Class 7 Maths NCERT Solutions for Chapter – 9 Rational Numbers Ex – 9.1

Rational Numbers

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:

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 1
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 2

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:

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 4
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 5

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

Solution:

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 6

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

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:

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 12

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 14
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 15
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 16

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:

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 17
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 18

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,
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 20
(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 common denominator.
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 21

(iii) First- we write each one of the given rational numbers with positive denominator :

Clearly, denominator of \frac { -7 }{ 8 }  is positive. The denominator of \frac { 14 }{ -16 }  is negative. So, we express it with 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 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 positive denominator.

Clearly, denominator of \frac { 1 }{ -3 }  is negative. So, expressing it with 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 positive denominator.
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 25

(vii) Since every negative rational number is less than 0,
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 26

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 }

Solution:

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 27
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 28

Question 10.
Write the following rational numbers in ascending order :
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 29
Solution:

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 30
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers 31