Rational Numbers: Order and Compare

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!


Integers/Rational Numbers and Operations

learning style
personality style
Grade Level
Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!


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: {15, -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:

15 = 1 ÷ 5 = 0.20

-2 = -2.0

1.5 = 1.5

Graph each number on a number line:

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:

  1. Why is it important to be able to convert fractions to decimals?
  2. 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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