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 solutions for class 7 maths chapter 9 rational numbers. What are the rational numbers?
Have you able to find the difference between the fraction number and a rational number?
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. For example, 5 is not a fraction since 5 is a negative integer but 5 is a rational number. Is zero a rational number? Think about it. Yes, zero is a rational number as 0 can be written as 0/1 or 0/2 or 0/3 .......which is of the form p/q where q is not equal to zero. Once you go through solutions of NCERT for class 7 maths chapter 9 rational numbers, you will get more clarity of the concepts. There are 14 questions in 2 exercises given in the textbook. 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.
9.1 Introduction
9.2 Need For Rational Numbers
9.3 What Are Rational Numbers?
9.4 Positive And Negative Rational Numbers
9.5 Rational Numbers On A Number Line
9.6 Rational Numbers In Standard Form
9.7 Comparison Of Rational Numbers
9.8 Rational Numbers Between Two Rational Numbers
9.9 Operations On Rational Numbers
Solutions of NCERT for class 7 maths chapter 9 rational numbers topic 9.3 what are rational numbers?
Question:1 Is the number rational? Think about it.
Answer:
Yes, is a rational number because it is written in the form: , where .
Solutions for class 7 maths chapter 9 rational numbers topic 9.3 subtopic equivalent rational numbers
Question: Fill in the boxes:
Answer:
(i)
can be written as:
Hence, we have
(ii)
can be written as:
Hence, we have
Solutions for class 7 maths chapter 9 topic 9.4 positive and negative rational numbers
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 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.
Solutions of NCERT for class 7 maths chapter 9 topic 9.6 rational numbers in standard form
Question: Find the standard form of
Answer:
(i) Given fraction .
We can make it in the standard form :
(i) Given fraction .
We can make it in the standard form :
CBSE NCERT solutions for class 7 maths chapter 9 rational numbers topic 9.8 rational numbers between two rational numbers
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 .
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:
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?
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:
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 =.
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:
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
NCERT solutions for class 7 maths chapter 9 rational numbers topic 9.9.1 addition
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
Answer:
The additive inverse of
The additive inverse of
The additive inverse of
Question:2 Find
Answer:
Solutions for class 7 maths chapter 9 rational numbers topic 9.9.3 multiplication
Question: What will be
Answer:
(i)
We can write the product as:
(i)
We can write the product as:
NCERT solutions for class 7 maths chapter 9 rational numbers topic 9.9.4 division
Question: What will be the reciprocal of
Answer:
The reciprocal of will be:
The reciprocal of will be:
Solutions for CBSE class 7 maths chapter 9 rational numbersExercise: 9.2
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,
Chapter No. 
Chapter Name 
Chapter 1 

Chapter 2 
CBSE NCERT solutions for class 7 maths chapter 2 Fractions and Decimals 
Chapter 3 

Chapter 4 
Solutions of NCERT for class 7 maths chapter 4 Simple Equations 
Chapter 5 
CBSE NCERT solutions for class 7 maths chapter 5 Lines and Angles 
Chapter 6 
NCERT solutions for class 7 maths chapter 6 The Triangle and its Properties 
Chapter 7 
Solutions of NCERT for class 7 maths chapter 7 Congruence of Triangles 
Chapter 8  NCERT solutions for class 7 maths chapter 8 comparing quantities 
Chapter 9 
CBSE NCERT solutions for class 7 maths chapter 9 Rational Numbers 
Chapter 10 
NCERT solutions for class 7 maths chapter 10 Practical Geometry 
Chapter 11 
Solutions of NCERT for class 7 maths chapter 11 Perimeter and Area 
Chapter 12 
CBSE NCERT solutions for class 7 maths chapter 12 Algebraic Expressions 
Chapter 13 
NCERT solutions for class 7 maths chapter 13 Exponents and Powers 
Chapter 14 
You will study the different types of numbers which you should know.
Happy learning!!!