Integers on a Number Line

In these lessons, we will learn

• how to locate and place integers on a number line
• how to represent and compare integers on a number line
• how to compare and order integers using a number line
• how to identify the opposite of a number

What is a Number Line?
A number line is a straight line where numbers are placed at equal intervals. It extends infinitely in both directions and serves as a visual representation for comparing and ordering numbers.

The following figure shows an integer number line. Scroll down the page for examples and solutions.

Integer Worksheets
Practice your skills with the following integer worksheets:
Printable & Online Integer Worksheets

Representing Integers on the Number Line:
Integers, which are whole numbers (0, 1, 2, 3, …) and their negatives (-1, -2, -3, …), are placed at specific points along the number line according to these rules:

1. The integer 0 is placed at the center of the number line. It acts as the reference point.
2. All positive integers (1, 2, 3, …) are located to the right of zero. They are placed at equal intervals, increasing in value as you move further to the right. The distance between 0 and 1 is the same as the distance between 1 and 2, between 2 and 3, and so on.
3. All negative integers (-1, -2, -3, …) are located to the left of zero. They are also placed at equal intervals, decreasing in value (becoming more negative) as you move further to the left. The distance between 0 and -1 is the same as the distance between -1 and -2, between -2 and -3, and so on.

When comparing and ordering numbers, we should refer to a number line and look at the position of the number on the line in relation to 0 to determine its value. Any number to the right is always greater than any number to the left. This applies to both positive and negative integers.

When placing integers on a number line, we first look at the sign to see whether it is a positive or negative number. Then we look at the digit to determine how far away from 0 the number should go. All negative numbers are less than 0 and placed to the left of the 0 on the number line.

Using the Number Line to Understand Integers:

1. Comparing Integers: You can easily see which of two integers is greater by observing their position on the number line. The integer further to the right is greater.
2. Opposites: Integers that are the same distance from zero but on opposite sides are called opposites (e.g., 3 and -3).
3. Arithmetic Operations: The number line can be used to visualize addition and subtraction of integers.
   Addition: To add a positive integer, move to the right. To add a negative integer, move to the left.
   Subtraction: To subtract a positive integer, move to the left. To subtract a negative integer, move to the right.

How to locate and plot integers on a number line?
Example:
Identify which of the following are integers and plot them on the number line.
0.3, -2, 1/3, -1.2, 0, 2, 9/7, 4.1, -3

• Show Step-by-step Solutions

Comparing and ordering integers
In this lesson, students learn to compare integers by graphing the integers on a number line. The integer to the left on the number line is always less than the integer to the right. Since negative integers are to the left on a number line, and positive integers are to the right, a negative integer is always less than a positive integer.

Example:
Write the following integers from the least to the greatest.
-12, 7, 0, -1, 11

• Show Step-by-step Solutions

Arranging Integers from Smallest to Largest on Number Line
Examples:
Arrange the following integers from the least to the greatest.
-7, 4, -10, 0, 18, -1

• Show Step-by-step Solutions

How to order integers on the number line and review the definitions of absolute value and opposites?
The absolute value of a number is the distance between the number and zero on the number line.
Opposites are two numbers that are the same distance from zero, but on the opposite side of zero on the number line.

• Show Step-by-step Solutions

Opposite of a given number
Identify each number in the left column with its opposite in the right column.

• Show Step-by-step Solutions

Integers on a Number Line
Learn to represent and compare integers on a number line.
Examples:

1. To what number is the arrow pointing?
   
2. What is the opposite of -80°F ?
   
3. Compare, write > or <. Use a number line to solve.
   2 ___ -7
   

Represent and Compare Integers on a Number Line
Examples:
Learn to represent and compare integers on a number line.

1. Graph -3 on the number line.
   
2. Use <, > or = to make a true sentence. Use a number line to compare.
   
3. Estimate the values for the points A to G and order the points from the least to the greatest.
   

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.