Class 9 Maths – The World of Numbers Exercise Set 3.1 Solutions | Ganita Manjari

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In this post, we have provided complete step-by-step solutions of Exercise Set 3.1 from the chapter “The World of Numbers” of Class 9 Maths Ganita Manjari.
All questions are solved carefully in an easy language so that students can understand every concept clearly and prepare well for exams.

Exercise Set 3.1 Solutions

Question 1

A merchant in the port city of Lothal is exchanging bags of spices for copper ingots. He receives 15 ingots for every 2 bags of spices. If he brings 12 bags of spices to the market, how many copper ingots will he leave with?

Solution

Number of copper ingots for 2 bags= 15

number of copper ingots for 1 bag = 15/2

number of copper ingots for 12 bags= 15/2 x 12 =90

Therefore, the merchant will leave with 90 copper ingots.

Question 2

Look at the sequence of numbers on one column of the Ishango bone: 11, 13, 17, 19. What do these numbers have in common? List the next three numbers that fit this pattern.

Solution

The numbers given are:11, 13, 17, 1911,\ 13,\ 17,\ 19

All these numbers are prime numbers.

A prime number is a number which has only two factors:

  • 1
  • the number itself

so the next prime numbers after 19.23, 29, 3123,\ 29,\ 31

Question 3

We know that Natural Numbers are closed under addition (the sum of any two natural numbers is always a natural number). Are they closed under subtraction? Provide a couple of examples to justify your answer.

Solution

Natural numbers are not closed under subtraction.

Let us understand with examples.

Example 1

9−4=5

Here, 5 is a natural number.

Example 2

4−9=−54 – 9 = -5

Here, −5 is not a natural number.

Thus, subtraction of two natural numbers does not always give a natural number.

Therefore, natural numbers are not closed under subtraction.

Question 4

Ancient Indians used the joints of their fingers to count, a practice still seen today. Each finger has 3 joints, and the thumb is used to count them. How many can you count on one hand? How does this relate to the ancient base-12 counting systems?

Solution

In one hand, there are 4 fingers excluding the thumb.

Each finger has 3 joints.

So, total number of joints: 4×3=12

Using the thumb to point at each joint, a person can count up to 12 on one hand.

This is related to the ancient base-12 counting system because people used these 12 joints for counting.

Hence, the counting system based on 12 became popular in ancient times.

Students should also practice other exercises and important questions from Ganita Manjari to strengthen their concepts and score better in examinations. You can also explore chapter-wise solutions, topper practice papers, periodic tests, worksheets, and important exam-oriented questions available on our website for Class 9 Maths preparation.