MCQ Questions for Class 8 Maths: Ch 1 Rational Numbers

1. The value of ½ x ⅗ is equal to:

(a) ½

(b) 3/10

(c) ⅗

(d) ⅖

► b) 3/10

2. Find the reciprocal of -2.

(a) 2

(b) -2

(c) -1/2

(d) None of these

► c) -1/2

3. How is -28/84 expressed as a rational number with numerator 4?

(a) 4/7

(b) -4/12

(c) 4/12

(d) 4/-7

► (b) -4/12

4. Which of the following statements is true?

(a) Every fraction is a rational number.

(b) Every rational number is a fraction.

(c) Every integer is a rational number.

(d) Both (a) and (c).

► (d) Both (a) and (c).

5. Which of the following is the reciprocal of the reciprocal of a rational number?

(a) -1

(b) 1

(c) 0

(d) The number itself

► (d) The number itself

6. What is the sum of the additive inverse and multiplicative inverse of 2?

(a) 3/2

(b) -3/2

(c) 1/2

(d) -1/2

► (b) -3/2

7. Which among the following is a rational number equivalent to -5/-3 ?

(a) -25/15

(b) 25/-15

(c) 25/15

(d) -25/30

► (c) 25/15

8. Which of the following is the reciprocal of a rational number?

(a) -1

(b) 1

(c) 2

(d) Both a and b

► (d) Both a and b

9. Write the additive inverse of 4/5.

(a) 1

(b) -4/5

(c) 4/5

(d) 0

► (b) -4/5

10. Find the multiplicative inverse of 1/4.

(a) 4

(b) -1/4

(c) -4

(d) 1/4

► (a) 4

11. What is the additive inverse of -2/3?

(a) 0

(b) 1

(c) 2/3

(d) -2/3

► (c) 2/3

12. The value of ½ + ¼ is equal to:

(a) ¾

(b) 3/2

(c) ⅔

(d) 1

► (a) ¾

13. Which of the following is the identity element under addition?

(a) 1

(b) -1

(c) 0

(d) None of these

► (c) 0

14. A number which can be written in the form, p/q where p and q are integers and _____ is called a rational number.

(a) q = 0

(b) q ≠ 0

(c) q = 1

(d) none of these

► (b) q ≠ 0

15. Which of the following statements is true?

(a) Every fraction is a rational number.

(b) Every rational number is a fraction.

(c) Every integer is a rational number.

(d) Both (a) and (c).

► (d) Both (a) and (c).

16. Which of the following is the Multiplicative identity for rational numbers?

(a) 1

(b) -1

(c) 0

(d) None of these

► (a) 1

17. Find the multiplicative inverse of -13.

(a) 13

(b) -13

(c) -1/13

(d) 12

► (c) -1/13

18. ________ is not associative for rational numbers.

(a) Subtraction or Division

(b) Addition or Multiplication

(c) Addition or Division

(d) Multiplication or Division

► (a) Subtraction or Division

19. Which number is in the middle if -1/6, 4/9, 6/-7, 2/5 and -3/4 arranged in descending order?

(a) 2/5

(b) 4/9

(c) -1/6

(d) -6/7

► (c) -1/6

20. Which of the following is the Multiplicative identity for rational numbers?

(a) 1

(b) -1

(c) 0

(d) None of these

► (a) 1

21. Which of the following forms a pair of equivalent rational numbers? 

(a) 24/40 and 35/50

(b) -25/35 and 55/-77

(c) -8/15 and -24/48 

(d) 9/72 and -3/21

► (b) -25/35 and 55/-77

22. What should be subtracted from -7/11 to get −2?

(a) 15/11

(b) -15/11

(c) 29/11

(d) -29/11

► (a) 15/11

Rational Numbers Class 8 Extra Questions Maths Chapter 1

Question 1.
Pick up the rational numbers from the following numbers.
67, −12, 0, 10, 1000
Solution:
Since rational numbers are in the form of ab where b ≠ 0.
Only 67, −12 and 0 are the rational numbers.

Question 2.
Find the reciprocal of the following rational numbers:
(a) −34
(b) 0
(c) 611
(d) 5−9
Solution:
(a) Reciprocal of −34 is −43
(b) Reciprocal of 0, i.e. 10 is not defined.
(c) Reciprocal of 611 is 116
(d) Reciprocal of 5−9 = −95

Question 3.
Write two such rational numbers whose multiplicative inverse is same as they are.
Solution:
Reciprocal of 1 = 11 = 1
Reciprocal of -1 = 1−1 = -1
Hence, the required rational numbers are -1 and 1.

Question 4.
What properties, the following expressions show?
(i) 23+45=45+23
(ii) 13×23=23×13
Solution:
(i) 23+45=45+23 shows the commutative property of addition of rational numbers.
(ii) 13×23=23×13 shows the commutative property of multiplication of rational numbers.

Question 5.
What is the multiplicative identity of rational numbers?
Solution:
1 is the multiplicating identity of rational numbers.

Question 6.
What is the additive identity of rational numbers?
Solution:
0 is the additive identity of rational numbers.

Question 7.
If a = 12, b = 34, verify the following:
(i) a × b = b × a
(ii) a + b = b + a
Solution:

Question 8.
Multiply 58 by the reciprocal of −38
Solution:

Question 9.
Find a rational number between 12 and 13.
Solution:
Rational number between

Question 10.
Write the additive inverse of the following:
(a) −67
(b) 101213
Solution:

Question 11.
Write any 5 rational numbers between −56 and 78. (NCERT Exemplar)
Solution:

Question 12.
Identify the rational number which is different from the other three : 23, −45, 12, 13. Explain your reasoning.
Solution:
−45 is the rational number which is different from the other three, as it lies on the left side of zero while others lie on the right side of zero on the number line.

Rational Numbers Class 8 Extra Questions Short Answer Type

Question 13.
Calculate the following:

Solution:

Question 14.
Represent the following rational numbers on number lines.
(a) −23
(b) 34
(c) 32
Solution:

Question 15.
Find 7 rational numbers between 13 and 12.
Solution:

Question 16.
Show that:

Solution:

Question 17.
If x = 12, y = −23 and z = 14, verify that x × (y × z) = (x × y) × z.
Solution:
We have x = 12, y = −23 and z = 14
LHS = x × (y × z)

Question 18.
If the cost of 412 litres of milk is ₹8912, find the cost of 1 litre of milk.
Solution:

Question 19.
The product of two rational numbers is 1556. If one of the numbers is −548, find the other.
Solution:
Product of two rational numbers = 1556
One number = −548
Other number = Product ÷ First number

Hence, the other number = −187

Question 20.
Let O, P and Z represent the numbers 0, 3 and -5 respectively on the number line. Points Q, R and S are between O and P such that OQ = QR = RS = SP. (NCERT Exemplar)
What are the rational numbers represented by the points Q, R and S. Next choose a point T between Z and 0 so that ZT = TO. Which rational number does T represent?
Solution:

As OQ = QR = RS = SP and OQ + QR + RS + SP = OP
therefore Q, R and S divide OP into four equal parts.

Question 21.
Let a, b, c be the three rational numbers where a = 23, b = 45 and c = −56 (NCERT Exemplar)
Verify:
(i) a + (b + c) = (a + b) + c (Associative property of addition)
(ii) a × (b × c) – (a × b) × c (Associative property of multiplication)
Solution:

Rational Numbers Class 8 Extra Questions Higher Order Thinking Skills (HOTS)

Question 22.
Rajni had a certain amount of money in her purse. She spent ₹ 1014 in the school canteen, bought a gift worth ₹ 2534 and gave ₹ 1612 to her friend. How much she have to begin with?
Solution:
Amount given to school canteen = ₹ 1014
Amount given to buy gift = ₹ 2534
Amount given to her friend = ₹ 1612
To begin with Rajni had

Question 23.
One-third of a group of people are men. If the number of women is 200 more than the men, find the total number of people.
Solution:
Number of men in the group = 13 of the group
Number of women = 1 – 13 = 23
Difference between the number of men and women = 23 – 13 = 13
If difference is 13, then total number of people = 1
If difference is 200, then total number of people
= 200 ÷ 13
= 200 × 3 = 600
Hence, the total number of people = 600

Question 24.
Fill in the blanks:
(a) Numbers of rational numbers between two rational numbers is ……….

Solution:
(a) Countless
(b) 611
(c) −32
(d) 35
(e) Commutative
(f) associative
(g) equivalent
(h) 311