Real numbers are fundamental to mathematics, encompassing various properties that... Show more
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Updated Mar 4, 2026
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Real Numbers: Easy Examples, Properties, and Worksheets for Kids
Shreeya Ram
@shreeyaram_iuea
Examples of Real Numbers and Their Properties
This page continues the exploration of real number properties, focusing on practical examples and applications of the concepts introduced earlier.
The multiplicative inverse property is demonstrated with the example 3 * (1/3) = 1, showing that multiplying a number by its reciprocal yields 1.
The distributive property of multiplication over addition is explained with the example 4 * (3 + 2) = 4 * 3 + 4 * 2, illustrating how multiplication can be distributed across addition.
The page then provides a series of examples to reinforce the understanding of real number properties:
Example 1 focuses on addition and multiplication with positive real numbers, showing 5 + 3 = 8 and 2 * 4 = 8.
Example 2 demonstrates commutativity and associativity with 7 + 9 = 9 + 7 and (3 + 4) + 2 = 3 + (4 + 2).
Example 3 illustrates the identity and inverse properties with 6 + 0 = 6, 5 * 1 = 5, and 8 + (-8) = 0.
Example 4 revisits the distributive property with 4 * (3 + 2) = 4 * 3 + 4 * 2.
These examples serve to reinforce the properties of real numbers with examples pdf content, providing practical applications of the theoretical concepts.
Example: The distributive property example 4 * (3 + 2) = 4 * 3 + 4 * 2 shows how multiplication can be distributed over addition, resulting in the same outcome.
Highlight: These examples demonstrate how the properties of real numbers are applied in various mathematical operations, forming the basis for more complex algebraic manipulations.
Vocabulary: The distributive property allows a number to be multiplied by a sum by multiplying the number by each addend separately and then adding the products.
This comprehensive overview of real numbers properties examples multiplication and other operations provides students with a solid foundation for understanding more advanced mathematical concepts.
Real Numbers and Their Properties
This page introduces the fundamental properties of real numbers, providing a solid foundation for understanding mathematical operations and relationships.
The closure property is explained for both addition and multiplication. For addition, the example 5 + 3 = 8 demonstrates that adding two real numbers always results in another real number. Similarly, for multiplication, 2 * 4 = 8 shows that multiplying real numbers yields a real number result.
The commutative property is illustrated for addition and multiplication. The example 7 + 9 = 9 + 7 shows that changing the order of addition doesn't affect the result. Likewise, 3 * 5 = 5 * 3 demonstrates commutativity in multiplication.
The associative property is explained using examples for both addition and multiplication. (3 + 4) + 2 = 3 + (4 + 2) shows that regrouping numbers in addition doesn't change the outcome. Similarly, (2 * 3) * 5 = 2 * (3 * 5) illustrates associativity in multiplication.
The identity property is covered for addition and multiplication. The additive identity is demonstrated with 6 + 0 = 6, showing that adding zero to any number leaves it unchanged. The multiplicative identity is shown with 5 * 1 = 5, illustrating that multiplying by one preserves the original number.
The inverse property is introduced for addition and multiplication. The additive inverse example 8 + (-8) = 0 shows how a number and its negative sum to zero.
Vocabulary: Closure property refers to the fact that performing an operation on members of a set always produces a result within that set.
Example: In the closure property for addition, 5 + 3 = 8 demonstrates that adding two real numbers (5 and 3) results in another real number (8).
Definition: The commutative property states that changing the order of operands does not change the result of the operation.
Highlight: Understanding these properties is crucial for algebraic manipulations and problem-solving in higher mathematics.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content in Algebra 1
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Real Numbers: Easy Examples, Properties, and Worksheets for Kids
Shreeya Ram
@shreeyaram_iuea
Real numbers are fundamental to mathematics, encompassing various properties that govern their behavior in operations. This guide explores the properties of real numbers with examples and answers, providing a comprehensive overview for students and mathematicians alike.
Real numbers properties... Show more
Examples of Real Numbers and Their Properties
This page continues the exploration of real number properties, focusing on practical examples and applications of the concepts introduced earlier.
The multiplicative inverse property is demonstrated with the example 3 * (1/3) = 1, showing that multiplying a number by its reciprocal yields 1.
The distributive property of multiplication over addition is explained with the example 4 * (3 + 2) = 4 * 3 + 4 * 2, illustrating how multiplication can be distributed across addition.
The page then provides a series of examples to reinforce the understanding of real number properties:
Example 1 focuses on addition and multiplication with positive real numbers, showing 5 + 3 = 8 and 2 * 4 = 8.
Example 2 demonstrates commutativity and associativity with 7 + 9 = 9 + 7 and (3 + 4) + 2 = 3 + (4 + 2).
Example 3 illustrates the identity and inverse properties with 6 + 0 = 6, 5 * 1 = 5, and 8 + (-8) = 0.
Example 4 revisits the distributive property with 4 * (3 + 2) = 4 * 3 + 4 * 2.
These examples serve to reinforce the properties of real numbers with examples pdf content, providing practical applications of the theoretical concepts.
Example: The distributive property example 4 * (3 + 2) = 4 * 3 + 4 * 2 shows how multiplication can be distributed over addition, resulting in the same outcome.
Highlight: These examples demonstrate how the properties of real numbers are applied in various mathematical operations, forming the basis for more complex algebraic manipulations.
Vocabulary: The distributive property allows a number to be multiplied by a sum by multiplying the number by each addend separately and then adding the products.
This comprehensive overview of real numbers properties examples multiplication and other operations provides students with a solid foundation for understanding more advanced mathematical concepts.
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Real Numbers and Their Properties
This page introduces the fundamental properties of real numbers, providing a solid foundation for understanding mathematical operations and relationships.
The closure property is explained for both addition and multiplication. For addition, the example 5 + 3 = 8 demonstrates that adding two real numbers always results in another real number. Similarly, for multiplication, 2 * 4 = 8 shows that multiplying real numbers yields a real number result.
The commutative property is illustrated for addition and multiplication. The example 7 + 9 = 9 + 7 shows that changing the order of addition doesn't affect the result. Likewise, 3 * 5 = 5 * 3 demonstrates commutativity in multiplication.
The associative property is explained using examples for both addition and multiplication. (3 + 4) + 2 = 3 + (4 + 2) shows that regrouping numbers in addition doesn't change the outcome. Similarly, (2 * 3) * 5 = 2 * (3 * 5) illustrates associativity in multiplication.
The identity property is covered for addition and multiplication. The additive identity is demonstrated with 6 + 0 = 6, showing that adding zero to any number leaves it unchanged. The multiplicative identity is shown with 5 * 1 = 5, illustrating that multiplying by one preserves the original number.
The inverse property is introduced for addition and multiplication. The additive inverse example 8 + (-8) = 0 shows how a number and its negative sum to zero.
Vocabulary: Closure property refers to the fact that performing an operation on members of a set always produces a result within that set.
Example: In the closure property for addition, 5 + 3 = 8 demonstrates that adding two real numbers (5 and 3) results in another real number (8).
Definition: The commutative property states that changing the order of operands does not change the result of the operation.
Highlight: Understanding these properties is crucial for algebraic manipulations and problem-solving in higher mathematics.
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Most popular content in Algebra 1
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user