Class 8 Maths Chapter 1 HOTS Questions - Rational Numbers

Q1: What are the multiplicative and additive identities of rational numbers?
Ans: 0 and 1 are the additive and multiplicative identity of rational numbers respectively.

Q2: Write the additive inverse of 19/-6 and -⅔
Ans: 19/-6 = 19/6 and -⅔ = 2/3

Q3: Write the multiplicative inverse of -13/19 and -7
Ans: -13/19 = -19/13 and -7 = -1/7

Q4: Mention a rational number which has no reciprocal.
Ans: A rational number “0” has no reciprocal or multiplicative inverse.

Q5: Mention any 4 rational numbers which are less than 5.
Ans: -1, 1, 2 and 3.

Q6: Mention the commutativity, associative and distributive properties of rational numbers. Also, check a × b = b × a and a + b = b + a for a = ½ and b = ¾
Ans: Commutative property:
For any two rational numbers a and b, a + b = b + a.
For any two rational numbers a and b, a × b = b × a.
Associative Property:
For any three rational numbers a, b and c,
(a + b) + c = a + (b + c)
Distributive property states that for any three numbers x, y and z,
x × ( y + z ) = (x × y) + ( x × z)
a*b = b*a
a*b = ½ * ¾ = 3/8
b*a = ¾ * ½ = 3/8
a + b = ¾ + ½ = 5/4
b + a = ½ + ¾ = 5/4

Q7: Write any 5 rational numbers between −2/5 and ½.
Ans: −2/5 can be written as −8/20.
1/2 can be written as 10/20.
So, rational numbers between these two numbers can be
−7/20,−6/20,−5/20,−4/20,−3/20,−2/20,−1/20,0,1/20,2/20,3/20,4/20.

Q8: If the product of any two rational numbers is 2 and one of them is 1/7, find the other?
Ans: Consider 2 rational numbers as “a” and “b”.
Given, a = 1/7 and a × b = 2
Now, 1/7 × b = 2
⇒ b = 7 × 2 = 14
So, the other rational number will be 14.

Q9: Mr X went shopping with a certain amount of money. He spent Rs. 10(¼) on buying a pen and Rs. 25(¾) in food. He then gave the remaining Rs. 16(½) to his friend. Calculate how much money he initially had.
Ans: To get the amount of money Mr X had initially, his purchases have to be added.
So,
Initial Money = Rs. [10(¼) + 25(¾) + 16(½)]

= Rs. (41/4 + 103/4 + 33/2)
By taking LCM, we get;
=Rs. (41  + 103 + 66)/4
= Rs. 210/4
Initial Money = Rs. 105/2 (or) Rs. 52(½)

Q10: Represent −𝟐/𝟏𝟏, −𝟓/𝟏𝟏, and −𝟗/ 𝟏𝟏 on the number line.
Ans: To represent these numbers, divide the number line into 11 parts. Now, the given rational numbers will be 2, 5 and 9 points away from 0.