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Comparing & Ordering Rational Numbers

Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has been teaching math for over 9 years. Amy has worked with students at all levels from those with special needs to those that are gifted.

Rational numbers, any number expressed in the division of two integers, can be compared and ordered to determine their size, even when the digits may appear larger or smaller. Follow the examples of comparing and ordering rational numbers to learn this concept. Updated: 11/03/2021

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!'

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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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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.

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Practice:
Comparing & Ordering Rational Numbers Quiz

Instructions: Choose an answer and click 'Next'. You will receive your score and answers at the end.

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Order the numbers from least to greatest:

4/5, 5/6, 7/8, 8/9

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