NCERT Solutions | Class 7 Maths Chapter 9 | Rational Numbers

CBSE Solutions | Maths Class 7

Check the below NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Pdf free download. NCERT Solutions Class 7 Maths were prepared based on the latest exam pattern. We have Provided Rational Numbers Class 7 Maths NCERT Solutions to help students understand the concept very well.

NCERT | Class 7 Maths

NCERT Solutions Class 7 Maths
Book:	National Council of Educational Research and Training (NCERT)
Board:	Central Board of Secondary Education (CBSE)
Class:	7th
Subject:	Maths
Chapter:	9
Chapters Name:	Rational Numbers
Medium:	English

Rational Numbers | Class 7 Maths | NCERT Books Solutions

You can refer to MCQ Questions for Class 7 Maths Chapter 9 Rational Numbers to revise the concepts in the syllabus effectively and improve your chances of securing high marks in your board exams.

NCERT Solutions for Class 7 Maths Chapte 9 Rational Numbers Exercise 9.1

Ex 9.1 Class 7 Maths Question 1.

List five rational numbers between
(i) -1 and 0
(ii) -2 and -1
(iii) \(\frac { -4 }{ 5 } \) and \(\frac { -2 }{ 3 } \)
(iv) –\(\frac { 1 }{ 2 } \) and \(\frac { 2 }{ 3 } \)

Solution:

Ex 9.1 Class 7 Maths Question 2.

Write four more rational numbers in each of the following patterns :
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 3

Solution:

Ex 9.1 Class 7 Maths Question 3.

Give four rational numbers equivalent to
(i) \(\frac { -2 }{ 7 } \)
(ii) \(\frac { 5 }{ -3 } \)
(iii) \(\frac { 4 }{ 9 } \)

Solution:

Ex 9.1 Class 7 Maths Question 4.

Draw the number line and represent the following rational numbers on it :
(i) \(\frac { 3 }{ 4 } \)
(ii) \(\frac { -5 }{ 8 } \)
(iii) \(\frac { -7 }{ 4 } \)
(iv) \(\frac { 7 }{ 8 } \)

Solution:

(i) In order to represent \(\frac { 3 }{ 4 } \) on the number line, we first draw a number line and mark a point O on it to represent zero. Now, mark the point P representing 3 on the number line as shown. Now, divide the segment OP into four equal parts. Let A, B, C be the points of division so that OA = AB =BC = CP. By construction, OA is three- fourth of OP. So, A represents the rational number \(\frac { 3 }{ 4 } \)
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 7

(ii) In order to represent \(\frac { -5 }{ 8 } \) on the number line, we first draw a number line and mark a point O on it to represent zero. Now, mark the point P representing -5 on it as shown. Now, divide the segment OP into eight equal parts. Let A, B, C, D, E, F, G be the points of division such that OA = AB = BC = CD = DE = EF = FG = GP. By construction, OA is one-eighth of OP. So, A represents the rational number \(\frac { -5 }{ 8 } \).
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 8

(iii) In order to represent \(\frac { -7 }{ 4 } \) on the number line, we first draw a number line and mark a point O on it to represent zero. Now, mark a point P to represent -7 on the number line. Now,divide the segment OP into 4 equal parts. Let A, B, C be the points of division so that OA = AB = BC = CP. By construction, OA is one-fourth of OP. Therefore, A represents the rational number \(\frac { -7 }{ 4 } \).
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 9

(iv) In order to represent \(\frac { 7 }{ 8 } \) on the number line, we first draw a number line and mark a point O on it to represent zero. Now, mark the point P to represent 7 on the number line. Now, divide the segment OP into 8 equal parts. Let A, B, C, D, E, F, G be the points of division such that OA = AB = BC = CD = DE = EF = FG = GP. By construction, OA is one-eighth of OP. Therefore, A represents the rational number \(\frac { 7 }{ 8 } \).
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 10

Ex 9.1 Class 7 Maths Question 5.

The points P, Q, R, S, T, U, A, and B on the number line are such that, TR = RS = SU and AP = PQ = QB. Name the rational numbers represented by P, Q, R, and S.
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 11

Solution:

Ex 9.1 Class 7 Maths Question 6.

Which of the following pairs represents the same rational number?
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 13

Solution:

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 16

Ex 9.1 Class 7 Maths Question 7.

Rewrite the following rational numbers in the simplest form :
(i) \(\frac { -8 }{ 6 } \)
(ii) \(\frac { 25 }{ 45 } \)
(iii) \(\frac { -44 }{ 72 } \)
(iv) \(\frac { -8 }{ 10 } \)

Solution:

Ex 9.1 Class 7 Maths Question 8.

Fill in the boxes with the correct symbol out of >, <, and =.
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 19

Solution:

(i) Clearly, \(\frac { -5 }{ 7 } \) is a negative rational number and \(\frac { 2 }{ 3 } \) is a positive rational number. We know that every negative rational number is less than every positive rational number. Therefore,

(ii) Clearly, denominators of the given rational numbers are positive. The denominators are 5 and 7. Their L.C.M. is 35. So, we first express each rational number with 35 as a common denominator.
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 21

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 21

(iii) First- we write each one of the given rational numbers with a positive denominator.
Clearly, denominator of \(\frac { -7 }{ 8 } \) is positive.
The denominator of \(\frac { 14 }{ -16 } \) is negative.
So, we express it with a positive denominator as follows:
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 22

(iv) Clearly, the denominators of the given rational numbers are positive. The denominators are 5 and 4.
Their L.C.M. is 20. So, we first express each rational number with 20 as a common denominator.
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 23

(v) First we write each one of the given rational numbers with a positive denominator.
Clearly, denominator of \(\frac { 1 }{ -3 } \) is negative.
So, expressing it with a positive denominator as follows:
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 24

(vi) First we write each one of the given rational numbers with a positive denominator.
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 25

(vii) Since every negative rational number is less than 0,

Ex 9.1 Class 7 Maths Question 9.

Which is greater in each of the following :
(i) \(\frac { 2 }{ 3 } \),\(\frac { 5 }{ 2 } \)
(ii) \(\frac { -5 }{ 6 } \),\(\frac { -4 }{ 3 } \)
(iii) \(\frac { -3 }{ 4 } \),\(\frac { 2 }{ -3 } \)
(iv) \(\frac { -1 }{ 4 } \),\(\frac { 1 }{ 4 } \)
(v) -3\(\frac { 2 }{ 7 } \),-3\(\frac { 4 }{ 5 } \)