Comparing & Ordering Integers on a Number Line

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 and Number Lines

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 in -2 degrees or -15 degrees? When you think about these options, you are already comparing integers. Now, do you know how to properly display these integers, and others, on a number line? If not, don't worry! By the end of this lesson, you will be a number line master. But first, let's start with a review.

Integers include the counting numbers, 0, and the opposites of the counting numbers. Counting numbers are the numbers you use to count (1, 2, 3, …, etc.). The opposites of the counting numbers are the negative versions of the counting numbers (-1, -2, -3, …, etc.). Since we started by talking about temperature, let's use a thermometer to give us an example of a set of integers. Think about an outdoor thermometer like the one in Picture 1.

A thermometer showing temperatures from -30 to 60 degrees

This thermometer is labeled with integers from -30 to 60, in increments of ten. In a warm environment, the temperature is a positive integer and, in a very cold environment, the temperature could be a negative integer.

In mathematics, we use often use a number line to give us a picture when we are dealing with integers. Like our thermometer in Picture 1, a number line is a straight line with tick marks at equal intervals that are labeled with integers in consecutive order. The thermometer is a number line with only the tens labeled, but a tick mark indicates every integer. Does that mean you have to use that same style for all of your number lines? Absolutely not! We will talk more about how to label the integers on your number lines as we continue the lesson.

Usually, we draw a number line as a horizontal line. Therefore, we will rotate our thermometer clockwise a quarter turn, as in Picture 2. Then, we are going to zoom in and look at the section of its number line from -10 to 10, with every integer labeled.

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

We will use this number line to help us to compare integers.

Comparing Integers on a Number Line

On a number line, the numbers increase from left to right. We know that 7 is greater than 3. We see that 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 numbers on the number line, even when we go to the negative side.

For example, -1 is less than 2, because -1 is to the left of 2. Think back to our thermometer. It is colder at -1 degree than it is at 2 degrees.

Even as we go further into the negatives, the numbers on the left are still always less than the numbers on the right. For example, -9 is less than -2. This is where many people get confused. Are you thinking about the fact that 9 is more than 2? That is true, but only for positive numbers. When comparing negative numbers, the higher digit means that it is more negative, which makes the number smaller. Again, think about temperatures: -9 degrees is colder than -2 degrees.

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