*Contributor: Erika Wargo. Lesson ID: 12702*

What's a rational number? Is it a number that's sane and can think clearly? It's simply a number that can be expressed as a fraction. You meet them in daily life, so get to know how to work with them!

categories

subject

Math

learning style

Visual

personality style

Beaver

Grade Level

Middle School (6-8)

Lesson Type

Quick Query

You are playing a game with your family and the object of the game is to finish with the most points. At the end of the game, you have 6 points, your brother has -5 points, your sister has -2 points, and your mom has 1 point. Who won the game? How can you use a number line to help compare the scores?

*Rational numbers* are numbers that can be expressed as a *fraction*.

Positive and negative rational numbers can be represented on a *number line*. A number line can be used to help you determine which number is larger and which is smaller. The numbers to the left on a number line are smaller than the numbers to the right on a number line.

In order to compare numbers, you need to use inequality signs:

Greater than: >

Less than: <

Equal to: =

As you watch a video to learn more about comparing rational numbers, address the following in your math journal:

- In your own words, explain the meaning of a rational number.
- What two rules should be followed when comparing rational numbers?
- How can you use a number line to help you compare rational numbers?

Discuss the questions above with a parent or teacher after you watch Learn League's *Comparing Rational Numbers*:

When comparing and ordering rational numbers, first convert each number to the same form. When comparing fractions and decimals, it may be easier to convert each number to a decimal first.

Watch a short video to review how to convert rational numbers. As you watch *Math Shorts Episode 11 - Converting Rational Numbers*, write in your math journal: How do you convert a fraction to a decimal?

Fractions can be converted to a decimal using long division. But you can also convert a fraction to a decimal by using a calculator. If the fraction were ¼, you would type in the numerator divided by the denominator: 1 ÷ 4 = 0.25.

**Example** Compare and order the following rational numbers from least to greatest: {^{1}⁄_{5}, -2, 1.5}

First, convert the rational numbers to be in the same form. Since there is a fraction and a decimal number, change all the numbers to decimals:

^{1}⁄_{5} = 1 ÷ 5 = 0.20

-2 = -2.0

1.5 = 1.5

Graph each number on a number line:

Write the numbers in order from least to greatest, or as they appear from left to right on the number line:

-2.0 < 0.20 < 1.5

In your math journal, write a response to the following:

- Why is it important to be able to convert fractions to decimals?
- Why is it important to be able to order and compare rational numbers?

In the *Got It?* section, you will practice ordering and comparing rational numbers through online games.

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