Back To Course

6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will be able to look at any rational number and compare it with any other rational number. Learn what you need to do so that you know which number is greater or lesser than another.

Sam runs over to you looking scared. He has a piece of paper in his hand. He tells you he desperately needs your help. He knows that you are learning math using really helpful video lessons, and he feels that you are the one that can help him with his problem. He shows you his paper. On it, you see this problem: Order these numbers from least to greatest: 1, 4, 0, 3, 3/2, 4/5, and 10.

Sam says, 'Can you help me?' You tell him of course you can. You look at these numbers and you realize that they are **rational numbers**, numbers that can be written as the division of two integers. All of the numbers can be written as a fraction of two integers. For example, the 1 can be rewritten as 1/1. The 4 can be rewritten as 4/1. The 3/2 and the 4/5 are already written as the fraction of two integers.

You ask Sam, 'Do you want to go over this problem right now?' Sam says, 'Yes!' You say, 'Okay! Let's get started then. Have a seat!'

You begin by telling him how to compare two rational numbers to each other. You point to the 3 and the 3/2. How can Sam tell which number is greater or lesser? You tell Sam that for the rational number 3/2, Sam first needs to divide it to get a decimal number. Dividing 3 by 2, we get 1.5. Sam can now look at the numbers 3 and 1.5 to see which is greater or lesser. 1.5 is greater than 1 and less than 2. Is this less than 3? Yes, so 1.5 is less than 3, and 3 is greater than 1.5.

To compare the numbers 4 and 4/5, the same process is followed. First, we divide the 4 by the 5. What do we get? We get 0.8. Is 0.8 greater or lesser than 4? Well, 0.8 is less than 1 and greater than 0. This is definitely less than 4. So, 4 is greater than 0.8.

You ask Sam, 'How do you feel about comparing rational numbers now?' Sam says, 'I understand that part now. What's next?'

You tell Sam that next comes the ordering the rational numbers part. Since you've already divided the rational numbers to find the equivalent decimal numbers, the numbers that you are ordering now are 1, 4, 0, 3, 1.5, 0.8, and 10. Looking at these numbers, which one is the least? We don't have any negative numbers, so 0 is the smallest. So, you tell Sam to write down 0 first.

You also tell Sam to cross off the 0 from the list since he already wrote it down as part of his answer. What number comes next? You see a 1 and you also see the 0.8. You know all the other numbers are bigger. Which one of these comes first? Well, the 0.8 is between 0 and 1, so the 0.8 comes next.

Then comes the 1. Sam crosses these two numbers out too from this original list. What comes after 1? We have 4, 3, 1.5, and 10 left. Which one is the least of these? The 1.5 is. So, 1.5 comes next. Sam writes the 1.5 after the 1 in his answer list and crosses off the 1.5 from the original problem list. Now we have 4, 3, and 10 left. What's next? The 3 is next, followed by the 4, and then the 10. And we are done! Sam's answer is 0, 0.8, 1, 1.5, 3, 4, and 10. Sam rewrites this using the original rational numbers for his final answer: 0, 4/5, 1, 3/2, 3, 4, and 10.

To make sure Sam really understood what you told him, you give Sam another problem to try. Order these numbers from least to greatest: 1/8, 0, 1, 4, -5, 4/5.

Sam looks at this problem, sees the fractional rational numbers, and converts them to decimal numbers right away so he can compare them to the other numbers. The 1/8 becomes 0.125, and the 4/5 becomes 0.8 after making the division. Now, the numbers that Sam needs to compare are 0.125, 0, 1, 4, -5, and 0.8. Which number is the smallest of the list? The -5 is the smallest because it is a negative number. Sam writes down the -5 as part of his answer, and he crosses off the -5 from the problem list.

What's next? Sam sees the 0.125, 0.8, 0, and 1 as possible next answers. But which one is the least? The 0.125 compared with the 0 is greater, so is the 0.8. Zero is smaller than both of these numbers. So, 0 comes next. 1 is the biggest. Since 1 is the largest, Sam needs to compare the 0.125 and the 0.8. Which one is smaller? The 0.125 is smaller than the 0.8, so the 0.125 comes next.

Then comes the 0.8 and then the 1. What is left from the problem list now? The 4 is left. So, Sam writes down the 4 at the very end of his ordered list. He now has -5, 0, 0.125, 0.8, 1, and 4. He rewrites this so that his final answer uses the numbers as originally written: -5, 0, 1/8, 4/5, 1, and 4.

You check Sam's work, and you give him a big smile, and you write a big A+ on his paper for a correct answer.

Let's review what we've learned. **Rational numbers** are numbers that can be written as the division of two integers. To compare rational numbers, we must first divide them to get a decimal number. After getting the equivalent decimal numbers, we can them compare them to other numbers to see which one is greater or lesser.

After this lesson, you should be able to:

- Define rational numbers
- Explain how to compare and order rational numbers

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
1 in chapter 12 of the course:

Back To Course

6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

- Computer Science 109: Introduction to Programming
- Introduction to HTML & CSS
- Introduction to JavaScript
- Computer Science 332: Cybersecurity Policies and Management
- Introduction to SQL
- Early Civilizations & The Ancient Near East
- Fundamental Overview of World War I
- The Virginia Dynasty & Jacksonian America
- 1920's America and the Great Depression
- Building the United States After the American Revolution
- CEOE Test Cost
- PHR Exam Registration Information
- Claiming a Tax Deduction for Your Study.com Teacher Edition
- What is the PHR Exam?
- Anti-Bullying Survey Finds Teachers Lack the Support They Need
- What is the ASCP Exam?
- ASCPI vs ASCP

- Subtraction in Java: Method, Code & Examples
- Hydrogen Chloride vs. Hydrochloric Acid
- Extraction of Aluminum, Copper, Zinc & Iron
- Iroquois Culture, Traditions & Facts
- Noun Clauses Lesson Plan
- Adverb of Manner Lesson Plan
- Timeline Project Ideas for High School
- Quiz & Worksheet - Multi-Dimensional Arrays in C
- Quiz & Worksheet - What is a Diastereoisomer?
- Quiz & Worksheet - Mauryan Empire Art & Culture
- Quiz & Worksheet - What is a Convergent Sequence?
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- NGSS | Next Generation Science Standards Guide for Teachers
- 8th Grade Math Worksheets & Printables

- Remedial Algebra II
- Macroeconomics Textbook
- Explorations in Core Math - Geometry: Online Textbook Help
- NMTA Health (505): Practice & Study Guide
- Harcourt Social Studies - US Civil War to the Present: Online Textbook Help
- Praxis Middle School Science: Mechanics in Physics
- AEPA: World Politics
- Quiz & Worksheet - Linear Equations & 3-D Graphing
- Quiz & Worksheet - Influence of Race & Ethnicity in Great Britain & U.S. Life & Policy
- Quiz & Worksheet - Overcoming Mistakes When Speaking
- Quiz & Worksheet - Act & Rule Utilitarianism in Business Ethics
- Quiz & Worksheet - Center of Mass

- Formula Mass of a Compound: Definition & Formula
- The Catcher in the Rye Chapter 19: Summary & Quotes
- Cool Math Puzzles
- First Grade Word Walls: List & Activities
- Teacher Appreciation Week Ideas
- Education Advocacy Groups & Organizations
- 4th Grade Math Centers
- Cost of Standardized Testing
- Next Generation Science Standards in California
- Cost of Standardized Testing
- How to Pass Algebra 1
- Common Core Standards in Rhode Island (RI)

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject