Class 8th Mathematics MCQ
Chapter 1: Rational Numbers Part 3
Q113. Tick (✓ ) the correct answer the following:
3 +5/− 7 = ?
1.-16/7
2.16/7
3.− 26/7
4.− 8/7
Ans: 2.16/7
Q114. a × (b × c) = (a × b) × c is called:
1. Associative law for addition
2. Associative law for multiplication
3. Commutative law for addition
4. Commutative law for multiplication
Ans: 2. Associative law for multiplication
Q115. The reciprocal of 1 is:
1. 1
2. -1
3. 0
4. Not defined.
Ans: 1. 1
Solution:
The reciprocal of 1 is the number itself.
Q116. Which of the following numbers lies in the middle of
3/4 and 7/4 :
1. 5.0
2. 3.0
3. 2.5
4. 1.25
Ans: 4. 1.25
Solution:
3/4 = 0.75 and
7/4 = 1.75
Here we see 1.25 lies between 0.75 and 1.75.
Q117. A number which can be expressed as
p/q where p and q are integers and q ≠ 0 is:
1. Natural number.
2. Whole number.
3. Integer.
4. Rational number.
Ans: 4. Rational number.
Solution:
A number Which can be experssed as
p/q , where p and q are integers q ≠ 0 is a rational number.
Q118. Mark (✓ ) against the correct answer of the following:
What should be added to
− 3/5 get − 1/3 ?
1.4/5
2.8/15
3.4/15
4.2/5
Ans: 3.4/15
Solution:
Let the number added be x
Then,
− 3/5 + x =− 1/3
⇒ x =1/3 −− 3/5
⇒ x =− 1 × 5 − ( − 3 ) × 3/15
⇒ x =− 5 + 9/15
⇒ x =4/15
Q119. Which of the following numbers is the simplest form of
3/4 +− 1/4 +− 5/4
1.9/4
2. −3/4
3. −9/4
4.7/4
Ans: 2. −3/4
Q120. Find the product of the
4/5 and the reciprocal of 5/8 .
1.32/24
2.31/25
3.32/25
4.22/25
Ans: 3.32/25
Solution:
The reciprocal of
5/8 =8/5
Now the product of the two given fractions
8/5 ×4/5 =32/25
Therefore, the product is 32/25 .
Q121. Write the following rational numbers in the descending order.
3/7 ,3/4 ,1/2 , 0
1.1/2 ,3/4 ,3/7 , 0
2.3/4 ,1/2 ,3/7 , 0
3. 0,3/7 ,1/2 ,3/4
4. 0,3/4 ,1/2 ,3/7
Ans: 2.3/4 ,1/2 ,3/7 , 0
Solution:
To start with, we change over the given numbers as like denominator.
LCM of 7, 4 and 2 = 28
Now,
3 × 7/4 × 7 =12/28
1 × 14/2 × 14 =14/28
Therefore, the order is
3/4 ,1/2 ,3/7 , 0.
Q122. If x + 0 = 0 + x = x, which is rational number, then 0 is called:
1. Identity for addition of rational numbers.
2. Additive inverse of x.
3. Multiplicative inverse of x.
4. Reciprocal of x.
Ans: 1. Identity for addition of rational numbers.
Solution:
We know that, the sum of any rational number and zero (0) is the rational number itself.
Now, x + 0 = 0 + x = x, which is a rational number, then 0 is called identity for addition of rational numbers.
Q123. The reciprocal 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
Q124. Find
− 3/5 ×7/9 ×21/13 ×− 2/3
1.99/193
2.98/195
3.98/190
4.90/140
Ans: 2.98/195
Solution:
We have
− 3/5 ×7/9 ×21/13 ×− 2/3
⇒− 3/5 ×21/13 ×− 2/3
⇒− 7/15 ×− 14/13
⇒98/195
Therefore, the product is 98/195 .
Q125. To get the product 1, we should multiply
8/21 by:
1.8/21
2.− 8/21
3.21/8
4.− 21/8
Ans: 3.21/8
Solution:
Let we should multiply
8
21 by x.
Then according to question, x ×
8
21 = 1
Hence, we should multiply
8
21 by
21
8 , for getting the product 1.
Q126. Tick (✓ ) the correct answer the following:
− 9/16 ×8/15 = ?
1.− 3/10
2.− 4/15
3.− 9/25
4.− 2/5
Ans: 2.− 3/10
Q127. Tick (✓ ) the correct answer the following:
− 5/9 ÷2/3 = ?
1.− 5/2
2.− 5/6
3.− 10/27
4.− 6/5
Ans: 2.− 5/6
Q128. Division of rational numbers is associative.
1. False
2. True
Ans: 1. False
Solution:
Division of rational numbers is not associative.
For example,
2/5 ÷1/2 ÷1/4 = 0.2
2/5 ÷1/2 ÷1/4 = 3.2
Hence,
2/5 ÷1/2 ÷1/4 ≠2/5 ÷1/2 ÷1/4
Q129. The multiplicative inverse of −1
1/7 is:
1.
8/7
2.
− 8/7
3.
7/8
4.
7/− 8
Ans: 4.
7/− 8
Solution:
We know that, if the product of two rational numbers is 1,
Then they are multiplicative inverse of each other.
Given number is −1
1/7 , i.e.
− 8
7 .
Let the multiplicative inverse of −
8
7 be x.
⇒
− 8
7 × x = 1
⇒ x = 1 × −
7
8
=
7
− 8
Hence,
7
− 8 is the multiplication inverse of −
8
7 .
Q130. Tick (✓ ) the correct answer the following:
2
3 +
− 4
5 +
7
15 +
− 11
20 = ?
1.
− 1
5
2.
− 4
15
3.
− 13
60
4.
− 7
30
( )
( )
( ) ( )
( )
( )
Ans: 2.
− 4
15
Solution:
LCM of 3, 5, 15 and 20 = 60
∴
2
3 +
− 4
5 +
7
15 +
− 11
20
=
40 + ( − 48 ) + 28 + ( − 33 )
60
=
40 − 48 + 28 − 33
60
=
68 − 81
60
=
− 13
60
Q131. Find two rational numbers be tween
1
3 and
5
6 .
1.
1
2 ,
2
3
2.
1
3 ,
2
3
3.
2
3 ,
4
3
4.
1
2 ,
1
3
Ans: 1.
1
2 ,
2
3
Solution:
First make the denomina same,
1 × 2
3 × 2 =
2
6
Now, two rational numbers between
2
6 and
5
6 are
3
6 ,
4
6
On simplifying the rational numbers, we get
1
2 ,
2
3
Therefore, the two rational number between
1
3 and
5
6 are
1
2 ,
2
3 .
Q132. Tick (✓ ) the correct answer the following:
− 5
16 +
7
12 = ?
1.
− 7
48
2.
1
24
3.
13
48
4.
1
3
Ans: 3.
13
48
Solution:
∵
− 5
16 +
7
12
=
− 5 + 28
48
=
13
48
Q133. Tick (✓ ) the correct answer the following:
Which of the following numbers is in standard form?
1.
− 12
26
2.
− 49
71
3.
− 9
16
4.
28
− 105
Ans: 3.
− 9
16
Solution:
We know that a number is called in standard form if the numerator and denominator has no common divisor except 1.
− 9
16 is in standard form.
( )
Q134. What should be subtracted from −
2
3 to get -1?
1.
2
3
2. −
2
3
3.
1
3
4. −
1
3
Ans: 3.
1
3
Solution:
Let x is subtracted from −
2
3
−
2
3 – x = − 1
– x = − 1 +
2
3
– x = −
2
3
x =
1
3
Q135. Which of the following numbers is the additive inverse of
7
29 :
1.
29
7
2. −
29
7
3. −
7
29
4.
7
29
Ans: 3. −
7
29
Solution:
Multiplicative inverse of
a
b is = −
a
b
Here; a = 7, b = 29
−
a
b = −
7
29
Q136. The value of
5
4 −
8
3 is:
1.
17/12
2.
− 17/12
3.
12/17
4.
− 12/17
Ans: 2.
− 17/12
Q137. Which of the following is the reciprocal of the reciprocal of a rational number?
1. -1
2. 1
3. 0
4. The number itself.
Ans: 4. The number itself.
Solution:
1 and -1 are the only rational numbers which are their own reciprocals. No other rational number is its own reciprocal.
We know that there is no rational number which when multiplied with 0, gives 1.
Therefore, rational number 0 has no reciprocal or multiplicative inverse.
Q138. Which of the following numbers is the product of
6
8 and
7
3 :
1. 1
2. -4
3. −7/4
4.7/4
Ans: 4.7/4
Solution:
Product
6
8 ×
7
3
=
42
24
=
7
4
Q139. Which of the following numbers is the decimal form of
1
4 :
1. -0.25
2. 2.5
3. 0.25
4. -2.5
Ans: 3. 0.25
Solution:
When we divide 1 by 4, we get 0.25.
Q140. A number which can be written in the form,
p
q where p and q are integers and _______ is called a rational number.
1. q = 0
2. q ≠ 0
3. q = 1
4. None of these
Ans: 2. q ≠ 0
Q141. Tick (✓ ) the correct answer the following:
What should be added to
7
12 to get
− 4
15 ?
1.
17/20
2.
− 17/20
3.
7/20
4.
− 7/20
Ans: 2.
− 17/20
Solution:
− 4
15 −
7
12
=
− 16 − 35
60
=
− 51
60
=
− 51 ÷ 3
60 ÷ 3
=
− 17
20
Q142. Mark (✓ ) against the correct answer of the following:
The product of two numbers is
− 1
4 . If one of them is
− 3
10 , then the other is-
1.
5/6
2.
− 5/6
3.
4/3
4.
− 8/5
Ans: 1.
5/6
Solution:
Let the required number be x
Now,
− 3
10 × x =
− 1
4
⇒ x =
− 1
4 ÷
− 3
10
⇒ x =
− 1
4 ×
10
− 3
⇒ x =
10
12
⇒ x =
5
6
Q143. Which of the following is the Multiplicative identity for rational numbers?
1. 1
2. -1
3. 0
4. None of these.
Ans: 1. 1
Solution:
Any number multiplied by 1 is equal to the number itself.
Ex: 5 × 1 = 5
Therefore, 1 is the multiplicative identity of rational numbers.
Q144. ______ Is not associative for rational numbers.
1. Subtraction or Division
2. Addition or Multiplication
3. Addition or Division
4. Multiplication or Division
Ans: 1. Subtraction or Division
Q145. The multipicative inverse of −
2
5 is:
1. −
2
5
2. −
5
2
3.
5
2
4. 1
Ans: 2. −
5
2
Q146. The reciprocal of
− 3
8 ×
− 7
13 is:
1.
104/21
2.
− 104/21
3.
21/104
4.
− 21/104
Ans: 1.
104/21
Solution:
Given number is
− 3
8 ×
− 7
13
The product of −
3
8 ×
− 7
13 =
21
104 .
Hence, the multiplicative inverse of
21
104 is
104
21 .
Q147. Which of the following is neither appositive nor a negative rational number?
1. 1
2. 0
3. Such a rational number doesn’t exist.
4. None of these.
Ans: 2. 0
Solution:
0 is the neutral point on the number line, it is neither positive nor negative rational number.
Q148. The multiplicative inverse of
1
2 is:
1. 1
2. -1
3. 2
4. 0
Ans: 3. 2
Q149. The additive identity for rational numbers is:
1. 1
2. -1
3. 0
4. None of these
Ans: 3. 0
Q150. Mark (✓ ) against the correct answer of the following:
− 5
4
− 1 = ?
1.
4/5
2.
− 4/5
3.
5/4
4.
3/5
Ans: 2.
− 4/5
Q151. The value of
− 10
3 ×
− 15
2 ×
17
19 × 0 is:
1. 35
2. 22.66
3. 0
4. 20
Ans: 3. 0
Solution:
Any number multiplied by zero is equal to zero.
Q152. Write the multiplicative inverse of 2
2
4 in decimal form,
1. 2.5
2. 0.4
3. 0.04
4. 5.2
Ans: 2. 0.4
Solution:
Converting the mixed number into improper fraction,
2/2 4 =
10/4
Multiplicative inverse of
10
4 is
4
10
The decimal form of
4
10 is 0.4
Q153. The numerical expression
3
8 +
( − 5 )
7 =
− 19
56 shows that:
1. Rational numbers are closed under addition.
2. Rational numbers are not closed under addition.
3. Rational numbers are closed under multiplication.
4. Addition of rational numbers is not commutative.
Ans: 2. Rational numbers are not closed under addition.
Solution:
We have
3
8 +
( − 5 )
7 =
− 19
56
Show that rational numbers are closed under addition.
3
8 and
− 5
7 are rational numbers and their addition is
− 19
56 which is also rational number
Note The sun of any two rational numbers is always a rational number.
Q154. Which of the following is the reciprocal of a rational number?
1. -1
2. 1
3. 2
4. Both (a) and (b)
Ans: 4. Both (a) and (b)
Q155. Mark (✓ ) against the correct answer of the following:
Reciprocal of
− 7/9 is:
1.9/7
2.− 9/7
3.7/9
4. None of these.
Ans: 2.− 9/7
Q156. What is the additive inverse of
− 2
3 ?
1. 0
2. 1
3.2/3
4.− 2/3
Ans: 3.
2/3
Q157. Tick (✓ ) the correct answer the following:
What should be subtracted from
− 5/3 to get 5/6 ?
1.5/2
2.3/2
3.5/4
4.− 5/2
Ans: 4. − 5/2
Q158. What must be added to −
5/16 to get 5/8 .
1.10/16
2. −10/16
3.15/16
4. −15/16
Ans: 3.
15/16
Q159. 1
2 is 2:
1. A natural number
2. A whole number
3. An integer
4. A rational number
Ans: 4. A rational number
Q160. The value of
1/2 ÷3/5 is equal to:
1.
6/5
2.
5/6
3.
3/10
4.
3/5
Ans: 2.5/6
Q161. 1 is the __________ for rational numbers.
1. Multiplicative identity
2. Addition of zero
3. Additive identity
4. None of these
Ans: 1. Multiplicative identity
Q162. Find
1/2 +− 3/4 +− 1/2 +3/4 .
1. 0
2. 1
3.
3/4
4.
1/2
Ans: 1. 0
Using the additive inverse of the rational numbers e.g. (x + (-x) = 0)
⇒ (0) + (0)
⇒ 0
Q163. For any three rational numbers a, b and c, a + (b + c) = _________.
1. (a + b) + c
2. (a + b) – c
3. (a – b) + c
4. (a – b) – c
Ans: 1. (a + b) + c
Q164. Between two given rational numbers, we can find:
1. One and only one rational number.
2. Only two rational numbers.
3. Only ten rational numbers.
4. Infinitely many rational numbers.
Ans: 4. Infinitely many rational numbers.
Solution:
We can find infinite many rational numbers between two given rational numbers.
Q165. Which of the following is the identity element under addition?
1. 1
2. -1
3. 0
4. None of these
Ans: 3. 0
Q166. The reciprocal of
1
x (x ≠ 0) is:
1. x
2.
1/x
3. 1
4. 0
Ans: 1. x
Q167. Which of the following is the Multiplicative identity for rational numbers?
1. 1
2. -1
3. 0
4. None of these
Ans: 1. 1
Q168. What should be subtracted from −
5
4 to get -1?
1. −1/4
2.
1/4
3. 1
4. −3/4
Ans: 1. −1/4
Solution:
Let X should be subtracted to −
5/4 to get -1.
−
5/4 – x = − 1
thus x = −
5/4 + 1
x = − 5 +
4/4
x = −
1/4
Hence, −
1/4 Should be subtracted to −
5/4 to get -1.
Q169. An integer can be:
1. Both positive and negative
2. None of the above
3. Only Positive
4. Only Negative
Ans: 1. Both positive and negative
Solution:
An integer can be both positive and negative as well as zero.
i.e. -3, -2, -1, 0, 1, 2, 3,….
Also Read Notes: –Class 8th Mathematics Chapter 1: Rational Numbers