Class 9 Maths The World of Numbers Exercise Set 3.4 Solutions | Ganita Manjari

by

Class 9 Maths – The World of Numbers

Exercise Set 3.4 Solutions | Ganita Manjari

Question 1

Represent the rational numbers 2/3, -5/4 and 1 1/2 on a single number line.

Solution

Convert mixed fraction into improper fraction:

1 1/2 = 3/2

Now the given rational numbers are:

-5/4 , 2/3 , 3/2

Their positions on the number line are:

-5/4 lies between -1 and -2
2/3 lies between 0 and 1
3/2 lies between 1 and 2

Therefore, these numbers can be represented on the same number line at their respective positions.

Question 2

Find three distinct rational numbers that lie strictly between -1/2 and 1/4.

Solution

We know:

-1/2 = -4/8

1/4 = 2/8

Now numbers lying between -4/8 and 2/8 are:

-3/8 , -2/8 , 1/8

Simplifying:

-3/8 , -1/4 , 1/8

Therefore, three rational numbers are:

-3/8 , -1/4 , 1/8

Question 3

Simplify the expression:

(-1/4) + (5/12)

Solution

LCM of 4 and 12 = 12

-1/4 = -3/12

Now,

-3/12 + 5/12

= 2/12

= 1/6

Therefore, the simplified value is:

1/6

Question 4

A tailor has 15 3/4 metres of fine silk. If making one kurta requires 2 1/4 metres of silk, exactly how many kurtas can he make?

Solution

Convert mixed fractions into improper fractions:

15 3/4 = 63/4

2 1/4 = 9/4

Now divide:

63/4 ÷ 9/4

= 63/4 × 4/9

= 63/9

= 7

Therefore, the tailor can make exactly:

7 kurtas

Question 5

Find three rational numbers between 3.1415 and 3.1416.

Solution

Three rational numbers between 3.1415 and 3.1416 are:

3.14151

3.14152

3.14153

Question 6

Can you think of other way(s) to find a rational number between any two rational numbers?

Solution

Yes.

One simple method is to find the average of the two rational numbers.

If two rational numbers are a and b, then a rational number between them is:

(a + b)/2

For example:

Between 2 and 4:

(2 + 4)/2

= 6/2

= 3

Therefore, 3 lies between 2 and 4.

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