The Number Line

Lesson 3.03

After completing this lesson, you will be able to say:

• I can locate a number and its opposite on a number line.

• I can determine that an opposite of an opposite is the number itself.

• I can find and position numbers on horizontal and vertical number lines.

Key Words

Number line:A straight line with tick marks along its length to indicate locations of numbers.

Integer:A whole number, a negative whole number, or 0, such as -405, -31, 0, 15, and 23.

Coordinate:A number used to indicate the position of a point.

Creating a Number line

Let’s make a number line that is centered at 0

In order to make a simple number line, you start by drawing a straight line with arrows on the end. Place a tick mark in the middle and label it 0.Then put tick marks evenly to the right.

Create the same 10 tick marks to the left of 0, the negative sign is used to represent numbers with opposite meaning. On a number line, the negative sign means that these numbers are to the left of zero. Label each tick mark up to -10

The number line

Your final product shows a number line with positive whole numbers, negative whole numbers, and 0. This represents a number line of integers

The Number Line

Points are plotted on the number line to represent locations of objects

Try It!

Explain the point’s location from 0 using the number line below.

Check your work

The point is at 30, which is 30 spaces to the right of 0.

The point is only 3 tick marks away from 0, but it is actually 30 units away. This is because there are 10 spaces between each of the tick marks. As long as the tick marks are equally spaced and are multiples of the same number, the number line is fine.

Try It

Describe the location of point A.

Check your work

This number line only shows the even numbers. The point is located halfway between the −6 and −4, which would be −5. The −5 is 5 spaces to the left of 0. Sometimes number lines can skip over integers, so be sure to look carefully at the tick marks.

Rational Numbers

Rational number:

A number that can be written as a ratio of two numbers; this includes all integers, fractions, and decimals that terminate.

Rational Numbers

Numbers are broken down into various groups depending on their characteristics.

As you can see, rational numbers include all of the number groups shown

Rational Numbers and the Number Line

Some number lines will look just like the ones you have been working with up until now. Fractions and decimals are simply plotted in between the integers, as they represent only part of a whole.

In the number line, the tick marks were all labeled with integers. So plotting the fractions and decimals can be a challenge, as you will have to place the point that makes the most sense.

For example, 11.1 is closer to 11 than it is to 12, so the number line should show this.

Rational Numbers and the number line

Try It

Check your work

Try It

Check your work

Opposites

Every rational number has an opposite. This is the number that is on the opposite side but is an equal number of units away from zero on a number line. Zero is its own opposite.

Examples: − (−4.5) = 4.5 − (−9) = 9

Try it

Check your work

The opposite of ¼ is -¼

Now that you completed this lesson, you should be able to say:

• I can locate a number and its opposite on a number line.

• I can determine that an opposite of an opposite is the number itself.

• I can find and position numbers on horizontal and vertical number lines.