Important Questions Class 8 Maths Chapter 1 Rational Numbers

Important questions for class 8 chapter 1- rational numbers are given here. These questions include short answer type questions and long answer type questions related to rational numbers which are important for class 8 maths examination. To score good marks in the exam, students can practice these questions which are based on NCERT syllabus.

Rational numbers are the numbers which can be represented in the form of p/q, where p and q are integers. Let us check here what are the important questions related to this chapter.

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Rational Numbers Important Questions For Class 8

The questions from rational numbers are segregated into short and long answer type questions.

Short Answer Type Questions:

1. What are the multiplicative and additive identities of rational numbers?

Solution: 0 and 1 are the additive and multiplicative identity of rational numbers respectively.

2. Write the additive inverse of 19/-6 and -⅔

Solution: 19/-6 = 19/6 and -⅔ = 2/3

3. Write the multiplicative inverse of -13/19 and -7

Solution: -13/19 = -19/13 and -7 = -1/7

4. Mention a rational number which has no reciprocal.

Solution: A rational number “0” has no reciprocal or multiplicative inverse.

5. Mention any 4 rational numbers which are less than 5.

Solution: 0, 1, 2 and 3.

Long Answer Type Questions:

6. 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

Solution: Commutative identity: a + b = b+ a, a – b ≠ b – a, a × b = b × a and a ÷ b ≠ b ÷ a

Associative property: a + (b + c), a – (b – c) ≠ (a – b) – c, a × (b × c) = (a × b) × c, and a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c

When a = ½ and b = ¾

Now, for checking a × b = b × a, consider LHS and RHS.

LHS = a × b = ½ × ¾ = ⅜

RHS = b × a = ¾ × ½ = ⅜

Thus, LHS = RHS (Hence proved).

7. Write any 5 rational numbers between −2/5 and ½.

Solution: To find rational numbers between any two numbers, make the denominator same first.

So, −2/5 ⇒ (−2×10)/ (5×10) = −20/50

And, ½ ⇒ (1×25)/ (2×25) = 25/50

Now, 5 rational numbers between −2/5 and ½ = 5 rational numbers between −20/50 and 25/50 So, 5 rational numbers = −18/50, −15/50, −2/50, 8 /50, and 20/50

8. If the product of any two rational numbers is 2 and one of them is 1/7, find the other?

Solution: 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.

9. 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.

Solution: To get the amount of money Mr X had initially, his purchases have to be added.

So,

Initial Money = 10(¼) + 25(¾) + 16(½)

= 41/4 + 103/4 + 33/2

By taking LCM, we get

Initial Money = 210/4

10. Represent −𝟐/𝟏𝟏, −𝟓/𝟏𝟏, and −𝟗/ 𝟏𝟏 on the number line.

Solution: 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.

Important Questions Class 8 Maths Chapter 1 Rational Numbers

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