AP 8th Maths Mock Test 2023 For Chapter - 1 : "Rational Numbers" Online Practice Test

1. How is - $\frac{7}{4}$ is expressed as a rational number with denominator 20 ?

- $\frac{70}{20}$

- $\frac{35}{20}$

$\frac{35}{20}$

None

2. Express $\frac{1}{4}$ and $\frac{1}{3}$ with same denominator.

$\frac{4}{12}$ and $\frac{3}{12}$

$\frac{3}{12}$ and $\frac{4}{12}$

$\frac{4}{7}$ and $\frac{3}{7}$

$\frac{3}{7}$ and $\frac{4}{7}$

3. Multiplicative inverse of $\frac{a}{b}$ is

- $\frac{a}{b}$

$\frac{b}{a}$

- $\frac{b}{a}$

4. Multiplicative inverse of $\frac{9}{7}$ is

$\frac{7}{9}$

$\frac{9}{7}$

- $\frac{9}{7}$

5. Multiplicative inverse of $\frac{a^{2}}{b}$ is

$\frac{b}{a^{2}}$

- $\frac{b}{a^{2}}$

- $\frac{a^{2}}{b}$

6. Multiplicative identity in the set of rationals is _____

-1

1 or -1

7. The reciprocal of '0' is _____

Any number

Not defined

8. The reciprocal of '0' is _____

Any number

Not defined

9. The reciprocal of ' $\infty$ ' is _____

Any number

Not defined

10. What is the sum of additive inverse and multiplicative inverse of -1?

-2

11. What is the sum of additive inverse and multiplicative inverse of 1?

-2

12. $\frac{-28}{84}$ can be expressed as a rational number as _______

$\frac{4}{7}$

$\frac{-4}{12}$

$\frac{4}{12}$

$\frac{4}{-7}$

13. What is the multiplicative inverse of $\frac{-28}{84} \times \frac{-3}{7}$ ?

$3\frac{11}{15}$

$5\frac{6}{7}$

$7\frac{3}{8}$

$\frac{56}{15}$

14. Which of the following is correct ?

$\frac{-9}{15} < \frac{-2}{3} < \frac{-4}{5}$

$\frac{-4}{5} < \frac{-2}{3} < \frac{-9}{15}$

$\frac{-2}{3} < \frac{-9}{15} < \frac{-4}{5}$

All

15. Which of the following are 3 rational numbers between -2 and -1 ?

$\frac{-1}{2}, \frac{-1}{3}, \frac{-1}{5}$

$\frac{-3}{2}, \frac{-7}{4}, \frac{-5}{4}$

$\frac{-12}{5}, \frac{-22}{5}, \frac{12}{5}$

$\frac{3}{2}, \frac{7}{4}, \frac{5}{4}$

16. Which of the following are 3 rational numbers between -3 and -2 ?

$\frac{-1}{2}, \frac{-1}{3}, \frac{-1}{5}$

$\frac{-5}{2}, \frac{-11}{2}, \frac{-17}{2}$

$\frac{-12}{5}, \frac{-22}{5}, \frac{12}{5}$

$\frac{5}{2}, \frac{11}{2}, \frac{17}{2}$

17. Which of the following are 3 rational numbers between 3 and 4 ?

$\frac{-1}{2}, \frac{-1}{3}, \frac{-1}{5}$

$\frac{7}{2}, \frac{13}{2}, \frac{19}{2}$

$\frac{-12}{5}, \frac{-22}{5}, \frac{12}{5}$

$\frac{-7}{2}, \frac{-13}{2}, \frac{-19}{2}$

18. Which of the following are 3 rational numbers between 4 and 7 ?

$\frac{-1}{2}, \frac{-1}{3}, \frac{-1}{5}$

$\frac{11}{2}, \frac{19}{2}, \frac{25}{2}$

$\frac{-12}{5}, \frac{-22}{5}, \frac{12}{5}$

$\frac{-11}{2}, \frac{-19}{2}, \frac{-25}{2}$

19. A rational number between $\frac{-2}{3}$ and $\frac{1}{4}$ is _____

$\frac{5}{12}$

$\frac{-5}{12}$

$\frac{5}{24}$

$\frac{-5}{24}$

20. A rational number between $\frac{-1}{3}$ and $\frac{5}{2}$ is _____

$\frac{13}{12}$

$\frac{-13}{12}$

$\frac{12}{13}$

$\frac{-12}{13}$

21. A rational number between $\frac{-1}{9}$ and $\frac{-1}{2}$ is _____

$\frac{-11}{36}$

$\frac{13}{36}$

$\frac{11}{36}$

$\frac{-12}{36}$

22. $1.2\overline{4}$ = _____

$\frac{124}{90}$

$\frac{112}{99}$

$\frac{112}{90}$

$\frac{124}{99}$

23. $0.\overline{36}$ = _____

$\frac{-14}{90}$

$\frac{14}{99}$

$\frac{4}{11}$

$\frac{-4}{99}$

24. If $\frac{p}{q}$ is the fractional form of $0.\overline{36}$ then p+q = ____

25. If $\frac{p}{q}$ is the fractional form of $0.\overline{4}$ then p+q = ____

26. If $\frac{p}{q}$ is the fractional form of $0.\overline{9}$ then p+q = ____

27. If x = $\frac{p}{q}$ , y = $\frac{p}{q}$ , then $(x+y) \div (x-y)$ = ______

$\frac{7}{13}$

$\frac{-7}{13}$

$\frac{-13}{7}$

$\frac{13}{7}$

28. The denominator of a fraction which equals to the decimal fraction of $0.\overline{125}$ is _____

900

1000

999

990

29. $0.\overline{9}$ +9.1 = _____

$9.\overline{91}$

$9.1\overline{9}$

10.1

$10.\overline{1}$

30. The reciprocal of 9 lies in the number system _____

N and W

31. The differences of the period and periodicity of $0.\overline{39}$ is ______

32. The product of $\frac{2}{11}$ and reciprocal of $\frac{-5}{14}$ is _____

$\frac{55}{28}$

$\frac{-55}{28}$

$\frac{28}{55}$

$\frac{-28}{55}$

33. The sum of 2 rational numbers is 8 and one of them is $\frac{-5}{6}$ . Then the second number is ____

$\frac{53}{6}$

$\frac{-53}{6}$

$\frac{43}{6}$

$\frac{13}{6}$

34. The negative of -2 multiplied by its reciprocal gives

-1

- $\frac{1}{4}$

35. Which of the following rational has a terminating decimal ?

$\frac{1}{7}$

$\frac{13}{28}$

$\frac{101}{40}$

$\frac{1}{3}$

36. a^{x - y}.a^{y - z}.a^{z - x} = ..............

xyz

37. Which of the rational numbers - $\frac{11}{28}$ , - $\frac{5}{7}$ , - $\frac{9}{14}$ , - $\frac{29}{42}$ is the greatest ?

- $\frac{11}{28}$

- $\frac{5}{7}$

- $\frac{9}{14}$

- $\frac{29}{42}$

38. The reciprocal of 0.75 is ................

1.3

0.25

- $\frac{3}{4}$

1. $\overline{3}$

39. $\frac{7}{8}$ - $\frac{2}{3}$ =

$\frac{5}{24}$

- $\frac{5}{24}$

40. If $\frac{x}{9}$ = $\frac{4}{x}$ then x = ..............

- 6

$\pm$ 6

41. Which of the following is not a rational number ?

- 0.3

- $\frac{2}{3}$

$\pi$

42. Rama : $\frac{5}{3}$ is a rational number and 5 is only a natural number
Shyama : Both $\frac{5}{3}$ and 5 are rational numbers
Which of the statements are true ?

Both are right

Only Rama is right

Only shyama is right

Both are wrong

43. Assertion A : Set of integers is closed under subtraction
Reason R : Difference of two integers is not necessarily an integer
Which of the following statements are true ?

A is true , R is false

R is true , A is false

Both A and R are true and R is correct explanation of A

Both A and R are true but R is not correct explanation of A

44. a $\div$ b = b $\div$ a holds only if ..............

a = 1 , b = 2

a = 0 or b = 0

a = b

a < b

45. Which of the following set of numbers has no identity element under + ?

1 or Z

46. Which of the following is different among the following rationals ?

$\frac{1}{7}$

$\frac{2}{3}$

$\frac{27}{8}$

$\frac{145}{6}$

47. 0. $\overline{4}$ + 0. $\overline{3}$ + 0. $\overline{2}$ = .............

0. $\overline{432}$

0.432

0.1

48. $\frac{2. \overline{9} }{4. \overline{9} }$ =

$\frac{1}{2}$

$\frac{3}{5}$

Not defined

49. In the following , multiplicative associative property is

$\frac{5}{2} \times [ \frac{3}{7} + \frac{9}{5}]$ = $[ \frac{5}{2} \times \frac{3}{7}] + [ \frac{5}{2} \times \frac{9}{5}]$

$[ \frac{5}{2} + \frac{3}{7}]$ + $\frac{9}{5}$ = $\frac{5}{2}$ + $[ \frac{3}{7} + \frac{9}{5}]$

$\frac{5}{2} \times [ \frac{3}{7}\times \frac{9}{5}]$ = $[ \frac{5}{2} \times \frac{3}{7}] \times \frac{9}{5}$

None

50. $\frac{1}{0}$ = ................

Not defined

Any number

51. Any integer division by zero =

That integer

Not defined

52. The rational number that does not have any reciprocal is ..............

- 1

Both 1 and - 1

53. Which of the following is only an integer but not a rational number ?

- 1

Does not exist

54. Find the natural number but not a rational number ?

- 1

Does not exist

55. The set of integers is not closed under

Addition

Subtraction

Multiplication

Division

56. $\forall$ a , b $\in$ Q we have a $\times$ b $\in$ Q . This states ...................... property under multiplication of rational number

Closure

Associative

Identity

Commutative

57. $\forall$ a , b $\in$ Q we have a + b = b + a . This states ...................... property under addition in Q

Closure

Associative

Identity

Commutative

58. Commutative property does not hold under subtraction in the set of ...................

Whole numbers

Integers

Rational

Never holds

59. $\forall$ a $\in$ Q we have a $\times$ 1 = a = 1 $\times$ a . This indicates ...................... property

Closure

Commutative

Identity

Inverse

60. Additive identity in the set of rational number is ..............

- 1

1 or - 1

61. Which property can be used in computing $\frac{2}{5} \times [5 \times \frac{7}{6}]$ + $\frac{1}{3} \times [3 \times \frac{4}{11}]$ ?

Closure

Commutative

Associative

Distributive

62. If 'n' is a prime number , then the periodicity of $\frac{1}{n}$ is ......................

n + 1

n - 1

63. How many integers are there in between -1 and 1 ?

Infinite

64. The set of rationals denoted by the letter ..............

65. IF (x + y)z = 1 then z is a multiplicative inverse of ..................

(x + y)

(x - y)

66. Write Y if Yes and N if No in place of i , ii , iii , iv in the following table to complete it in order

Y , N , Y , Y

Y , N , Y , N

N , N , Y , Y

N , N , Y , N

67. Match the following of Column - 1 with Column -2.

Column - 1 Column - 2

$\forall a , b \in Q , ab \in Q$ ( ) p) Commutative property
$\forall a , b \in Q , a+b = b+a$ ( ) q) Associative property
$\forall a , b,c \in Q , a(bc) = (ab)c$ ( ) r) Closure property

a - p, b - q, c - r

a - r, b - p, c - q

a - r, b - q, c - p

a - p, b - r, c - q

68. A bus is moving at an average speed of $60 \frac{2}{5}$ km/hr. How much distance it will cover in $7 \frac{1}{2}$ hours ?

423 km

433 km

443 km

453 km

69. What is the multiplicative inverse of $-\frac{73}{29}$ ?

$-\frac{29}{73}$

$\frac{29}{73}$

$\frac{73}{29}$

70. The area of a rectangular park whose length is $36\frac{3}{5}$ m and breadth is $16\frac{2}{3}$ m _____

1830 sq.m

1220 sq.m

610 sq.m

305 sq.m

71. Arrange the steps in order to express $15.7\overline{32}$ in $\frac{p}{q}$ form

10x = 157.3232.......
1000x = 15732.3232........
Subtracting we get x = $\frac{15575}{990}$
Let x = $15.7\overline{32}$

ii, i, iii, iv

iv, ii, i, iii

iii, i, ii, iv

iv, ii, iii, i

72. Identify the rational number shown A marked in the following number line.

$\frac{3}{7}$

$\frac{4}{6}$

$\frac{4}{7}$

$\frac{5}{7}$

73. Write a rational number for the points labelled with letters P, Q, R, S in order on number line.

$\frac{-3}{2},\frac{-5}{4},\frac{-3}{4},\frac{-1}{4}$

$\frac{-1}{4},\frac{-3}{4},\frac{-5}{4},\frac{-3}{2}$

$\frac{6}{4},\frac{5}{4},\frac{3}{4},\frac{1}{4}$

$\frac{1}{4},\frac{3}{4},\frac{5}{4},\frac{6}{4}$

74. Which letter of the number indicates $\frac{17}{5}$ in the following ?

75. The sets of natural numbers, whole numbers, integers and rational numbers can be put as in the following figures.

76. Integers are combination of

Negative numbers and Positive numbers

Whole numbers and Positive numbers

Whole numbers and Negative numbers

Positive numbers and zero

77. The additive identity is

- 1

Infinite

78. Identify the property in 2+3 = 3+2

Commutative property

Associative property

Closure property

None

79. Identify the property in 3 $\times$ 0 = 0 $\times$ 3

Commutative property

Associative property

Closure property

None

80. Identify the property in 3-2 $\neq$ 2-3

Commutative property

Associative property

Closure property

None

81. Identify the property in 3 $\div$ 2 $\neq$ 2 $\div$ 3

Commutative property

Associative property

Closure property

None

82. Identify the property in 2+(3+0) = (2+3)+0

Associative property

Closure property

Commutative property

None

83. Identify the property in 2-(3-0) $\neq$ (2-3)-0

Associative property

Closure property

Commutative property

None

84. Identify the property in 2 $\div$ (3 $\div$ 0) $\neq$ (2 $\div$ 3) $\div$ 0

Associative property

Closure property

Commutative property

None

85. Identify the property in 2 $\times$ (3 $\times$ 0) $\neq$ (2 $\times$ 3) $\times$ 0

Associative property

Closure property

Commutative property

None

86. Do natural numbers obey associative property under addition ?

Yes

Slightly obeyed

Can't say

87. Do whole numbers obey associative property under addition ?

Yes

Slightly obeyed

Can't say

88. Do integers obey associative property under addition ?

Yes

Slightly obeyed

Can't say

89. Do integers obey associative property under addition ?

Yes

Slightly obeyed

Can't say

90. Do rational numbers obey associative property under addition ?

Yes

Slightly obeyed

Can't say

91. Do rational numbers obey associative property under multiplication ?

Yes

Slightly obeyed

Can't say

92. Do integers obey associative property under multiplication ?

Yes

Slightly obeyed

Can't say

93. Do whole numbers obey associative property under multiplication ?

Yes

Slightly obeyed

Can't say

94. Do natural numbers obey associative property under multiplication ?

Yes

Slightly obeyed

Can't say

95. {1 , 2 , 3 ,.........} is the set of

Natural numbers

Whole numbers

Integers

Rational number

96. {0 , 1 , 2 , 3 ,.........} is the set of

Natural numbers

Whole numbers

Integers

Rational number

97. {...........- 3 , - 2 , - 1 , 0 , 1 , 2 , 3 ,.........} is the set of

Natural numbers

Whole numbers

Integers

Rational number

98. Rational numbers are ................. under addition

Closure

Commutative

Both

None

99. Hamid : $\frac{5}{3}$ is rational and 5 is natural number
Hamida : $\frac{5}{3}$ , 5 are rational
The correct statements are

Only hamid is correct

Only hamida is correct

Both are correct

Both are false

100. Zero is

Whole numbe

Integer

Rational number

All

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