MCQ on Rational Numbers for Class 8
Class 8 Maths Chapter 1 Rational Numbers MCQ
MCQ of Rational Numbers Class 8
I. Choose the correct answer.
Question 1.
Solution of x – 7 = 0 is a _________ number.
A) Natural
B) Whole
C) Integer
D) All the above
Answer:
D) All the above
Question 2.
Rational numbers are denoted with _________ .
A) N
B) Q
C) W
D) Z
Answer:
B) Q
Question 3.
The general form of a rational number is \(\frac{\mathbf{q}}{\mathbf{p}}\). Where ‘q’ is a _________ .
A) none zero whole number
B) integer
C) non zero integer
D) natural number
Answer:
C) non zero integer
Question 4.
If a, b are whole numbers, then (a + b) is also a whole number. This property is called _________ .
A) closure under addition
B) closure under subtraction
C) Associative under addition
D) All the above
Answer:
A) closure under addition
Question 5.
Which of the following statements are true
A) All natural numbers are whole numbers
B) All whole numbers are integers
C) All natural, whole, integers are rational numbers
D) All the above
Answer:
D) All the above
Question 6.
(- 1) is a _________ .
A) Whole number
B) Integer
C) Rational number
D) B & C
Answer:
D) B & C
Question 7.
If A, B and (A x B) are three numbers which belongs to same number set. Then A, B may belong to _________ numbers.
A) Natural
B) Rational
C) Whole
D) Any of the above
Answer:
D) Any of the above
Question 8.
Which number system has the property of closure under division ?
A) Natural
B) Integers
C) Whole
D) None of the above
Answer:
D) None of the above
Question 9.
Zero is called additive identity of _________ .
A) Natural
B) Integers
C) Rational
D) All the above
Answer:
D) All the above
Question 10.
Multiplicative identity of Rational Numbers is _________ .
A) -1
B) 0
C) 1
D) none
Answer:
C) 1
Question 11.
The Associative law of Rational numbers say that _________ (under addition or multiplication)
A) order is important
B) order is not important
C) whether ‘0’ is among them or not
D) none of above
Answer:
B) order is not important
Question 12.
(3 – 4) – 5 ≠ 3 – (4 – 5) is an example for the rule _________ .
A) subtraction is not associative
B) subtraction is not commutative
C) subtraction is not closure
D) all the above
Answer:
A) subtraction is not associative
Question 13.
\(\frac{-5}{8}\) is additive inverse of _________ .
A) – 5 and 8
B) \(\frac{5}{8}\)
C) \(\frac{-8}{5}\)
D) \(\frac{8}{5}\)
Answer:
B) \(\frac{5}{8}\)
Question 14.
{\(\frac{7}{9}\) × \(\frac{-11}{15}\)} + {\(\frac{7}{9}\)} × \(\frac{8}{15}\) can be written
A) \(\frac{7}{9}\) [\(\frac{-11}{15}\) × \(\frac{-8}{15}\)]
B) \(\frac{7}{9}\) [\(\frac{-11}{15}\) + \(\frac{-8}{15}\)]
C) \(\frac{7}{9}\) [\(\frac{-11}{15}\) × \(\frac{8}{15}\)]
D) \(\frac{7}{9}\) [\(\frac{-11}{15}\) + \(\frac{8}{15}\)]
Answer:
D) \(\frac{7}{9}\) [\(\frac{-11}{15}\) + \(\frac{8}{15}\)]
Question 15.
The law behind splitting a product as a sum of the products, is _________ .
A) closure under addition
B) commutative under addition
C) associative under addition
D) distributive under addition
Answer:
D) distributive under addition
Question 16.
– (- x) = x can be written for all ‘x’ in which ‘x’ is a _________ number.
A) Natural
B) Rational
C) Whole
D) Any of above
Answer:
D) Any of above
Question 17.
The value of (\(\frac{-1}{2}\) × \(\frac{3}{4}\)) + (\(\frac{-1}{2}\) × \(\frac{1}{4}\) ) is equal to _________ .
A) \(\frac{-1}{9}\) × (1)
B) \(\frac{+1}{2}\)
C) \(\frac{-1}{2}\) × (\(\frac{3}{4}\) × \(\frac{1}{4}\) )
D) none
Answer:
A) \(\frac{-1}{9}\) × (1)
Question 18.
The associative property is applicable to __________ .
A) +, ×
B) ×, ÷
C) -, +
D) -, ÷
Answer:
C) -, +
Question 19.
A rational number is in the form of \(\frac{\mathbf{q}}{\mathbf{p}}\) where ?
A) q, p ≠ 0
B) p ≠ 0
C) q, p = 0
D) q ≠ 0, p = 0
Answer:
B) p ≠ 0
Question 20.
\(\frac{-3}{5}\) ÷ \(\frac{-5}{3}\) = ________ .
A) \(\frac{9}{25}\)
B) \(\frac{-9}{5}\)
C) 1
D) none
Answer:
A) \(\frac{9}{25}\)
Question 21.
\(\frac{3}{4}\) × \(\frac{5}{6}\) + \(\frac{3}{4}\) × \(\frac{-1}{6}\) = ________ .
A) \(\frac{1}{6}\)
B) \(\frac{1}{2}\)
C) \(\frac{2}{3}\)
D) \(\frac{-3}{5}\)
Answer:
B) \(\frac{1}{2}\)
Question 22.
\(\frac{2}{7}\) × \(\frac{1}{5}\) + \(\frac{2}{7}\) × \(\frac{2}{5}\) + \(\frac{2}{7}\) × \(\frac{3}{5}\)
= \(\frac{2}{7}\) × (\(\frac{1}{5}\) + \(\frac{2}{5}\) + \(\frac{1}{6}\)) is an example for _________ .
A) multiplicative association
B) distributive association
C) closure under addition
D) none
Answer:
A) multiplicative association
Question 23.
Product of additive identity and reciprocal of a rational number is always equal to _________ .
A) zero
B) 1
C) that number
D) none
Answer:
A) zero
Question 24.
Which of these are rational numbers ?
37, \(\frac{36.29}{2}\), 25.49, \(\frac{-37}{69}\)
A) Only \(\frac{-37}{69}\)
B) Only \(\frac{-37}{69}\) and \(\frac{36.29}{2}\)
C) Only 37, \(\frac{-37}{69}\) and \(\frac{36.29}{2}\)
D) All of these
Answer:
D) All of these
Question 25.
p and q are any two rational numbers and @ is an operation such that p @ q is NOT EQUAL to q @ p.
Which of these could be the operation @ ?
A) Either addition or mulitiplication
B) Either multiplication or division
C) Either subtraction or division
D) (@ cannot be addition, subtraction, multiplication or division as p @ q is always equal to q @ p)
Answer:
C) Either subtraction or division
Question 26.
Which of the following numbers lies between the two numbers marked on the number line below
A) \(\frac{-8}{7}\)
B) \(\frac{-7}{8}\)
C) -7.8
D) -8.7
Answer:
C) -7.8
Question 27.
Which number when multiplied with 2\(\frac{1}{5}\) will result in 1 ?
A) \(\frac{5}{1}\)
B) \(\frac{5}{2}\)
C) \(\frac{5}{11}\)
D) \(\frac{5}{21}\)
Answer:
C) \(\frac{5}{11}\)
Question 28.
Which of the following statements is TRUE ?
A) 3 ÷ \(\frac{1}{3}\) = \(\frac{1}{3}\) ÷ 3
B) (3 ÷ \(\frac{1}{3}\)) ÷ 3 = 3 ÷ (\(\frac{1}{3}\) ÷ 3)
C) 3 ÷ (3 + 3) = (3 ÷ 3) + (3 ÷ 3)
D) (3 – \(\frac{1}{3}\) ÷ 3 = (3 ÷ 3) – (\(\frac{1}{3}\) ÷ 3)
Answer:
D) (3 – \(\frac{1}{3}\) ÷ 3 = (3 ÷ 3) – (\(\frac{1}{3}\) ÷ 3)
Question 29.
A rational number is one which can be written in the form \(\) where x and y are integers and y is not zero. For example – 2.5 is rational number as it can be written as – \(\frac{5}{2}\)
Which of these is NOT a rational number ?
A) 2.353535 …………….
B) –\(\frac{1}{4}\)
C) \(\frac{3}{0}\)
D) 0
Answer:
C) \(\frac{3}{0}\)
Question 30.
Which of the following rational numbers has a recurring decimal expansion ?
A) \(\frac{6}{15}\)
B) \(\frac{12}{18}\)
C) \(\frac{23}{25}\)
D) \(\frac{123}{400}\)
Answer:
B) \(\frac{12}{18}\)
Question 31.
Which of the following points represents -1\(\frac{2}{3}\) on a number line ?
A) K
B) L
C) M
D) N
Answer:
A) K
Question 32.
In which of the following cases will the sum of p and q be greater than the product of p and q ?
A) When p and q are both negative numbers
B) When p and q both lie between 0 and 1
C) When p and q both lie between 1 and 10
D) It is not possible for any value of p and q
Answer:
B) When p and q both lie between 0 and 1
Question 33.
A rational number R is marked on the number line shown below.
Which of the following number lines shows the approximate location of (-\(\frac{1}{\mathbf{R}}\)) ?
Answer:
Question 34.
Ritu, Tarun and Imran did the following operations on – \(\frac{12}{55}\) and \(\frac{15}{31}\)
Ritu : – \(\frac{12}{55}\) + \(\frac{15}{31}\)
Tarun: – \(\frac{12}{55}\) × \(\frac{15}{31}\) ; Imran: – \(\frac{12}{55}\) ÷ \(\frac{15}{31}\)
Who will get a rational number ?
A) Only Ritu
B) Only Ritu and Tarun
C) All – Ritu, Tarun and Imran
D) None of Ritu, Tarun and Imran
Answer:
C) All – Ritu, Tarun and Imran
Question 35.
How many rational numbers are there between \(\frac{62}{79}\) and \(\frac{64}{79}\) ?
A) 1
B) 79
C) 100
D) Infinitely many
Answer:
D) Infinitely many
Question 36.
p and q are two rational numbers such that their product is – 2 If p is – \(\frac{4}{7}\), what is \(\frac{\mathbf{p}}{\mathbf{q}}\) ?
A) \(\frac{8}{7}\)
B) \(\frac{7}{2}\)
C) –\(\frac{2}{7}\)
D) –\(\frac{8}{49}\)
Answer:
D) –\(\frac{8}{49}\)
Question 37.
How many pieces of rope, each measuring 3\(\frac{3}{4}\) metres, can be cut from a 30 metres long rope?
A) 6
B) 8
C) 10
D) 12
Answer:
B) 8
Question 38.
Which one of the following is the railtional number lying between \(\frac{6}{7}\) and \(\frac{7}{8}\)?
A) \(\frac{94}{112}\)
B) \(\frac{95}{112}\)
C) \(\frac{97}{112}\)
D) \(\frac{99}{112}\)
Answer:
C) \(\frac{97}{112}\)
Question 39.
The multiplicative inverse of ‘-2’.
A) \(\frac{3}{2}\)
B) \(\frac{-3}{2}\)
C) \(\frac{1}{2}\)
D) \(\frac{-1}{2}\)
Answer:
D) \(\frac{-1}{2}\)
Question 40.
Which of the following is a rational number between \(\frac{1}{3}\) and \(\frac{5}{3}\)
A) \(\frac{7}{3}\)
B) \(\frac{4}{3}\)
C) \(\frac{5}{3}\)
D) \(\frac{6}{3}\)
Answer:
B) \(\frac{4}{3}\)
Question 41.
For what value of x, \(\frac{-12}{x}\) is equal to 3
A) -4
B) 4
C) 3
D) -3
Answer:
A) -4
Question 42.
42(4 + 2) = (42 × 4) + (42 + 2) is an example of _________
A) Closure property
B) Commutative property
C) Associative property
D) Distributive property
Answer:
D) Distributive property
Question 43.
What is the value of k ?
A) -13
B) -9
C) 9
D) 13
Answer:
A) -13
Question 44.
Which of the following will be the PRODUCT of additive inverse and reciprocal of a number ?
A) -1
B) 0
C) 1
D) a decimal number
Answer:
A) -1
Question 45.
Read the following statements and select the correct option.
Statement 1 : ALL Whole numbers are Rational Numbers.
Statement 2 : ALL Natural numbers are Rational Numbers.
A) 1 is true 2 is false
B) 1 is true 2 is false
C) 1 is true 2 false
D) 1 is true 2 is false
Answer:
A) 1 is true 2 is false
Question 46.
Which of the following is NOT a rational number ?
A) √5
B) √9
C) 1
D) 1.3
Answer:
A) √5
Question 47.
\(\frac{-14}{17}\) × \(\frac{-17}{14}\) _______
A) 0
B) 1
C) -1
D) \(\frac{196}{289}\)
Answer:
B) 1
Question 48.
Which of the following is TRUE about rational numbers ?
A) Not closed under subtraction
B) Not closed under addition
C) Closed under division
D) Closed under addition and division
Answer:
D) Closed under addition and division
Question 49.
Additive identity is __________
A) 0
B) 1
C) – 1
D) 0 and 1
Answer:
A) 0
II. Fill in the blanks.
1. If a, b are multiplicative inverses of each other then (a × b) = __________ .
Answer:
1
2. Which Rational number has no reciprocal ? __________ .
Answer:
Zero
3. Example for a rational number for which its reciprocal also equal to itself __________ .
Answer:
1 and -1
4. Which number line can be extended to right from the number zero but not to left from zero ? __________ .
Answer:
whole numbers
5. Give a pair of examples for Rational numbers which lie in between 0.7 and 0.77? __________ .
Answer:
0.71, 0.711, 0.72, ……. etc.
6. Give a, b are two rational number. Then __________ is always another rational number in between them.
Answer:
\(\frac{a+b}{2}\), \(\frac{a+b}{3}\) or \(\frac{a+b}{5}\) ……. \(\frac{a+b}{n}\)
7. Mutliply \(\frac{4}{5}\) with multiplicative inverse of \(\frac{-5}{4}\). Then you get __________ .
Answer:
\(\frac{-16}{25}\)
8. Reciprocal of ‘x’ is always \(\frac{1}{x}\) where x is __________ .
Answer:
not equal to zero
9. A rational number which is equal to its negative is __________ .
Answer:
zero
10. 
in this number line A, B, C, D represents _________ .
Answer:
Rational
11. 
in the above number line ‘P’ is mid point of 2, 4 and ‘Q’ is mid point of 4 and 6. Then this number line represents _________ .
Answer:
Integer line
12. Given a, b, c, and ‘d’ are (non-zero) rational numbers. Such, that ac = bd. Then \(\frac{a}{b}\) and \(\frac{c}{d}\) are called ________ .
Answer:
reciprocal of each other
13. Sum of \(\frac{4}{5}\) and additive inverse of \(\frac{-4}{5}\)
is __________ .
Answer:
\(\frac{8}{5}\)
14. Sum of additive inverses of \(\frac{3}{4}\) and \(\frac{-3}{4}\) is _________ .
Answer:
zero
15. Negative number of a rational number is nothing but its _________ .
Answer:
Additive inverse
16. Reciprocal of a rational number is nothing but its_________ .
Answer:
multiplicative inverse
17. _________ is the additive identity of Natural numbers.
Answer:
No, natural number
18. _________ is the multiplicative identity of Rational numbers.
Answer:
1
19. _________ is the additive identity of Intergers.
Answer:
0
III. Match the following.
Question 1.
| A | B |
| 1) Not closed under subtraction | a) division |
| 2) \(\frac{-2}{5}\) + \(\frac{5}{7}\) = …………. | b) associative under addtion |
| 3) Subtraction and which are not associative for rational numbers. | c) \(\frac{11}{35}\) |
| 4) Which property holds good under addition all number sets. | d) natural numbers |
| 5) a + (b + c) = (a + b) + c | e) addition |
Answer:
(1, d) (2, c) (3, a), (4, e) (5, b)
| A | B |
| 1) Not closed under subtraction | d) natural numbers |
| 2) \(\frac{-2}{5}\) + \(\frac{5}{7}\) = …………. | c) \(\frac{11}{35}\) |
| 3) Subtraction and which are not associative for rational numbers. | a) division |
| 4) Which property holds good under addition all number sets. | e) addition |
| 5) a + (b + c) = (a + b) + c | b) associative under addtion |
Question 2.
| A | B |
| 1) not a natural number | a) -4 |
| 2) not a whole number | b) 5 |
| 3) not a rational number | c) \(\frac{6}{0}\) |
| 4) additive inverse of – 5 | d) \(\frac{-1}{5}\) |
| 5) multiplicative inverse of – 5 | e) 0 |
Answer:
(1, e) (2, a), (3, c) (4, b), (5, d)
| A | B |
| 1) not a natural number | e) 0 |
| 2) not a whole number | a) -4 |
| 3) not a rational number | c) \(\frac{6}{0}\) |
| 4) additive inverse of – 5 | b) 5 |
| 5) multiplicative inverse of – 5 | d) \(\frac{-1}{5}\) |