NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Mathematics (Maths) Class 7

Created by: Praveen Kumar

Class 7 : NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

The document NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes is a part of the Class 7 Course Mathematics (Maths) Class 7.
All you need of Class 7 at this link: Class 7

Exercise 9.1

Question 1:

List five rational numbers between:

(i) -1 and 0   
 (ii) -2 and - 1

(iii) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
(iv)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Answer 1: 

(i) -1 and 0
 Let us write -1 and 0 as rational numbers with denominator 6.

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Therefore, five rational numbers between -1 and 0 would be

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(ii) -2 and -1
Let us write -2 and -1 as rational numbers with denominator 6.

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Therefore, Five rational numbers between -2 and -1 would be

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

 

(iii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Let us write  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes as rational numbers with the same denominators.

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Therefore, five rational numbers between NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes would be

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iv)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Let us write  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notesas rational numbers with the same denominators.

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Therefore, five rational numbers between  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes would be  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Question 2: 

Write four more rational numbers in each of the following patterns:  

(i) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
(ii) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
(ii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
(iii) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Answer 2: 

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Therefore, the next four rational numbers of this pattern would be

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(ii)   NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
Therefore, the next four rational numbers of this pattern would be

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Therefore, the next four rational numbers of this pattern would be

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iv)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Therefore, the next four rational numbers of tins pattern would be

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Question 3:

Give four rational numbers equivalent to:

(i) -2/7
(ii) 5/-3
(iii) 4/9
(iv) -2/7

Answer 3:

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Therefore, four equivalent rational numbers are NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(ii) 5/-3

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Therefore, four equivalent rational numbers are  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iii) 4/9

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Therefore, four equivalent rational numbers are  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Question 4: 

Draw the number line and represent the following rational numbers on it: 

(i) 3/4
 (ii) -5/8
 (iii) -7/4
 (iv) 7/8

Answer 4: 

(i) 3/4

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(ii) -5/8

  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iii)  -7/4

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iv) 7/8

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

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 Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Answer 5: 

Therefore,  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Similarly  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Thus, the rational numbers represented P, Q, R and S are  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes respectively.

Question 6: 

Which of the following pairs represent the same rational numbers: 

(i)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
 (ii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
 (iii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
 (iv)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
 (v)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
 (vi)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
 (vii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Answer 6: 

(i) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes    [Converting into lowest term]
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(ii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes [Converting into lowest term]

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes [Converting into lowest term]

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iv)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes  [Converting into lowest term]

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(v)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes   [Converting into lowest term]

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(vi)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes   [Converting into lowest term]

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(vii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes  [Converting into lowest terra]
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Question 7:

Rewrite the following rational numbers in the simplest form:

(i) -8/6
 (ii) 25/45
 (iii) -44/72
 (iv) -8/10

Answer 7:

(i) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes           [H.C.F. of 8 and 6 is 2]
(ii) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes                [H.C.F. of 25 and 45 is 5]
(iii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes   [H.C.F. of 44 and 72 is 4]
(iv) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes          [H.C.F. of 8 and 10 is 2]

Question 8: 

Fill in the boxes with the correct symbol out of <, > and =:

(i) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
(ii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
(iii) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
(iv)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
(v) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
(vi)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
(vii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Answer 8: 

(i) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes Since, the positive number if greater than negative number.

(ii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
(iii) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
(iv) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
(v)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
(vi)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
(vii) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes Since, 0 is greater than every negative number.

Question 9: 

Which is greater in each of the following: 

(i) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
(ii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
 (iii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
 (iv)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
 (v)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Answer 9: 

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
(iv) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes Since positive number is always greater than negative number.
(v) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Question 10: 

Write the following rational numbers in ascending order: 

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Answer 10: 

(i)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
(ii) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes [Converting into same denominator!

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iii) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Exercise 9.2 

Question 1: 

Find the sum: 

(i) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
 (ii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
 (iii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
 (iv)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
 (v)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
 (vi) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
 (vii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Answer 1: 

(i) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(ii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes          [L.C.M. of 3 and 5 is 15]
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes   [L.C.M of 10 and 15 is 30]
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iv) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes  [L.C.M. of 11 and 9 is 99]
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(v)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes   [L.C.M. of 19 and 57 is 57]
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(vi)NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes    [L.C.M. of 3 and 5 is 15]
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Question 2: 

Find: 

(i)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
 (ii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev NotesNCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
 (iii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes
 (iv)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Answer 2: 

(i) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes    [L.C.M. of 24 and 36 is 72|
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(ii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes  [L.C.M of 63 and 21 is 63|
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes    [L.C.M.ofl3 and 15 is 195]
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iv)   NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes  [L.C.M. of 8 and 11 is 88]
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(v)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes [L.C.M. of 9 and 1 is 9]
NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Question 3: 

Find the product: 

(i)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(ii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iii)   NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iv)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(v)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(vi)   NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Answer 3:

(i)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(ii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iv)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(v)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(vi)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Question 4: 

Find the value of: 

(i) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(ii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iv)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(v)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(vi)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(vii) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

Answer 4: 

(i)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(ii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iii)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(iv)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(v)   NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(vi)  NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

(vii) NCERT Solutions Chapter 9 - Rational Numbers, Maths, Class 7 | EduRev Notes

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