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Comparing & Ordering Rational Numbers

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  • 0:03 Rational Numbers
  • 1:17 Comparing Rational Numbers
  • 2:23 Ordering Rational Numbers
  • 4:24 Example
  • 6:41 Lesson Summary
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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.

Rational Numbers

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!'

Comparing Rational Numbers

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.

Ordering Rational Numbers

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.

Example

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.

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