Class 8th Mathematics MCQ
Chapter 1: Rational Numbers Part 2
Q57. Find the reciprocal of ‘0’.
1. 1
2. 0
3. Does not exist
4. -1
Ans: 3. Does not exist
Solution:
Reciprocal of ‘0’
1
0 which does not exist.
Therefore, Zero has no reciprocal.
Q58. −
3
8 +
1
7 = +
− 3
8 is an example to show that:
1. Addition of rational numbers is commutative.
2. Rational numbers are closed under addition.
3. Addition of rational number is associative.
4. Rational numbers are distributive under addition.
Ans: 1. Addition of rational numbers is commutative.
Q59. Tick (✓ ) the correct answer the following:
The sum of two numbers is− 4/3 . If one of the numbers is -5, what is the other?
1.− 11/3
2.11/3
3.− 19/3
4.19/3
Ans: 2.
11/3
Solution:
Sum of two numbers =
− 4
3
One number = -5
Second number =
− 4
3 − ( − 5)
=
− 4/3 +5/1
=
− 4 + 15/3
=
11/3
Q60. x + y
2 is a rational number.
1. Between x and y.
2. Less than x and y both.
3. Greater than x and y both.
4. Less than x but greater than y.
Ans: 1. Between x and y.
Solution:
Let x and y be two numbers.
Case-I If x < y
Then,
x + y
2 lies in between x and such that
Case-II If x < y
Then,
x + y
2 lies in between x and y such that
Q61. Which of the following statements is false?
1. Natural numbers are commutative for addition.
2. Whole numbers are commutative for addition.
3. Integers are not commutative for addition.
4. Rational numbers are commutative for addition.
Ans: 3. Integers are not commutative for addition.
Q62. Which of the following statements is true?
1. Natural numbers are commutative for subtraction.
2. Whole numbers are commutative for subtraction.
3. Integers are commutative for subtraction.
4. Rational numbers are not commutative for subtraction.
Ans: 4. Rational numbers are not commutative for subtraction.
Q63. 0 is not:
1. A natural number
2. A whole number
3. An integer
4. A rational number
Ans: 1. A natural number
Q64. Multiplicative inverse of a negative rational number is:
1. A positive rational number.
2. A negative rational number.
3. 0
4. 1
Ans: 2. A negative rational number.
Solution:
We know that, the product of two rational numbers is 1, taken they are multiplication inverse of each other, e.g.
Suppose, p is negative rational number, i.e.
1
p is the multiplicative inverse of -p,
Then, −p ×
1
− p = 1
Hence, multiplicative inverse of a negative rational number is a negative rational number.
Q65. Which of the following is commutative for rational numbers?
1. Multiplication and division
2. Subtraction and division
3. Addition and subtraction
4. Addition and multiplication
Ans: 4. Addition and multiplication
Q66. a + b = b + a is called:
1. Commutative law of addition
2. Associative law of addition
3. Distributive law of addition
4. None of these
Ans: 1. Commutative law of addition
Q67. Find the multiplicative inverse of
1/4 .
1. 4
2.− 1/4
3. -4
4.1/4
Ans: 1. 4
Q68. -(-x) is same as:
1. − x
2. x
3.
1
x
4.
− 1
x
Ans: 2. x
Solution:
-(-x) = x
Negative of negative rational number is equal to positive rational number.
Q69. Find the reciprocal of -2.
1. 2
2. -2
3.− 1/2
4. None of these
Ans: 3.
− 1/2
Q70. Which among the following is a rational number equivalent to
− 5/− 3 ?
1.
− 25/15
2.
25/− 15
3.
25/15
4.
− 25/30
Ans: 3.
25
15
Q71. What is the value of
3/4 +5/6 +2/7 ?
1.
157/84
2.
10/84
3.167/84
4.134/84
Ans: 1.
157/84
Solution:
Given,
3/4 +5/6 +2/7
LCM of 4, 6 and 7 = 84
Now, making the denominators the same and adding the given rational numbers, we get;
⇒
63/84 +70/84 +24/84
⇒
157/84
Q72. If a and b are two rational numbers, then:
1.a+b/2 < a
2.a+b/2 < b
3.a+b/2 = a
4.a+b/2 > b
Ans: 2.
a+b/2 < b
Q73. Tick (✓ ) the correct answer the following:
The product of two rational numbers is
− 28
81 . If one of the numbers is
14/27 then the other one is:
1.− 2/3
2.2/3
3.3/2
4.− 3/2
Ans: 1.
− 2/3
Solution:
Product of two numbers =
− 28/81
One numbers =
14/27
∴ Other number =
− 28/81 ÷14/27
=
− 28/81 ×27/14
=
− 2/3
Q74. What is the reciprocal of
1/9 ?
1. 1
2. None of the above
3. 9
4. 0
Ans: 3. 9
Q75. What is the sum of
2/3 and 4/9 ?
1.
10/3
2.
6/3
3.
10/9
4.
6/9
Ans: 3.
10/9
Q76. Which of the following is the product of
7/8 and − 4/21 ?
1.− 1/6
2.1/12
3.− 16/63
4.− 147/16
Ans: 1.
− 1/6
Q77. The value of
1/2 +1/4 is equal to:
1. 1
2.3/4
3.2/3
4.3/2
Ans: 2.
3/4
Solution:
1/2 +1/4
Making the denominator equal:
2/4 +1/4 =
( 2 + 1 )
4 =3/4
Q78.
Which of the following is the product of
− 7/8 and 4/21 ?
1.− 1/6
2. 12
3.− 63/16
4.− 16/147
Ans: 1.− 1/6
Q79. Tick (✓ ) the correct answer the following:
− 3/7− 1 = ?
1.7/3
2.− 7/3
3.3/7
4. None of these.
Ans: 2.− 7/3
Solution:
− 3/7− 1 =− 7/3
∵ x − 1 =1/x
Q80. Which of the following statements is false?
1. Natural numbers are closed under subtraction.
2. Whole numbers are not closed under subtraction.
3. Integers are closed under subtraction.
4. Rational numbers are closed under subtraction.
Ans: 1. Natural numbers are closed under subtraction.
Q81. Which of the following statements is true?
1. Natural numbers are not associative for multiplication.
2. Whole numbers are not associative for multiplication.
3. Integers are associative for multiplication.
4. Rational numbers are not associative for multiplication.
Ans: 3. Integers are associative for multiplication.
Q82. The multiplicative identity of rational numbers is:
1. 1
2. 2
3. -1
4. 0
Ans: 1. 1
Solution:
Any number multiplied by 1 is equal to the number itself.
5 × 1 = 5
Therefore, 1 is the multiplicative identity of rational numbers.
Q83. Write the additive inverse of
4/5 .
1. 1
2. −4/5
3.4/5
4. 0
Ans: 2. −4/5
Q84. A number of the form
p/q is said to be a rational number if:
1. p and q are integers.
2. p and q are integers and q ≠ 0
3. p and q are integers and p ≠ 0
4. p and q are integers and p ≠ 0 also q ≠ 0
Ans: 2. p and q are integers and q ≠ 0.
Solution:
A number of the form
p/q is said to be a rational number, if p and q are integers.
Q85. Which of the following statements is true?
1. Natural numbers are associative for addition.
2. Whole numbers are not associative for addition.
3. Integers are not associative for addition.
4. Rational numbers are not associative for addition.
Ans: 1. Natural numbers are associative for addition.
Q86. Which of the following is the identity element?
1. 1
2. -1
3. 0
4. None of these.
Ans: 3. 0
Solution:
The additive identity element is 0.
We know that the sum of 0 and any number is the number itself. Let the number be x.
∴ x + 0 = 0
⇒ x = 0
Q87. The reciprocal of any rational number p and q, where p and q are integers and q ≠ 0, is:
1.p/q
2. 1
3. 0
4.q/p
Ans: 4.
q/p
Solution:
The reciprocal of any rational number
p/q ,
Where p and q are integers and q ≠ 0 is
q/p .
Q88. Mark (✓ ) against the correct answer of the following:
What should be subtracted from
− 2/3 to get3/4 ?
1.− 11/12
2.− 13/12
3.− 5/4
4.− 17/12
Ans: 4.− 17/12
Solution:
Let the number be x
Now,
− 2/3 − x =3/4
⇒ − 1 ×2
3 + x =3/4
⇒
2/3 + x =− 3/4
⇒ x =− 3/4 + Additive inverse of2/3
⇒ x =− 3/4 −− 2/3
⇒ x =− 3/4 +2/3
⇒ x =− 3 × 3/4 × 3 +2 × 4/3 × 4
⇒ x =− 9/12 +− 8/12
⇒ x =− 17/12
Q89. What is the sum of the additive inverse and multiplicative inverse of 2?
1.3/2
2.− 3/2
3.1/2
4.− 1/2
Ans: 2.− 3/2
Q90. Tick (✓ ) the correct answer the following:
8/− 15 +4/− 3 = ?
1.28/15
2.− 28/15
3.− 4/5
4.− 4/15
Ans: 2.− 28/15
Solution:
8/− 15 +4/− 3
=8 + 20/− 15
=28/− 15
=− 28/15
Q91. Tick (✓ ) the correct answer the following:
Reciprocal of− 3/4 is:
1.4/3
2.3/4
3.− 4/3
4. 0
Ans: 3.− 4/3
Solution:
Reciprocal of − 3/4 is − 4/3
Q92. Mark (✓ ) against the correct answer of the following:
4/3 ÷ ? =− 5/2
1.− 8/5
2.8/5
3.− 8/15
4.8/15
Ans: 3.− 8/15
Solution:
We have,
4/3 ÷ x =− 5/2
⇒4/3 ×1/x =− 5/2
⇒1/x =− 5/2
4/3
⇒1/x =− 5/2 ×3/4
⇒1/x =− 15/8
⇒1/x =8/− 15
⇒1/x =8 × − 1/− 15 × − 1
⇒1/x =− 8/15
Q93. Which of the following statements is false?
1. Natural numbers are commutative for multiplication.
2. Whole numbers are commutative for multiplication.
3. Integers are not commutative for multiplication.
4. Rational numbers are commutative for multiplication.
Ans: 3. Integers are not commutative for multiplication.
Q94. How many rational numbers are there in between
3/4 and 1?
1. 2
2. Countless
3. 0
4. 1
Ans: 2. Countless
Solution:
We can write
3/4 as
30/40 and 1 as 40/40 .
Hence the rational numbers between them are:
31/40 ,32/40 ,33/40 ,34/40 ,35/40 ,36/40 ,37/40 ,38/40 ,39/40 .
Note: There are countless rational numbers between any two rational numbers.
Q95. If x be any rational number then x + 0 is equal to:
1. x
2. 0
3. -x
4. Not defined.
Ans: 1. x
Solution:
If x is any rational number,
Then x + 0 = x [0 is the additive identity]
Q96. The rational number which is equal to negative is:
1. 0
2. -1
3. 1
4.1/2
Ans: 1. 0
Q97. Tick (✓ ) the correct answer the following:
The product of two numbers is − 16/35 . If one of the numbers is − 15/14 then the other is-
1. − 2/5
2. 8/15
3.32/75
4.− 8/3
Ans: 3.32/75
Solution:
Let x be the required number
Then,
− 15/14 × x =− 16/35
⇒ x =− 16/35 ÷− 15/14
⇒ x =− 16/35 ×14/− 15
⇒− 224/− 525 =224/525
=224 ÷ 7/525 ÷ 7
=32/75
Q98. Which number is in the middle if
− 1/6 ,4/9 ,6/− 7 ,2/5 and− 3/4 arranged in descending order?
1.2/5
2.4/9
3.− 1/6
4.− 6/7
Ans: 3.− 1/6
Q99. What is the value of 100 divided by 0?
1. 1
2. Undefined
3. 0
4. 100
Ans: 2. Undefined
Q100. The negative of 2 is:
1. 2
2.1/2
3. − 2
4. −1/2
Ans: 3. − 2
Q101. (a + b) + c = a + (b + c) is called:
1. Commutative law for multiplication
2. Commutative law for addition
3. Associative law for addition
4. Associative law for multiplication
Ans: 3. Associative law for addition
Q102. The additive identity of rational numbers is:
1. 2
2. -1
3. 0
4. 1
Ans: 3. 0
Solution:
Any number added to zero is equal to the number itself.
5 + 0 = 5
Therefore, 0 is the additive identity of rational numbers.
Q103. Which of the following statements is false?
1. Natural numbers are closed under addition.
2. Whole numbers are closed under addition.
3. Integers are closed under addition.
4. Rational numbers are not closed under addition.
Ans: 4. Rational numbers are not closed under addition.
Q104. Which of the following is the reciprocal of a?
1. a
2. − a
3.1/a
4. −1/a
Ans: 3.
1/a
Solution:
We can get reciprocal of a number just be interchanging its numerator and denominator. Thus, the reciprocal of a is
1/a .
Q105. What should be added to −5/4 to get -1?
1. −1/4
2.1/4
3. 1
4. −3/4
Ans: 2.
1/4
Q106. The additive inverse of −
3/4 is:
1. −3/4
2. 1
3. 0
4.3/4
Ans: 4.3/4
Q107. Which of the following statements is true?
1. Natural numbers are closed under multiplication.
2. Whole numbers are not closed under multiplication.
3. Integers are not closed under multiplication.
4. Rational numbers are not closed under multiplication.
Ans: 1. Natural numbers are closed under multiplication.
Q108. Which of the following is an example of distributive property of multiplication over addition for rational numbers.
1. −1/4 ×2/3 +− 4/7 = −1/4 ×2/3 + −1/4 ×− 4/7
2. −1/4 ×2/3 +− 4/7 =1/4 ×2/3 −− 4/7
3. −1/4 ×2/3 +− 4/7 =2/3 + −1/4 ×− 4/7
4. −1/4 ×2/3 +− 4/7 =2/3 +− 4/7 −1/4
Ans:1. −1/4 ×2/3 +− 4/7 = −1/4 ×2/3 + −1/4 ×− 4/7
Solution:
We know that, the distributive property of multiplication over addition for rational numbers can be expressed as a x (b + c) = ab + ac, where a, b
and c are rational numbers.
Is the example of distributive property of multiplication over addition for rational numbers.
Q109. The negative of -2 is:
1. -2
2. 2
3. −1/2
4.1/2
Ans: 2. 2
Q110. The value of
1/2 ×3/5 is equal to:
1.3/5
2.2/5
3.1/2
4.3/10
Ans: 4.3/10
Q111. One (1) is:
1. The identity for addition of rational numbers.
2. The identity for subtraction of rational numbers.
3. The identity for multiplication of rational numbers.
4. The identity for division of rational numbers.
Ans: 3. The identity for multiplication of rational numbers.
Solution:
One (1) is the identity for multiplication of rational numbers.
That means,
If a is a rational number.
Then, a – 1 = 1 – a = a
Note: One (1) is the multiplication identity for integers and whole number also.
Q112. Which of the following statement is true?
1. The difference of two rational numbers is always a rational number.
2. Addition of two rational numbers is associative.
3. Addition of two rational numbers is commutative.
4. All of the above.
Ans: 4. All of the above.
Solution:
As we know that difference of two rational numbers is always a rational number.
9 (The difference of two rational numbers is always a rational number)
And, −
21 (Addition of two rational numbers is commutative)
Also,
15 (Addition of two numbers is associative)
There all the given statements are true.
Also Read Notes: –Class 8th Mathematics Chapter 1: Rational Numbers