NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers, are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers.

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers

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

Question 1.
List five rational numbers between

1. – 1 and 0
2. – 2 and -1
3. – \(\frac { 4 }{ 5 } \) and – \(\frac { 2 }{ 3 } \)
4. – \(\frac { 1 }{ 2 } \) and \(\frac { 2 }{ 3 } \)

Solution:

Question 2.
Write four more rational numbers in each of the following patterns :

Solution:

Question 3.
Give four rational numbers equivalent to:

1. \(\frac { -2 }{ 7 } \)
2. \(\frac { 5 }{ -3 } \)
3. \(\frac { 4 }{ 9 } \)

Solution:

(i) Four rational numbers equivalent to \(\frac { -2 }{ 7 } \) are

(ii) Four rational numbers equivalent to \(\frac { 5 }{ -3 } \) are

(iii) Four rational numbers equivalent to \(\frac { 4 }{ 9 } \) are

Question 4.
Draw the number line and represent the following rational numbers on it:

1. \(\frac { 3 }{ 4 } \)
2. \(\frac { -5 }{ 8 } \)
3. \(\frac { -7 }{ 4 } \)
4. \(\frac { 7 }{ 8 } \)

Solution:

Question 5.
The points P, Q, R, S, T, U, A and B on this number line are such that, TR = RS = SU and AP = PQ = QB. Name the rational numbers represented by P, Q, R and S.

Solution:
The rational number represented by P is 2 \(\frac { 1 }{ 3 } \) = \(\frac { 7 }{ 3 } \)
The rational number represented by Q is 2 \(\frac { 2 }{ 3 } \) = \(\frac { 8 }{ 3 } \)
The rational number represented by R is -1 \(\frac { 1 }{ 3 } \) = \(\frac { -4 }{ 3 } \)
The rational number represented by S is -1 \(\frac { 2 }{ 3 } \) = \(\frac { -5 }{ 3 } \)
The rational numbers represented by P,
Q, R and S are 2 \(\frac { 1 }{ 3 } \), 2 \(\frac { 2 }{ 3 } \), – 1 \(\frac { 1 }{ 3 } \) and – 1 \(\frac { 2 }{ 3 } \) respectively

Question 6.
Which of the following pairs represent the same rational number?

Solution:
(i) \(\frac { -7 }{ 21 } \) is a negative rational number and \(\frac { 3 }{ 9 } \) is a positive rational number. So, the given pair does not represent the same rational number.

So, the given pair represents the same rational number.

So, the given pair represents the same rational number.

So, the given pair represents the same rational number.

So, the given pair represents the same rational number.
(vi) \(\frac { 1 }{ 3 } \) is a positive rational number and \(\frac { -1 }{ 9 } \) is a negative rational number. So, the given pair does not present the same rational number.

Thus, \(\frac { -5 }{ -9 } \) is a positive rational number and \(\frac { 5 }{ -9 } \) is a negative rational number. So, the given pair does not represent the same rational number.

Question 7.
Rewrite the following rational numbers in the simplest form :

Solution:

Question 8.
Fill in the boxes with the correct symbol out of >, < and =

Solution:

Question 9.
Which is greater in each of the following?


Solution:

Question 10.
Write the following rational numbers in ascending order :

Solution:

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.2

Question 1.
Find the sum:

Solution:

Question 2.
Find :

Solution:

Question 3.
Find the product :

Solution:

Question 4.
Find the value of :

Solution:

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers MCQ

Important Multiple Choice Questions

1. The numerator of the rational number \(\frac { 3 }{ 5 } \) is
(a) 3
(b) 5
(c) 2
(d) 8

2. The numerator of the rational number \(\frac { 1 }{ 100 } \) is
(a) 100
(b) 1
(c) 10
(d) 99

3. The denominator of the rational number \(\frac { 4 }{ 7 } \) is
(a) 7
(b) 4
(c) 3
(d) 11

4. The denominator of the rational number \(\frac { 7 }{ 13 } \) is
(a) 13
(b) 7
(c) 6
(d) 91

5. The numerator of the rational number \(\frac { -3 }{ 4 } \) is
(a) -3
(b) 3
(c) 4
(d) -4

6. The numerator of the rational number \(\frac { -2 }{ 9 } \) is
(a) -2
(b) 2
(c) -9
(d) 9

7. The denominator of the rational number \(\frac { 5 }{ -3 } \) is
(a) 5
(b) -3
(c) 3
(d) 8

8. The denominator of the rational number \(\frac { 3 }{ -7 } \) is
(a) 7
(b) -7
(c) 3
(d) -3.

9. The numerator of the rational number \(\frac { -2 }{ -5 } \) is
(a) 2
(b) -2
(c) 5
(d) -5.

10. the numerator of the rational number \(\frac { -5 }{ -3 } \) is
(a) -5
(b) 5
(c) -3
(d) 3

11. The denominator of the rational number \(\frac { -2 }{ -9 } \) is
(a) -2
(b) 2
(c) 9
(d) -9.

12. The denominator of the rational number \(\frac { -6 }{ -5 } \) is
(a) 6
(b) -6
(c) 5
(d) -5.

13. The denominator of the rational number \(\frac { -13 }{ -11 } \) is
(a) -13
(b) 13
(c) 11
(d) -11.

14. The numerator of the rational number 0 is
(a) 0
(b) 1
(c) 2
(d) 3.

15. The denominator of the rational number 0 is
(a) 0
(b) 1
(c) -1
(d) any non-zero integer.

16. The numerator of a rational number 8 is
(a) 2
(b) 4
(c) 6
(d) 8.

17. The denominator of the rational number 8 is
(a) 8
(b) 2
(c) 4
(d) 1.

18. The numerator of the rational number – 9 is
(a) -9
(b) 9
(c) 1
(d) -1.

19. The denominator of the rational number – 9 is
(a) -9
(b) 9
(c) -1
(d) 1.

20. If \(\frac { 3 }{ 4 } \) = \(\frac { ? }{ 12 } \), then ? =
(a) 3
(b) 6
(c) 9
(d) 12

21. if \(\frac { 4 }{ 5 } \) = \(\frac { 12 }{ ? } \), then ? =
(a) 5
(b) 10
(c) 15
(d) 25

22. if \(\frac { -4 }{ 7 } \) = \(\frac { ? }{ 14 } \), then ? =
(a) -4
(b) -8
(c) 4
(d) 8

23. if \(\frac { -7 }{ 11 } \) = \(\frac { 14 }{ ? } \), then ? =
(a) 11
(b) -11
(c) 22
(d) -22

24. if \(\frac { -3 }{ -5 } \) = \(\frac { 9 }{ ? } \), then ? =
(a) 15
(b) -15
(c) 9
(d) -9

25. if \(\frac { -8 }{ -9 } \) = \(\frac { -16 }{ ? } \), then ? =
(a) 18
(b) -18
(c) 9
(d) -9

26. Which of the following is a negative rational number?
(a) \(\frac { 1 }{ 2 } \)
(b) \(\frac { 3 }{ 4 } \)
(c) \(\frac { -4 }{ -5 } \)
(d) \(\frac { 2 }{ -3 } \)

27. Which of the following is a positive rational number?
(a) \(\frac { -1 }{ 2 } \)
(b) \(\frac { 2 }{ -3 } \)
(c) \(\frac { -3 }{ -4 } \)
(d) -5

28. The rational number \(\frac { 12 }{ 40 } \) in standard 40 form is
(a) \(\frac { 3 }{ 10 } \)
(b) \(\frac { 6 }{ 10 } \)
(c) \(\frac { 3 }{ 20 } \)
(d) \(\frac { 6 }{ 20 } \)

29. The rational number \(\frac { -21 }{ 28 } \) in standard form is
(a) \(\frac { -3 }{ 4 } \)
(b) \(\frac { 3 }{ 4 } \)
(c) \(\frac { 3 }{ 7 } \)
(d) \(\frac { -3 }{ 7 } \)

30. The rational number \(\frac { -6 }{ -25 } \) in standard form is
(a) \(\frac { 6 }{ 25 } \)
(b) \(\frac { -6 }{ 25 } \)
(c) \(\frac { 6 }{ -25 } \)
(d) \(\frac { -6 }{ 25 } \)

31. Which of the following rational numbers -2 is equivalent to \(\frac { -2 }{ 5 } \) ?
(a) \(\frac { -4 }{ 10 } \)
(b) \(\frac { -2 }{ 10 } \)
(c) \(\frac { -4 }{ 5 } \)
(d) \(\frac { -6 }{ 25 } \)

32. Which of the following rational numbers is not equivalent to \(\frac { 7 }{ -4 } \) ?
(a) \(\frac { 14 }{ -8 } \)
(b) \(\frac { 21 }{ -12 } \)
(c) \(\frac { 28 }{ -16 } \)
(d) \(\frac { 7 }{ -8 } \)

33. Which of the following rational numbers is not to equivalent to \(\frac { 3 }{ 5 } \) ?
(a) \(\frac { 6 }{ 10 } \)
(b) \(\frac { -3 }{ -5 } \)
(c) \(\frac { 9 }{ 15 } \)
(d) \(\frac { 12 }{ 24 } \)

34. Which of the following is correct?
(a) \(\frac { 1 }{ -2 } \) > \(\frac { -1 }{ 3 } \)
(b) \(\frac { 1 }{ -2 } \) < \(\frac { -1 }{ 3 } \)
(c) \(\frac { 1 }{ -2 } \) = \(\frac { -1 }{ 3 } \)
(d) None of these

35. Which of the following is correct?
(a) 0 > \(\frac { -4 }{ 9 } \)
(b) 0 < \(\frac { -4 }{ 9 } \)
(c) 0 = \(\frac { 4 }{ 9 } \)
(d) None of these

36. Which of the following is correct?
(a) – \(\frac { 4 }{ 5 } \) < – \(\frac { 3 }{ 10 } \)
(b) – \(\frac { 4 }{ 5 } \) > – \(\frac { 3 }{ 10 } \)
(c) – \(\frac { 4 }{ 5 } \) = – \(\frac { 3 }{ 10 } \)
(d) None of these

37. The reciprocal of \(\frac { -2 }{ 5 } \) is
(a) \(\frac { -5 }{ 2 } \)
(b) \(\frac { 5 }{ 2 } \)
(c) \(\frac { 2 }{ 5 } \)
(d) \(\frac { -2 }{ 5 } \)

38. The sum \(\frac { 5 }{ 4 } \) + (- \(\frac { 25 }{ 4 } \)) =
(a) -5
(b) 5
(c) 4
(d) -4

39. The sum – \(\frac { 3 }{ 4 } \) + 0 =
(a) \(\frac { 3 }{ 4 } \)
(b) – \(\frac { 3 }{ 4 } \)
(c) 1
(d) 0

40. \(\frac { 17 }{ 11 } \) – \(\frac { 6 }{ 11 } \) =
(a) 1
(b) -1
(c) 6
(d) 3

41. \(\frac { 2 }{ -5 } \) × \(\frac { -5 }{ 2 } \) =
(a) 1
(b) -1
(c) 2
(d) -5

42. – \(\frac { 6 }{ 5 } \) × 1 =
(a) – \(\frac { 6 }{ 5 } \)
(b) \(\frac { 6 }{ 5 } \)
(c) – \(\frac { 5 }{ 6 } \)
(d) \(\frac { 5 }{ 6 } \)

43. – \(\frac { 6 }{ 5 } \) + 1 =
(a) – \(\frac { 6 }{ 5 } \)
(b) \(\frac { 6 }{ 5 } \)
(c) \(\frac { 5 }{ 6 } \)
(d) – \(\frac { 5 }{ 6 } \)

44. \(\frac { 2 }{ 9 } \) × \(\frac { 27 }{ 8 } \) =
(a) \(\frac { 4 }{ 3 } \)
(b) \(\frac { 3 }{ 4 } \)
(c) 3
(d) 4

45. \(\frac { 7 }{ 12 } \) ÷ ( – \(\frac { 7 }{ 12 } \)) =
(a) 1
(b) -1
(c) 7
(d) -7

ANSWERS

HINTS/SOLUTIONS

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