NCERT Solutions for Class 7 Maths Chapter 9Â Rational Numbers
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. 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. 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.
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NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Topics
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
NCERT Solutions for class 7 maths chapter 9 rational numbers topic 9.3
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:
Answer:
(i)
can be written as:
Hence, we have
(ii)
can be written as:
Hence, we have
NCERT Solutions for class 7 maths chapter 9 topic 9.4
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.
NCERT Solutions for class 7 maths chapter 9 topic 9.6
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 :
NCERT solutions for class 7 maths chapter 9 rational numbers topic 9.8
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 .
NCERT Solutions for class 7 maths chapter 9 rational numbers exercise 9.1
Question: 1(i) 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 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
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:
NCERT Solutions for class 7 maths chapter 9 rational numbers topic 9.9.2
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:
NCERT Solutions for class 7 maths chapter 9 rational numbers topic 9.9.3
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
Question: What will be the reciprocal of
Answer: The reciprocal of will be:
The reciprocal of will be:
NCERT Solutions for class 7 maths chapter 9 rational numbers exercise: 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,
NCERT Solutions for Class 7 Maths Chapter-wise
Chapter No. | Chapter Name |
Chapter 1 | |
Chapter 2 | NCERT solutions for class 7 maths chapter 2 Fractions and Decimals |
Chapter 3 | |
Chapter 4 | NCERT solutions for class 7 maths chapter 4 Simple Equations |
Chapter 5 | 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 | NCERT solutions for class 7 maths chapter 7 Congruence of Triangles |
Chapter 8 | NCERT solutions for class 7 maths chapter 8 comparing quantities |
Chapter 9 | NCERT solutions for class 7 maths chapter 9 Rational Numbers |
Chapter 10 | NCERT solutions for class 7 maths chapter 10 Practical Geometry |
Chapter 11 | NCERT solutions for class 7 maths chapter 11 Perimeter and Area |
Chapter 12 | 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 | |
Chapter 15 | NCERT solutions for class 7 maths chapter 15 Visualising Solid Shapes |
NCERT Solutions for Class 7 Subject wise
Benefits of NCERT solutions for class 7 maths chapter 9 rational numbers
You will study the different types of numbers which you should know.
- 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!!!
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