Answer:
1. Answer: (b) a whole number
Explanation: 0 is not a natural number. It is a whole number. Natural numbers only include positive integers.
2. Answer: (a) Commutative property
Explanation: Commutative property says that the numbers can be added in any order, and you will still get the same answer. a+b = b+a is a clear example of the commutative property.
3. Answer: (a) associative property
Explanation: a+(b+c) = (a+b)+c is associative property of whole numbers.
4. Answer: (a) 0
Explanation: The additive identity property says that if you add a real number to zero or add zero to a real number, then you get the same real number back. The number zero is known as the identity element. Then zero(0) is the additive identity of a real number and all rational numbers are real. Hence, 0 is the additive identity of rational numbers.
5.Answer: (d) all of the above
Explanation: We know that whole numbers are a subset of integers which in turn are a subset of rational numbers. Also, 1 is the multiplicative identity for rational numbers because the product of 1 and any rational number is the rational number itself. Thus, 1 is the multiplicative identity for whole numbers, integers, and rational numbers.
6. Answer: (a) -23
Explanation: Additive inverse of 23 will be -23.
7. Answer: (d) Infinite number of rational numbers
Explanation: Infinite number of rational numbers exist between any two distinct rational numbers. We know that a rational number is a number which can be written in the form of p/q
where p and q are integers and \(q\neq0\)
8. Answer: (a) 0
Explanation: The rational number that does not have a reciprocal 0 because reciprocal of 0 is undefined.
9. Answer: (b) 2-1
Explanation: Therefore, the reciprocal of the number 2 is 1/2or 2−1
10. Answer: (c) Both positive and negative
Explanation: An integer can be both positive and negative as well as zero. i.e. …-3, -2, -1, 0, 1, 2, 3,…
11. Answer: (a) p/q
Explanation: A rational number can be represented in the form p/q where p and q are integers and q is not equal to zero.
12. Answer: (b) 3/10
Explanation: 1/2 x3/5
= (1 x 3)/(2 x 5)
= 3/10
13. Answer: (d) 5/6
Explanation: (1/2) ÷ (3/5)
= (1/2) x (5/3)
= (1 x 5)/(2 x 3)
= 5/6
14. Answer: (c) Addition and Multiplication
Explanation: As per associative property:
A + (B + C) = (A + B) + C
A × (B × C) = (A × B) × C
15. Answer: (c) 10/9
Explanation: 2/3+ 4/9
⇒ 2/3 x (3/3) + 4/9
⇒ 6/9 + 4/9
⇒ 10/9
16. Answer: (a) 1/6
Explanation: The product of 2/9 and 3/4:
⇒ 2/9 x 3/4
⇒ (2 x 3)/(9 x 4)
⇒ (2 x 3)/(3 x 3 x 2 x 2)
By canceling the common terms from numerator and denominator, we get;
⇒ 1/(3×2)
⇒ 1/6
17. Answer: (d) Countless
Explanation: Let us 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.
There are countless rational numbers between any two rational numbers.
18. Answer: (a) 1/3
Explanation: Let x be subtracted from -2/3.
-2/3 – x = -1
-x = -1 + 2/3
-x = -1/3
x = 1/3
19. Answer: (a) 0
Explanation: Any number multiplied by zero is equal to zero.
20. Answer: (a) 0.25
Explanation: \(\frac{1}{4}=\frac{1\times25}{4\times25}\)
= 25/100
= 0.25
21. Answer: (b) 3
Explanation: Let the required number be x.
\(\frac{15-x}{19-x}=\frac{3}{4}\)
60−4x = 57−3x
x = 3
22. Answer: (a) Subtraction or Division
Explanation: subtraction and division are not associative for rational numbers.
23. Answer:(d) 1/13
Explanation: The multiplicative inverse of 13 is (13)1 = \(\frac{1}{13}\)
24.Answer: (b) -3/2
Explanation: the additive inverse of 2 is −2
the multiplicative inverse of 2 is 1/2
the sum of the additive and the multiplicative inverse is
= -2 + 1/2
= -3/2
25. Answer: (d) 1/4
Explanation: The product of 3 /10 and 5/6:
⇒ 3/10 x 5/6
⇒ (3 x 5)/(10 x 6)
⇒ 15/60
⇒ 1/4
Click here Practice MCQ Question for Rational Numbers Class 8