VMC VIQ Scholarship Test
ApplyRegister for Vidyamandir Intellect Quest. Get Scholarship and Cash Rewards.
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.
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
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,
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 |
Happy learning!!!
Also Check NCERT Books and NCERT Syllabus here:
Admit Card Date:04 October,2024 - 29 November,2024
Admit Card Date:04 October,2024 - 29 November,2024
Application Date:07 October,2024 - 22 November,2024
Application Correction Date:08 October,2024 - 27 November,2024
Register for Vidyamandir Intellect Quest. Get Scholarship and Cash Rewards.
As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters
As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters
Accepted by more than 11,000 universities in over 150 countries worldwide
Register now for PTE & Unlock 20% OFF : Use promo code: 'C360SPL20'. Valid till 30th NOV'24! Trusted by 3,500+ universities globally
As per latest 2024 syllabus. Study 40% syllabus and score upto 100% marks in JEE