How to Compare and Order Integers: A Step-by-Step Guide with Examples, Worksheets & MCQs

Published: 16 Feb 2025

Welcome to our guide on ordering and comparing integers! In this post, you’ll learn how to use number lines and real-life examples to easily figure out how integers line up and relate to each other. With clear steps, free downloadable worksheets, and fun MCQs for Grades 6-8, you’ll quickly master these essential math skills. Let’s get started!

Absolute or Numerical value of an Integer

Absolute or Numerical value is the value of integers which is measured from ( 0 ). Absolute value is denoted by vertical bars by using the symbol (| | ).

The absolute or numerical value of any integer (positive or negative) is always positive.

The absolute value of ( |+10| ) is ( 10 ) .
The absolute value of ( |-10 | ) is ( 10 ) .
The absolute value of ( |0 | ) is ( 0 ) .

Note:
The distance of (10) and (-10) is same from (0) but in opposite directions.

Numerical or Absolute Value

The numerical value or absolute value of the same positive or negative numbers is equal.
The numerical value of ( +7 ) and ( -7 ) is equal which is ( ‘7’ )

Feature of Integers
Integers have two features:

Numerical Value
Signs ( (+, -) )

Numerical value is the value of integers measured from “(0)”.
The sign (+ ) or (- ) with Numerical Value shows the direction relative to zero.

( spadesuit +37 { ^oC} ) shows high temperature (Hotness).
( spadesuit -5 { ^oC} ) shows low temperature (Coldness).

Represent Integers on a Number Line

The arrows on both sides indicated that positive and negative integers keep counting.
Positive integers are to the right of zero.
Negative integers are to the left of zero.

Note:

The distance between any two points on the number line is always same or equal.
Positive and Negative integers are represented on the number line in opposite direction.

Ordering and Comparing Integers on a Number Line

On a number line, the values of integers increase in the right direction and decrease in the left direction.
On a number line, zero is greater than all integers to the left and smaller than all integers to the right.
On a number line, the integers to the right of “0” are greater than those to the left of “0”.
On a number line, zero separates positive and negative integers.

Ordering and Comparing Integers on Number Line

Greater, Smaller, and Consecutive Numbers

On a number line, each number is smaller than all the numbers to its right and greater than all the numbers to its left.
(5>3) means (5) is greater than (3).
(6<9) means (6) is smaller than (9).

“Numbers that are next to each other in counting are called consecutive numbers.”
For example: ( 1, 2, 3 ) or ( -3, -2, -1 )

Example:
Which is greater ( -10 or 3 ) ?
Solution:
On the number line, ( -10 ) lies to the left of ( 3 ).
So, ( 3 ) is greater than ( -10 ).

Ascending and Descending Order

Definitions:

Ascending Order: Arrangement of numbers from smallest to greatest.
Descending Order: Arrangement of numbers from greatest to smallest.

Comparing of Integers without using Number Line

Positive integers (e.g. (1, 2, 3)) are always greater than negative integers (e.g. (-1, -2, -3)).
For positive integers, the larger value is always greater (e.g. (5 > 3)).
For negative integers, the smaller value is always greater (e.g.(-3 > -5) ).
Zero $0$ is greater than all negative integers and smaller than all positive integers.

Example:
Which is smaller ( -5 or -9 ).
Solution:
Here, both the integers have negative signs. Thus, the largest integer is smaller. So ( -9 ) is smaller than ( -5 )

$ Arrange -8,9,-9,8,0,5,-5,6 $ in ascending and descending order.

( -8,9,-9,8,0,5,-5,6 )
Step 1: Separate Positive, Negative, and Zero Integers
Positive integers: (9, 8, 5, 6)
Negative integers: (-8, -9, -5)
Zero: (0)

Step 2: Order Each Group
Integers having positive signs, the greater integer is always greater.
( 9>8>6>5 )
Integers having negative signs, then the smallest integer is greater.
( -5>-8>-9 )
(0) is smaller than the positive and greater than the negative integers. Thus, it lies between them.

Step 3: Ascending and Descending Order
Ascending Order: ( -9, -8, -5, 0, 5, 6, 8, 9 )
Descending Order: ( 9,8,6,5,0,-5,-8,-9 )