Class 9 Maths The World of Numbers Exercise Set 3.3 Solutions | Ganita Manjari

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Class 9 Maths – The World of Numbers

Exercise Set 3.3 Solutions | Ganita Manjari

Question 1

Prove that the following rational numbers are equal.

(i) 2/3 and 4/6

Solution

2/3 = (2×2)/(3×2)

= 4/6

Hence,

2/3 = 4/6

(ii) 5/4 and 10/8

Solution

5/4 = (5×2)/(4×2)

= 10/8

Hence,

5/4 = 10/8

(iii) -3/5 and -6/10

Solution

-3/5 = (-3×2)/(5×2)

= -6/10

Hence,

-3/5 = -6/10

(iv) 9/3 and 3

Solution

9/3 = 3

Hence,

9/3 = 3

Question 2

Find the sum.

(i) 2/5 + 3/10

Solution

LCM of 5 and 10 = 10

2/5 = 4/10

Now,

4/10 + 3/10

= 7/10

(ii) 7/12 + 5/8

Solution

LCM of 12 and 8 = 24

7/12 = 14/24

5/8 = 15/24

Now,

14/24 + 15/24

= 29/24

(iii) -4/7 + 3/14

Solution

LCM of 7 and 14 = 14

-4/7 = -8/14

Now,

-8/14 + 3/14

= -5/14

Question 3

Find the difference.

(i) 5/6 − 1/4

Solution

LCM of 6 and 4 = 12

5/6 = 10/12

1/4 = 3/12

Now,

10/12 − 3/12

= 7/12

(ii) 11/8 − 3/4

Solution

LCM of 8 and 4 = 8

3/4 = 6/8

Now,

11/8 − 6/8

= 5/8

(iii) -7/9 − (-2/3)

Solution

-7/9 − (-2/3)

= -7/9 + 2/3

LCM of 9 and 3 = 9

2/3 = 6/9

Now,

-7/9 + 6/9

= -1/9

Question 4

Find the product.

(i) 2/3 × 3/10

Solution

2/3 × 3/10

= 2/10

= 1/5

(ii) 7/11 × 5/8

Solution

7/11 × 5/8

= 35/88

(iii) -4/7 × 5/14

Solution

-4/7 × 5/14

= -20/98

= -10/49

Question 5

Find the quotient.

(i) 2/3 ÷ 3/10

Solution

2/3 ÷ 3/10

= 2/3 × 10/3

= 20/9

(ii) 7/11 ÷ 5/8

Solution

7/11 ÷ 5/8

= 7/11 × 8/5

= 56/55

(iii) -4/7 ÷ 5/14

Solution

-4/7 ÷ 5/14

= -4/7 × 14/5

= -8/5

Question 6

Show that:

(1/2 + 3/4) × 8/3 = 1/2 × 8/3 + 3/4 × 8/3

Solution

LHS:

(1/2 + 3/4) × 8/3

LCM of 2 and 4 = 4

1/2 = 2/4

2/4 + 3/4 = 5/4

Now,

5/4 × 8/3

= 10/3

Now RHS:

1/2 × 8/3 + 3/4 × 8/3

= 4/3 + 2

= 4/3 + 6/3

= 10/3

Hence,

LHS = RHS

Question 7

Simplify using distributive property:

7/9 (6/7 − 3/4)

Solution

7/9 × (6/7 − 3/4)

= 7/9 × 6/7 − 7/9 × 3/4

= 2/3 − 7/12

LCM of 3 and 12 = 12

2/3 = 8/12

Now,

8/12 − 7/12

= 1/12

Question 8

Find the rational number x such that:

5/6 (x + 3/5) = 5/6 x + 1/2

Solution

5/6 (x + 3/5)

= 5/6 × x + 5/6 × 3/5

= 5x/6 + 1/2

RHS is also:

5x/6 + 1/2

Hence, both sides are equal for every value of x.

Therefore, x can be any rational number.

Students preparing for Class 9 Maths Ganita Manjari should practice all exercise sets and end-of-chapter exercises regularly for better understanding of concepts and excellent exam preparation. Below is the complete chapter-wise list of exercises from Chapters 1 to 4. Students can explore all solutions, worksheets, practice papers, and important questions chapter-wise.

Chapter 1 – Orienting Yourself: The Use of Coordinates

  • Exercise Set 1.1 Solutions
  • Exercise Set 1.2 Solutions
  • End of Chapter Exercises Solutions

Chapter 2 – Introduction to Linear Polynomials

Chapter 3 – The World of Numbers

  • Exercise Set 3.1 Solutions
  • Exercise Set 3.2 Solutions
  • Exercise Set 3.3 Solutions
  • Exercise Set 3.4 Solutions
  • Exercise Set 3.5 Solutions
  • End of Chapter Exercises Solutions

Chapter 4 – Exploring Algebraic Identities

  • Exercise Set 4.1 Solutions
  • Exercise Set 4.2 Solutions
  • Exercise Set 4.3 Solutions
  • Exercise Set 4.4 Solutions
  • Exercise Set 4.5 Solutions
  • End of Chapter Exercises Solutions