning 5 > 2.
• 0 is to the right of -3, meaning 0 > -3.
• 2 is to the right of -1, meaning 2 > -1.
• -4 is to the left of -3, meaning -4 < -3.
• -3 is to the left of 4, meaning -3 < 4.

1. Every positive integer is greater than 0.
2. Every positive integer is greater than every negative integer.
3. Zero is greater than every negative integer but smaller than every positive integer.
4. Every negative integer is smaller than every positive integer.

Ascending Order
Question: Arrange the following integers in ascending order:
5, −8, 0, 3, −5, −10, 9, and −2
Solution:

• First, draw a number line
  
• The given integers in ascending order (from smallest to largest) are
  -10 < -8 < -5 < -2 < 0 < 3 < 5 < 9 

Descending Order
Question: Arrange the following integers in descending order:
6, −4, 5, −7, 0, −6, −2, 3
Solution:

• First, draw a number line:
  
• The integers in descending order (from largest to smallest) are
  6 > 5 > 3 > 0 > -2 > -4 > -6 > -7