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Edited By Ravindra Pindel | Updated on Aug 16, 2023 10:11 AM IST

**NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers: **In earlier classes, you have studied whole numbers, natural numbers, integer numbers. In this article, you will get CBSE NCERT rational numbers class 7 solutions. Fractions number is a rational number that contains only positive integers whereas the rational number contains positive and negative integers. All fractions are rational numbers but all rational numbers are not fractions.

This Story also Contains

- NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers - Free CBSE PDF
- NCERT Solutions for Maths Chapter 9 Rational Numbers Class 7 - Important Formulae
- NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers - Important Points
- NCERT Solutions for Maths Chapter 9 Rational Numbers Class 7
- NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers (Intext Questions and Exercise)
- NCERT Solutions for Maths Chapter 9 Rational Numbers Class 7 Topic 9.3
- NCERT rational numbers class 7 solutions Topic 9.4
- NCERT Solutions for Class 7 Maths Chapter 9 Topic 9.6
- NCERT Solutions for Maths Chapter 9 Rational Numbers Class 7 Topic 9.8
- NCERT Solutions for Class 7 Chapter 9 Rational Numbers Maths Exercise 9.1
- NCERT Solutions for Chapter 9 Maths Class 7 Rational Numbers Topic 9.9.1
- NCERT Solutions for Chapter 9 Maths Class 7 Rational Numbers Topic 9.9.2
- NCERT Solutions for Class 7th Math Chapter 9 Rational Numbers Topic 9.9.3
- NCERT Solutions for Class 7th Math Chapter 9 Rational Numbers Topic 9.9.4
- NCERT Solutions for Class 7th Math Chapter 9 Rational Numbers Exercise: 9.2
- Rational Numbers Class 7 Maths Chapter 9-Topics

Once you go through NCERT Solutions for Class 7 you will get more clarity of the concepts. You must refer to the NCERT Syllabus for Class 7 Maths for better understanding. There are 14 questions in 2 exercises given in NCERT. In CBSE NCERT solutions for Class 7 Maths chapter 9 rational numbers, you will get all detailed explanations of all these questions including practice question given at end of the very topic. You can get NCERT Solutions by clicking on the above link. Here you will get solutions to two exercises of this chapter.

Rational number = p/q, Where p and q are integers and q ≠ 0.

Numerator and Denominator: In the p/q , p is the numerator and q is the denominator.

Comparison of Rational Numbers:

p/q < a/b If pb < aq

p/q > a/b If pb > aq

Operations on Rational Number:

Addition of rational numbers : (p/q) + (a/b) = ((p×b) + (a×q))/(q×b)

Subtraction of rational numbers: (p/q) - (a/b) = ((p×b) - (a×q))/(q×b)

Multiplication of rational numbers: p/q) × (a/b) = (p×a)/(q×b)

Division of rational numbers: (p/q) ÷ (a/b) = (p×b)/(q×a)

Reciprocal of p/q = q/p

(Rational number)(Reciprocal) = 1

__For more____, Download Ebook - ____NCERT Class 7 Maths: Chapterwise Important Formulas And Points__

A rational can be expressed in the form of p/q , Where p and q are integers and q ≠ 0.

**Numerator and Denominator:** In the p/q , p is the numerator and q is the denominator.

We obtain another **equivalent rational number** by multiplying the numerator and denominator with the same nonzero integer.

+ sign and positive integer: a position to the right of 0.

- sign and negative integer: a position to the left of 0.

**Rational Numbers in Standard Form: **

Its denominator is a positive integer.

The numerator and denominator have no common factor other than 1.

Examples: 3/5 , -5/8 , 2/7, etc.

**Comparison of Rational Numbers:**

p/q < a/b If pb < aq

p/q > a/b If pb > aq

**Operations on Rational Number:**

Addition of rational numbers : (p/q) + (a/b) = ((p×b) + (a×q))/(q×b)

Subtraction of rational numbers: (p/q) - (a/b) = ((p×b) - (a×q))/(q×b)

Multiplication of rational numbers: p/q) × (a/b) = (p×a)/(q×b)

Division of rational numbers: (p/q) ÷ (a/b) = (p×b)/(q×a)

**Reciprocal of a rational number: **

Reciprocal of p/q = q/p

Product of rational numbers with its reciprocal is always 1.

Free download **NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers PDF **for CBSE Exam.

** Question:1 ** Is the number rational? Think about it.

** Answer: **Yes , is a rational number because it is written in the form: , where .

** Question: ** Fill in the boxes:

(i) (ii)

** Answer: **

** (i) **

can be written as:

Hence, we have

** (ii) **

can be written as:

Hence, we have

** Question:1 ** Is 5 a positive rational number?

** Answer: ****Yes**, 5 can be written as a positive rational number , where 5 and 1 are both positive integers and denominator not equal to zero.

** Question:2 ** List five more positive rational numbers.

** Answer: **Five more positive rational numbers are:

** Question:1 ** Is – 8 a negative rational number?

** Answer: ****Yes**, is a negative rational number because it can be written as , where the numerator is negative integer and denominator is a positive integer.

** Question:2 ** List five more negative rational numbers.

** Answer: **Five more negative rational numbers are:

** Question: ** Which of these are negative rational numbers?

(i) (ii) (iii) (iv) 0 (v) (vi)

** Answer:** (i) here, the numerator is -2 which is negative and the denominator is 3 which is positive.

Hence, the fraction is negative.

(ii) here, the numerator is 5 which is positive and the denominator is 7 which is also positive.

Hence, the fraction is positive.

(iii) here, the numerator is 3 which is positive and the denominator is -5 which is negative.

Hence, the fraction is negative.

(iv) 0 zero is neither a positive nor a negative number.

(v) here, the numerator is 6 which is positive and the denominator is 11 which is also positive.

Hence, the fraction is positive.

(vi) here, the numerator is -2 which is negative and the denominator is -9 which is also a negative integer.

Hence, the fraction is overall a positive fraction.

** Question: ** Find the standard form of

(i) (ii)

** Answer: **(i) Given fraction .

We can make it in the standard form :

(i) Given fraction .

We can make it in the standard form :

** Question: ** Find five rational numbers between

** Answer: **LCM of 7 and 8 is 56.

Hence we can write given fractions as:

and

Therefore, we can find five rational numbers between .

** Question: ** ** 1(i) ** List five rational numbers between:

–1 and 0

** Answer: **To find five rational numbers between we will convert each rational numbers as a denominator , we have

So, we have five rational numbers between

Hence, the five rational numbers between -1 and 0 are:

** Question: ** ** 1(ii) ** List five rational numbers between:

–2 and –1

** Answer: **To find five rational numbers between we will convert each rational numbers as a denominator , we have

So, we have five rational numbers between

Hence, the required rational numbers are

** Question: ** ** 1(iii) ** List five rational numbers between:

** Answer: **To find five rational numbers between we will convert each rational numbers with the denominator as , we have

Since there is only one integer i.e., -11 between -12 and -10, we have to find equivalent rational numbers.

Now, we have five rational numbers possible:

Hence, the required rational numbers are

** Question: ** ** 1(iv) ** List five rational numbers between:

** Answer: **To find five rational numbers between we will convert each rational numbers in their equivalent numbers, we have

Making denominator as LCM(2,3)=6

that is

Now, we have five rational numbers possible:

Hence, the required rational numbers are

** Question: ** ** 2(i) ** Write four more rational numbers in each of the following patterns:

** Answer: **We have the pattern:

Now, following the same pattern, we have

Hence, the required rational numbers are:

** Question: ** ** 2(ii) ** Write four more rational numbers in each of the following patterns:

** Answer: **We have the pattern:

Now, following the same pattern, we have

Hence, the required rational numbers are:

** Question: ** ** 2(iii) ** Write four more rational numbers in each of the following patterns:

** Answer: **We have the pattern:

Now, following the same pattern, we have

Hence, the required rational numbers are:

** Question: ** ** 2(iv) ** Write four more rational numbers in each of the following patterns:

** Answer: **We have the pattern:

Now, following the same pattern, we have

Hence, the required rational numbers are:

** Question: ** ** 3(i) ** Give four rational numbers equivalent to:

** Answer: ** can be written as:

Hence, the required equivalent rational numbers are

** Question: ** ** 3(ii) ** Give four rational numbers equivalent to:

** Answer:** can be written as:

Hence, the required equivalent rational numbers are

** Question: ** ** 3(iii) ** Give four rational numbers equivalent to:

** Answer:** can be written as:

Hence, the required equivalent rational numbers are

** Question: ** ** 4(i) ** Draw the number line and represent the following rational numbers on it:

** Answer: **Representation of on the number line,

** Question: ** ** 4(ii) ** Draw the number line and represent the following rational numbers on it:

** Answer:** Representation of on the number line,

** Question: ** ** 4(iii) ** Draw the number line and represent the following rational numbers on it:

** Answer: **Representation of on the number line,

** Question: ** ** 4(iv) ** Draw the number line and represent the following rational numbers on it:

** Answer: **Representation of on the number line,

** Answer: **Given TR = RS = SU and AP = PQ = QB then, we have

There are two rational numbers between A and B i.e., P and Q which are at equal distances hence,

The rational numbers represented by P and Q are:

Also, there are two rational numbers between U and T i.e., S and R which are at equal distances hence,

The rational numbers represented by S and R are:

** Question: ** ** 6 ** Which of the following pairs represent the same rational number?

(i) (ii)

(iii) (iv)

(v) (vi)

(vii)

** Answer: **To compare we multiply both numbers with denominators:

(i) We have

Here, they are equal but are in opposite signs hence, do not represent the same rational numbers.

(ii) We have

So, they represent the same rational number.

(iii) We have

Here, Both represents the same number as these minus signs on both numerator and denominator of will cancel out and gives the positive value.

(iv) We have

So, they represent the same rational number.

(v) We have

So, they represent the same rational number.

(vi) We have

So, They do not represent the same rational number.

(vii) We have

Here, the denominators of both are the same but .

So, do not represent the same rational numbers.

** Question: ** ** 7 ** Rewrite the following rational numbers in the simplest form:

(i) (ii) (iii) (iv)

** Answer:** (i) can be written as:

(ii) can be written in the simplest form:

(iii) can be written as in simplest form:

** Question: ****8 ** Fill in the boxes with the correct symbol out of >, <, and =.

(i) (ii) (iii)

(iv) (v) (vi)

(vii)

** Answer:**** (i) **

Hence,

** (ii) **

Hence,

** (iii) **

Hence,

** (iv) **

Hence,

** (v) **

Hence,

** (vi) **

Hence,

** (vii) **

Zero is always greater than every negative number.

Therefore,

** Question: ** ** 9 ** Which is greater in each of the following:

(i) (ii)

(iii) (iv)

(v)

** Answer: ****(i) **

Since,

So,

** (ii) **

Since,

So,

** (iii) **

Since,

So,

** (iv) **

As each positive number is greater than its negative.

** (v) **

So,

** Question: ****10(i) ** Write the following rational numbers in ascending order:

** Answer: **(i) Here the denominator value is the same.

Therefore,

Hence, the required ascending order is

** Question: ** ** 10(ii) ** Write the following rational numbers in ascending order:

** Answer: **Given

LCM of .

Therefore, we have

Since

Hence, the required ascending order is

** Question: ** ** 10(iii) ** Write the following rational numbers in ascending order:

** Answer: **Given

LCM of .

Therefore, we have

Since

Hence, the required ascending order is

** Question: ** Find:

** Answer: **For the given sum:

Here the denominator value is same that is 7 hence we can sum the numerator as:

For the given sum:

Here also the denominator value is the same and is equal to 5 hence we can write it as:

** Question:(i) ** Find:

** Answer: **Given sum:

Taking LCM of 7 and 3 we get; 21

Hence we can write the sum as:

** Question:(ii) ** Find:

** Answer: **Given sum:

Taking LCM of 6 and 11 we get; 66

Hence we can write the sum as:

** Question:1 ** What will be the additive inverse of

-3/9, -9/11, 5/7

** Answer: **The additive inverse of

The additive inverse of

The additive inverse of

** Question:2 ** Find

** Answer: **

** Question: ** What will be

(i) (ii)

** Answer:** (i)

We can write the product as:

(i)

We can write the product as:

** Question: ** What will be the reciprocal of

** Answer: **The reciprocal of will be:

The reciprocal of will be:

** Question: ** ** 1(i) ** Find the sum:

** Answer:** Given sum:

Here the denominator is the same which is 4.

** Question: ** ** 1(ii) ** Find the sum:

** Answer:** Given sum:

Here the LCM of 3 and 5 is 15.

Hence, we can write the sum as:

** Question: 1(v) ** Find the sum :

** Answer: **Given sum:

Taking LCM of 19 and 57, we have 57

We can write the sum as:

** Question: ** ** 1(vi) ** Find the sum:

** Answer: **Given sum:

Adding any number to zero we get, the number itself

Hence,

- Need For Rational Numbers
- What Are The Rational Numbers?
- Positive And Negative Rational Numbers
- Rational Numbers On A Number Line
- Rational Numbers In A Standard Form
- Comparison Of Rational Numbers
- Rational Numbers Between Two Rational Numbers
- Operations On Rational Numbers

Chapter No. | Chapter Name |

Chapter 1 | |

Chapter 2 | |

Chapter 3 | |

Chapter 4 | |

Chapter 5 | |

Chapter 6 | |

Chapter 7 | |

Chapter 8 | Comparing quantities |

Chapter 9 | Rational Numbers |

Chapter 10 | |

Chapter 11 | |

Chapter 12 | |

Chapter 13 | |

Chapter 14 | |

Chapter 15 | Visualising Solid Shapes |

### You will study the different types of numbers which you should know in NCERT Class 7 Mathematics book .

- It will help you in your homework as all the practice questions including questions given below every topic are covered in this article.
- You will also learn addition, multiplication, subtraction, and division of rational numbers.
- You will also get solutions to the practice questions given below every topic which will give you conceptual clarity.
- You should practice all the NCERT questions including examples. If you facing difficulties in doing so, you can take help from the NCERT solutions for Class 7 Maths chapter 9 Rational Numbers.

** Happy learning!!! **

**Also Check NCERT Books and NCERT Syllabus here:**

1. What is rational number?

A number can be expressed in the form of p/q, where p and q are integers and q is not equal to 0 is called a rational number. Students can deeper understanding of rational number in class 7 math chapter 9. You can download rational numbers class 7 pdf to study both offline and online mode.

2. How do you perform operations with rational numbers?

- For addition and subtraction, find a common denominator, perform the operation on the numerators, and keep the denominator the same.
- For multiplication, multiply the numerators and denominators separately.
- For division, multiply by the reciprocal of the second number (divisor) and follow the multiplication rule.

3. How many exercises in NCERT solution Class 7 Maths chapter 9?

There are 2 exercises in NCERT solution Class 7 Maths chapter 9.

Rational Numbers Exercise 9.1- 10 questions

Rational Numbers Exercise 9.2- 4 questions

4. How do you convert a recurring decimal into a fraction?

- To convert a recurring decimal into a fraction, represent the recurring part as 'x' and subtract it from the whole decimal.
- Solve for 'x' to get an equation. Multiply both sides by the appropriate power of 10 to eliminate the recurring part.
- This will give you an equation that you can solve to find the fraction equivalent of the recurring decimal.

Sep 11, 2023

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Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages. Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.

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The career as a Talent Agent is filled with responsibilities. A Talent Agent is someone who is involved in the pre-production process of the film. It is a very busy job for a Talent Agent but as and when an individual gains experience and progresses in the career he or she can have people assisting him or her in work. Depending on one’s responsibilities, number of clients and experience he or she may also have to lead a team and work with juniors under him or her in a talent agency. In order to know more about the job of a talent agent continue reading the article.

If you want to know more about talent agent meaning, how to become a Talent Agent, or Talent Agent job description then continue reading this article.

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Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.

A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.

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Career as a Music Teacher is a fun and exciting job if you are skilled and passionate about this career. A Music Teacher is responsible for teaching students music, instruments, techniques, technology, singing, and many more. He or she helps students to analyze musical works, and concepts of music and assigns and evaluates lessons.

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An individual who is pursuing a career as a producer is responsible for managing the business aspects of production. They are involved in each aspect of production from its inception to deception. Famous movie producers review the script, recommend changes and visualise the story.

They are responsible for overseeing the finance involved in the project and distributing the film for broadcasting on various platforms. A career as a producer is quite fulfilling as well as exhaustive in terms of playing different roles in order for a production to be successful. Famous movie producers are responsible for hiring creative and technical personnel on contract basis.

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The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.

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In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.

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Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

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Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

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A career as news anchor requires to be working closely with reporters to collect information, broadcast newscasts and interview guests throughout the day. A news anchor job description is to track the latest affairs and present news stories in an insightful, meaningful and impartial manner to the public. A news anchor in India needs to be updated on the news of the day. He or she even works with the news director to pick stories to air, taking into consideration the interests of the viewer.

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For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

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In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion. Ever since internet cost got reduced the viewership for these types of content has increased on a large scale. Therefore, the career as vlogger has a lot to offer. If you want to know more about the career as vlogger, how to become a vlogger, so on and so forth then continue reading the article. Students can visit Jamia Millia Islamia, Asian College of Journalism, Indian Institute of Mass Communication to pursue journalism degrees.

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Careers in videography are art that can be defined as a creative and interpretive process that culminates in the authorship of an original work of art rather than a simple recording of a simple event. It would be wrong to portrait it as a subcategory of photography, rather photography is one of the crafts used in videographer jobs in addition to technical skills like organization, management, interpretation, and image-manipulation techniques. Students pursue Visual Media, Film, Television, Digital Video Production to opt for a videographer career path. The visual impacts of a film are driven by the creative decisions taken in videography jobs. Individuals who opt for a career as a videographer are involved in the entire lifecycle of a film and production.

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An SEO Analyst is a web professional who is proficient in the implementation of SEO strategies to target more keywords to improve the reach of the content on search engines. He or she provides support to acquire the goals and success of the client’s campaigns.

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A career as a gemologist is as magnificent and sparkling as gemstones. A gemologist is a professional who has knowledge and understanding of gemology and he or she applies the same knowledge in his everyday work responsibilities. He or she grades gemstones using various equipment and determines its worth. His or her other work responsibilities involve settling gemstones in jewellery, polishing and examining it.

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Production Manager Job Description: A Production Manager is responsible for ensuring smooth running of manufacturing processes in an efficient manner. He or she plans and organises production schedules. The role of Production Manager involves estimation, negotiation on budget and timescales with the clients and managers.

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A Commercial Manager negotiates, advises and secures information about pricing for commercial contracts. He or she is responsible for developing financial plans in order to maximise the business's profitability.

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**Quality Assurance Manager Job Description:** A QA Manager is an administrative professional responsible for overseeing the activity of the QA department and staff. It involves developing, implementing and maintaining a system that is qualified and reliable for testing to meet specifications of products of organisations as well as development processes.

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Are you searching for a Reliability Engineer job description? A Reliability Engineer is responsible for ensuring long lasting and high quality products. He or she ensures that materials, manufacturing equipment, components and processes are error free. A Reliability Engineer role comes with the responsibility of minimising risks and effectiveness of processes and equipment.

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A Safety Manager is a professional responsible for employee’s safety at work. He or she plans, implements and oversees the company’s employee safety. A Safety Manager ensures compliance and adherence to Occupational Health and Safety (OHS) guidelines.

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ITSM Manager is a professional responsible for heading the ITSM (Information Technology Service Management) or (Information Technology Infrastructure Library) processes. He or she ensures that operation management provides appropriate resource levels for problem resolutions. The ITSM Manager oversees the level of prioritisation for the problems, critical incidents, planned as well as proactive tasks.

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Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

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An IT Consultant is a professional who is also known as a technology consultant. He or she is required to provide consultation to industrial and commercial clients to resolve business and IT problems and acquire optimum growth. An IT consultant can find work by signing up with an IT consultancy firm, or they can work on their own as independent contractors and select the projects they want to work on.

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A Data Architect role involves formulating the organisational data strategy. It involves data quality, flow of data within the organisation and security of data. The vision of Data Architect provides support to convert business requirements into technical requirements.

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An AI Data Analyst is responsible for procuring, preparing, cleansing and modelling data utilising machine learning models and new analytical methods. He or she designs and creates data reports in order to provide support to stakeholders to make better decisions.

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An Automation Test Engineer job involves executing automated test scripts. He or she identifies the project’s problems and troubleshoots them. The role involves documenting the defect using management tools. He or she works with the application team in order to resolve any issues arising during the testing process.

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A UX Architect is someone who influences the design processes and its outcomes. He or she possesses a solid understanding of user research, information architecture, interaction design and content strategy.

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