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Important Questions for CBSE Class 7 Maths Chapter 9 - Rational Numbers

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Last updated date: 23rd Apr 2024
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CBSE Class 7 Maths Chapter - 9 Important Questions - Free PDF Download

Here, we are presenting important questions for Class 7 Maths Chapter 9 for the students preparing for Class 7 Maths exams but unable to prioritize questions for Chapter 7 Rational Numbers. Refer to Vedantu’s important questions on Rational Number for Class 7 that are prepared by our subject experience teachers after extensive research of the topic and analysis of the past exam trends.

By practicing the questions on Rational numbers for Class 7, you can build your confidence to attempt the questions as you can evaluate your answers with the solutions given and make necessary corrections wherever required. Students are recommended to practice the important questions for Class 7 Maths Chapter 9 repeatedly to understand how tricky problems are solved and to enhance the speed of solving problems, which in turn help in strengthening the time management skills.

Read the article below to know how important questions for rational numbers are effective for your exam preparation. Register Online for NCERT Solutions Class 7 Science tuition on Vedantu.com to score more marks in the CBSE board examination. Vedantu is a platform that provides free CBSE Solutions (NCERT) and other study materials for students. Maths Students who are looking for better solutions can download Class 7 Maths NCERT Solutions to help you to revise the complete syllabus and score more marks in your examinations.

Study Important Questions for Class 7 Maths Chapter 9 - Rational Numbers

1 Mark Questions

1. Reduce \[\dfrac{55}{66}\] into the standard form.

Ans: We know that both $55$ and $66$ are divisible by $11$,

$\dfrac{55\div 11} {66\div 11} $

$ =\dfrac{5}{6} $


2. Fill in the blanks.

(a)$\dfrac{5}{6}.....\dfrac{9}{5}$

(b)$\dfrac{3}{4}......\dfrac{1}{2}$

(c)$\dfrac{2}{5}.......\dfrac{3}{4}$

Ans: (a)$\dfrac{5}{6}  < \dfrac{9}{5}$

(b)$\dfrac{3}{4} > \dfrac{1}{2}$

(c)$\dfrac{2}{5} < \dfrac{3}{4}$


3. Find the additive inverse of $-\dfrac{3}{8}$.

Ans: $\dfrac{3}{8}$


4. Reduce the following to the simplest form.

(a)$\dfrac{36}{54}$

(b)\[\dfrac{8}{72}\]

Ans: 

(a) HCF of $36$ and $54$ is $18$.

Dividing both numerator and denominator by $18$,

$\dfrac{36\div 18} {54\div 18} $

$ =\dfrac{2}{3} $


(b) HCF of $8$ and $72$ is $8$.

Dividing both numerator and denominator by $8$,

$\dfrac{8\div 8} {72\div 8} $

$ =\dfrac{1}{9} $ 


5. Write four more numbers in the following pattern $-\dfrac{1}{2}$, $-\dfrac{1}{3}$, $-\dfrac{2}{4}$, $-\dfrac{2}{6}$,….

Ans: 

$ -\dfrac{1}{2}\times \dfrac{3}{3}=-\dfrac{3}{6} $

$ -\dfrac{1}{2}\times \dfrac{4}{4}=-\dfrac{4}{8} $ 

$ -\dfrac{1}{3}\times \dfrac{3}{3}=-\dfrac{3}{9}  $  

$ -\dfrac{1}{3}\times \dfrac{4}{4}=-\dfrac{4}{12}  $  

Therefore, $-\dfrac{1}{2}$, $-\dfrac{1}{3}$, $-\dfrac{2}{4}$, $-\dfrac{2}{6}$, $-\dfrac{3}{6}$, $-\dfrac{4}{8}$, $-\dfrac{3}{9}$, $-\dfrac{4}{12}$


6. Do $-\dfrac{4}{9}$ and $-\dfrac{16}{36}$ represent the same number?

Ans: $-\dfrac{4}{9}$ and $-\dfrac{16}{36}$ 

$-\dfrac{4}{9}=-\dfrac{4\times 4}{9\times 4}=-\dfrac{16}{36}$

Or $-\dfrac{16}{36}=-\dfrac{16\div 4}{36\div 4}=-\dfrac{4}{9}$

Hence, both represent the same number.


7. List five rational numbers between $-4$ and $-3$.

Ans: 

$-4\times \dfrac{6}{6}=\dfrac{-24}{6}$

$-3\times \dfrac{6}{6}=\dfrac{-18}{6}$

The rational numbers are

$-\dfrac{23}{6},-\dfrac{22}{6},-\dfrac{21}{6},-\dfrac{20}{6},-\dfrac{19}{6}$


8. Give four equivalent numbers for \[\dfrac{3}{8}\].

Ans: 

$ \dfrac{3}{8}\times \dfrac{2}{2}=\dfrac{6}{16}  $  

$ \dfrac{3}{8}\times \dfrac{3}{3}=\dfrac{9}{24}  $  

$ \dfrac{3}{8}\times \dfrac{4}{4}=\dfrac{12}{32}  $  

$ \dfrac{3}{8}\times \dfrac{5}{5}=\dfrac{15}{40}  $  

$ \dfrac{3}{8}\times \dfrac{2}{2}=\dfrac{6}{16}  $  


9. Draw the number line and represent $-\dfrac{7}{3}$ on it.

Ans: This fraction represents two full parts and one part out of 3 equal parts. The negative sign indicates that it is on the negative side of the number line.

Therefore, each space between two integers on the number line must be divided into 3 equal parts.

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10. Rewrite the following rational numbers in the simplest form.

(a)$\dfrac{12}{36}$

(b)$\dfrac{39}{104}$

Ans: 

(a) HCF of $12$ and $36$ is $12$.

Dividing both numerator and denominator by $12$,

$\dfrac{12\div 12}{ 36\div 12}  $  

$ =\dfrac{1}{3}  $  


(b) HCF of $39$ and $104$ is $13$.

Dividing both numerator and denominator by $13$,

$\dfrac{39\div 13}{ 104\div 13} $  

$ =\dfrac{3}{8}  $  


11. Find the value of $\dfrac{4}{14}\div \dfrac{28}{80}$.

Ans: $\dfrac{4}{14}\div \dfrac{28}{80}$

$ =\dfrac{4}{14}\times \dfrac{80}{28}  $  

$ =\dfrac{40}{49}  $  


12. Find the product of $\dfrac{15}{22}\times \dfrac{11}{5}$.

Ans: $\dfrac{15}{22}\times \dfrac{11}{5}$

$ =\dfrac{3}{2}  $  

$ =1\dfrac{1}{2}  $  


13. Find the value of $\dfrac{5}{8}+\dfrac{1}{3}$.

Ans: LCM of $8$ and $3$ is $24$

$\dfrac{5}{8}\times \dfrac{3}{3}=\dfrac{15}{24}  $  

$ \dfrac{1}{3}\times \dfrac{8}{8}=\dfrac{8}{24}  $  

Therefore,

$ \dfrac{15}{24}+\dfrac{8}{24}  $  

$ =\dfrac{5+8}{24}  $  

$ =\dfrac{23}{24}  $  


3 Marks Questions

14. Find the value of 

(a)$\dfrac{3}{4}+\dfrac{1}{2}$

(b)$\dfrac{5}{8}+\dfrac{3}{4}$

Ans: (a) LCM of $4$ and $2$ is $4$

$ \dfrac{3}{4}\times \dfrac{1}{1}=\dfrac{3}{4}  $  

$ \dfrac{1}{2}\times \dfrac{2}{2}=\dfrac{2}{4}  $  

Therefore,

$ \dfrac{3}{4}+\dfrac{2}{4}  $  

$ =\dfrac{3+2}{4}  $  

$ =\dfrac{5}{4}  $  


(b) LCM of $4$ and $8$ is $8$

$ \dfrac{5}{8}\times \dfrac{1}{1}=\dfrac{5}{8}  $  

$ \dfrac{3}{4}\times \dfrac{2}{2}=\dfrac{6}{8}  $  

Therefore,

$ \dfrac{5}{8}+\dfrac{6}{8}  $  

$ =\dfrac{5+6}{8}  $  

$ =\dfrac{11}{8}  $  

$ =1\dfrac{3}{8}  $  


15. Simplify

(a)$\dfrac{2}{5}-\dfrac{1}{2}$

(b)$\dfrac{1}{5}-\dfrac{3}{4}$

Ans: 

(a) LCM of $5$ and $2$ is $10$

$ \dfrac{2}{5}\times \dfrac{2}{2}=\dfrac{4}{10}  $  

$ \dfrac{1}{2}\times \dfrac{5}{5}=\dfrac{5}{10}  $  

Therefore,

$ \dfrac{4}{10}-\dfrac{5}{10}  $  

$ =\dfrac{4-5}{10}  $  

$ =-\dfrac{1}{10}  $  


(b) LCM of $5$ and $4$ is $20$

$ \dfrac{1}{5}\times \dfrac{4}{4}=\dfrac{4}{20}  $  

$ \dfrac{3}{4}\times \dfrac{5}{5}=\dfrac{15}{20}  $  

Therefore,

$ \dfrac{4}{15}-\dfrac{15}{20}  $  

$ =\dfrac{4-15}{20}  $  

$ =-\dfrac{11}{20}  $  


16. Find the product of 

(a) $\dfrac{14}{3}\times \dfrac{21}{63}$

(b) $\dfrac{2}{5}\times \dfrac{8}{9}$

Ans:

(a) $\dfrac{14}{3}\times \dfrac{21}{63}$

$ =\dfrac{2\times 7}{1\times 9}  $  

$ =\dfrac{14}{9}  $  

$ =1\dfrac{5}{9}  $  


(b) $\dfrac{2}{5}\times \dfrac{8}{9}$

$ =\dfrac{2\times 8}{5\times 9}  $  

$ =\dfrac{16}{45}  $  


17. Find the value of 

(a) $-\dfrac{2}{3}\div \dfrac{3}{4}$

(b) $\dfrac{1}{4}\div \dfrac{5}{8}$

Ans: 

(a) $-\dfrac{2}{3}\div \dfrac{3}{4}$

$ =-\dfrac{2}{3}\times \dfrac{3}{4}  $  

$ =-\dfrac{8}{9}  $  


(b) $\dfrac{1}{4}\div \dfrac{5}{8}$

$ =\dfrac{1}{4}\times \dfrac{8}{5}  $  

$ =\dfrac{2}{5}  $  


18. Insert six rational numbers between  $\dfrac{3}{8}$ and $\dfrac{3}{5}$.

Ans: Convert both the denominators into the same denominator.

$\dfrac{3}{8}\times \dfrac{5}{5}=\dfrac{15}{40}$

$\dfrac{3}{5}\times \dfrac{8}{8}=\dfrac{24}{40}$

Therefore, 

$\dfrac{16}{24}$ $\dfrac{17}{24}$ $\dfrac{18}{24}$ $\dfrac{19}{24}$ $\dfrac{20}{24}$ $\dfrac{21}{24}$ 


Download Important Questions of Rational Numbers Class 7 With Solutions - Free PDF

The collection of important questions of Rational numbers Class 7 with solutions are prepared by the subject experts after carrying a thorough analysis of the past year exam trends and latest syllabus.  All questions on Rational Numbers for Class 7 with accurate solutions will come in handy to revise important topics of the chapter. Moreover, the solutions given here will help students to understand the method to frame the stepwise solutions in Class 7 Maths Exam 2024.

The set of important questions of rational number Class 7 provided here is perfect study material for the quick and effective revision of the chapter before the exam as questions of different formats like short answers, long answers are prepared and provided separately by the subject experts.

If you find any doubt concerning any topic of the chapter, you can clear it by practicing these important questions on Rational Numbers. Hence, students are suggested to download important questions of Rational Number Class 7 free pdf through the link provided here.


A Quick Overview of Class 7 Maths Chapter 9 Rational Numbers

Rational numbers are numbers that can be represented in the form of a fraction. It is a part of the real number system. A number is said to be in rational form if it has both numerator and denominator. More specifically, the definition of rational number states that any number can be represented in the ratio of p and q, where p and q are integers and the value of q is not equals to zero.

As per the Ancient Greek Mathematician, rational numbers are used to measure almost everything. Here are some real-life examples of rational numbers.

  • Taxes are represented in the form of rational numbers.

  • Divide pizza or anything among your friends.

  • Interest rate on saving accounts, loan, and mortgage are expressed in rational form.

  • When you complete half of the portion of your work, you say 50% of ½  of the work is completed.

Let us now understand some of the important terms of Class 7 Maths Chapter 9 Rational Numbers.


What Are Rational Numbers?

A rational number is defined as a number that can be written in the form of p/q, where p and q are integers, and q does not equal to 0. For example, 3/5 is a rational number because p = 3, and q = 5 are integers.


What are Positive and Negative Rational Numbers

Positive rational numbers are numbers whose both and numerators and denominators are positive integers. For example, 3/5 is a positive rational number because both the numerator and denominator of this number are positive.

Negative rational numbers are numbers whose either numerator or denominator are negative integers. For example, -3/5 is a negative rational number as the numerator of this number is negative.


How Rational Numbers can be Expressed in Standard Form?

A Rational p/q is said to be in standard form if its denominator that is q is positive and both numerator and denominator i.e. p and q have no other common divisor other than 1.


How to Obtain Rational Numbers Between Two Rational Numbers

We can obtain a rational number between two rational numbers p and q simply by dividing it by 2.

For Example,

  • The rational number between 3/1 and 4/1 is 7/2 as 3/1 + 4/1 = 7/2.

  • For a negative and positive rational number like -3/20 and 3/20 is -2/20,-1/20, 0/20, 1/20, etc.

  • For determining a rational number between two rational numbers with different denominators, we first determine the equivalent fraction with the same denominator then find the rational number between them. For example, we can determine a rational number between -1/3 and 5/20 by converting -1/3 to (-1/3) x (3/3) = -39. Accordingly, we have -2/9,-1/9, 0/9, 1/9, 2/9, 3/9, 4/9.


How to Add Two Rational Numbers?

Two rational numbers with similar denominators can be added simply by adding the numerators while keeping the denominators the same whereas two rational numbers with different denominators can be added taking the LCM of the two denominators. Then, we find the equivalent rational numbers of the given rational number with this LCM as their denominators. Then, we add two rational numbers.

Example: Let us add (-7/5) + (-2/3)

Step 1: LCM of 5 and 3 is 15.

Step 2: (-7/5) +  -2/3 = [-7(3) + (-2)(5)]/15

Step 3: (-7/5) + (-2/3) = [-21 + (-10)]/15 = [-21 -10]/15 = -31/15


How to Subtract Two Rational Numbers?

Two rational numbers with similar denominators can be added simply by subtracting the numerators while keeping the denominators the same whereas two rational numbers with different denominators can be subtracted by making the values of two denominators the same by finding LCM of denominator values.

Example: Let us add (-7/5) - (-2/3)

Step 1: LCM of 5 and 3 is 15

Step 2: (-7/5) - (-2/3) = [-7(3) - (-2)(5)]/15

Step 3: (-7/5) - (-2/3)  = [-21 - (-10)]/15 = [-21 + 10]/15= -11/15


How to Multiply Two Rational Numbers?

The formula two find multiplication of two rational numbers is given by”

Product of Rational Numbers Formula  = ({Product of numerators}/{Product of denominators})

Example:

Find the product of 6/5 × 4/3

The product of 6/5 × 4/3 = 24/15

The multiplication of a rational number with its reciprocal is always equal to 1.


How to Divide Two Rational Numbers?

The division of two rational numbers is similar to the division of fractions, Here are the steps to find the division of two rational numbers.

Step 1: Find the reciprocal of the divisor value.

Step 2: Find the product of numerator and denominator to obtain the result.

Example:

Find the Value of 6/5 ÷ 9/7

Step 1: The reciprocal of 97is 79

Step 2:  Division of two rational number is

6/5 × 7/9 = 42/45


List of the Topics and Subtopics Covered in Class 7 Maths Chapter 9

  • 9.1: Introduction To Rational Numbers

  • 9.2: Need for Rational numbers

  • 9.3: What are Rational Numbers?

  • 9.4: Positive and Negative Rational Numbers

  • 9.5: Rational Number on Number Line

  • 9.6: Rational Number In Standard Form

  • 9.7: Comparison of Rational Numbers

  • 9.8: Rational Numbers Between Two Rational Number

  • 9.9: Operation on Rational Numbers

  • 9.9.1: Addition

  • 9.9.2: Subtraction

  • 9.9.3: Multiplication

  • 9.9.4: Division

To practice the important question on all the topics discussed below, download Important Questions of Rational Numbers Class 7 free pdf now.


How Solving Questions on Rational Number For Class 7 will be Beneficial for Students?

Here are some of the benefits of solving questions on Rational numbers for Class 7.

  • Students will be familiarized with the different types of questions, complexity level of questions, and important topics of the chapter to focus on.

  • Students will be able to develop time management skills and problem-solving skills.

  • Students can analyse the level of their preparation based on the marks obtained. They can also analyse their strength and weakness and accordingly improve them.

  • Solving these questions repeatedly will help students to revise the complete chapter thoroughly.

  • Solving the questions will also help students to attempt the questions asked in the exam more confidently as they will be habitual to solve different types of questions.

  • Candidates are suggested to solve the questions and then cross their answers from the solutions provided. The attempt helps them to gain real-time exam experience.

  • Practicing the questions enable students to assess their preparedness and understand the techniques to decode problems asked in the exam.

To explore all the benefits mentioned above, it is recommended to download Questions on Rational for Class 7 free pdf now.


Conclusion

When studying CBSE Class 7 Maths Chapter 9 on Rational Numbers, it's crucial to grasp key concepts. Understanding how to represent fractions, compare them, and perform operations like addition, subtraction, multiplication, and division with rational numbers is fundamental. Additionally, learning to convert fractions into decimals and vice versa is essential. Practice solving word problems and equations involving rational numbers to strengthen your problem-solving skills. Remember to simplify fractions and find the lowest common multiple when needed. By mastering these concepts, you'll be well-prepared to handle rational numbers and their applications in various mathematical problems. Consistent practice and a solid understanding will help you excel in this chapter.

FAQs on Important Questions for CBSE Class 7 Maths Chapter 9 - Rational Numbers

Q1. How can I access NCERT Solutions for Chapter 9 Rational Numbers of Class 7 Maths?


Ans: Using Vedantu’s NCERT Solutions for Chapter 9 Rational Numbers of Class 7 Maths, students will be able to easily prioritise questions for the chapter Rational Numbers. The PDF has questions that are prepared by experienced subject teachers after continuous research of the topic and can be easily downloaded by visiting Vedantu’s official website (vedantu.com) free of cost. The questions are also based on past exam trends. By continuous practice and hard work, the student can gain confidence in tackling problems on rational numbers and solve them. This will also help the student to understand how tricky questions are solved.

Q2. What are rational numbers according to Chapter 9 Rational Numbers of Class 7 Maths?

Ans: Rational numbers can be expressed as numbers that are in the ratio of x and y. Here x (numerator) and y (denominator) are positive integers and y is not equal to 0. X and y should not have any common divisors other than 1. There are positive and negative rational numbers. Positive rational numbers are those whose numerator as well as denominator are positive integers, whereas negative rational numbers have either the numerator or denominator number as negative.

Q3. How can we obtain rational numbers between two rational numbers according to Chapter 9 Rational Numbers of Class 7 Maths?


Ans: Rational numbers refer to numbers that don’t have 0 as the denominator, and where both the denominator and the numerator are integers. To obtain rational numbers between two rational numbers we can simplify it by dividing it by 2. For example; the rational number between 3/2 and 4/2 is 7/4 as 3/2+4/2=7/2.

We can perform all the operations such as add, subtract, multiple and divide with rational numbers. Rational numbers can perform operations only with other rational numbers and will not be able to with irrational numbers.


Q4. What are the Important Topics Covered in NCERT Solutions of Chapter 9 Rational Numbers of Class 7 Maths?


Ans: NCERT Solutions for Class 7 Maths Chapter 9 is one of the most important chapters in Mathematics. There are many important concepts and topics that are covered in this chapter from the examination point of view. The important topics covered are Introduction to rational numbers, need for rational numbers, what are rational numbers, positive and negative rational numbers, rational numbers on the number line,  In the standard form of rational numbers, operations on rational numbers (addition, subtraction, multiplication and division) and obtaining rational numbers between two rational numbers. 


Q5. How do you represent rational numbers in their standard form as explained in Chapter 9 Rational Numbers of Class 7 Maths?


Ans: Rational numbers are a part of the real number system. Rational numbers are represented in terms of a fraction in their standard form. Rational numbers are represented in the ratio of x and y. Here x (numerator) and y (denominator)  are positive integers and y is not equal to 0. Rational numbers are used to represent almost everything. For example; taxes are done in decimals, division of pizza or anything. These numbers are fractions and hence rational numbers.