Important Questions for Class 8 Maths Chapter 1 PDF Download

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. Reciprocal of −2 is ___

Solution: Reciprocal of any number will be the inverse of that number.

That is, the reciprocal of a is 1a .

Hence, the reciprocal of −2 is −12 .

5. Zero has ____ reciprocal

Solution: The product of any number with 0 will be 0 and hence, zero has no reciprocal.

Long Answer Type Questions

1. Mention the commutativity, associative and distributive properties of rational numbers. Also, check a × b = b × a and a + b = b + a for a = 1/2 and b = 3/4

Solution: 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 x b = b x a
• a x b = 1/2 x 3/4 = 3/8
• b x a = 3/4 x 1/2 = 3/8
• a + b = 3/4 + 1/2 = 5/4
• b + a = 1/2 + 3/4= 5/4

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

Solution: −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.

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

Solution: Consider two rational numbers: "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.

4. 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 initially had, his purchases must be added.

So, Initial Money = 10(¼) + 25(¾) + 16(½) = 41/4 + 103/4 + 33/2 By taking LCM, we get Initial Money = 105/2

Benefits of Solving Important Questions for Class 8 Maths Chapter 1