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Comparing & Ordering Integers on a Number Line

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  • 0:04 Integers
  • 0:57 Number Line
  • 1:33 Comparing Integers
  • 2:36 Ordering Integers
  • 3:40 Lesson Summary
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Lesson Transcript
Instructor: Miriam Snare

Miriam has taught middle- and high-school math for over 10 years and has a master's degree in Curriculum and Instruction.

This lesson will help you better understand integers and number lines. We will look at how to compare two integers as well as how to place integers on a number line in the correct order.

Integers

Would you rather go outside when it's 40 degrees or when it's 60 degrees? How about if you lived in Alaska, would you rather go out when it's -2 degrees or -15 degrees? When you think about these options, you're already comparing integers.

Integers include the counting numbers, 0, and the opposites of the counting numbers. Counting numbers are the numbers you use to count (like 1, 2, 3). The opposites of the counting numbers are the negative versions of the counting numbers (such -1, -2, -3). Let's use a thermometer as an example of a set of integers.

This thermometer is labeled with integers from -30 to 60 in increments of ten.

A thermometer showing temperatures from -30 to 60 degrees

In a warm environment, the temperature is a positive integer, while in a very cold environment, the temperature may be a negative integer.

Number Line

In mathematics, we often use a number line, or a straight line with tick marks at equal intervals labeled with integers in consecutive order. A thermometer is a number line where only the tens are labeled. However, a tick mark indicates every integer.

Usually, we draw a number line as a horizontal line. Therefore, we'll rotate our thermometer clockwise a quarter turn, as shown in this image.

A thermometer with temperatures form -30 to 60 degrees and a number line from -10 to 10

Then, we'll zoom in and look at the section of the number line from -10 to 10, where every integer is labeled. We'll use this number line to compare integers.

Comparing Integers

On a number line, the numbers increase from left to right. For example, 3 is to the left of 7 on the number line, which establishes the relationship that the numbers increase from left to right. This relationship holds true for all of the numbers on a number line, even on the negative side. For instance, -1 is less than 2, because -1 is to the left of 2. Think back to our thermometer. It's colder at -1 degree than it is at 2 degrees.

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