Some important questions for class 8 chapter 1- rational numbers are given here. These questions include short answer type questions, long answer type questions and HOTS questions related to rational numbers which are important for class 8 maths exam.

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## Rational Numbers Important Questions For Class 8 (Chapter 1)

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.

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