Class 9 Maths Chapter 3 Exercise 3.1: The World of Numbers
Numbers are not just about calculations; they also have patterns and properties that make them easier to understand. In Exercise 3.1, students get to explore these ideas through questions that encourage them to think about numbers and find the logic behind each result. The Class 9 Maths Chapter 3 Exercise 3.1 solutions explain these steps clearly so you can follow the reasoning without getting stuck.
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If you are working through the complete Ganita Manjari syllabus, NCERT Solutions Class 9 Maths can help you move from one exercise to the next with the relevant solutions in one place. These Maths NCERT Solutions Class 9 Chapter 3 exercise 3.1 are useful when you want to verify an answer, understand a tricky step, or quickly revisit a question before a test.
FAQs on NCERT Solutions for Class 9 Maths Chapter 3 Exercise 3.1 2026-27
1. Why are 11, 13, 17 and 19 called prime numbers?
Each of these numbers has only two factors: 1 and the number itself. Hence, all four are prime numbers.
2. What comes after 19 in the prime number pattern given in Exercise 3.1?
The next three prime numbers after 19 are 23, 29, and 31.
3. Can a natural number be obtained every time we subtract two natural numbers?
No. For example, 7 − 4 = 3, which is a natural number, but 4 − 7 = −3, which is not a natural number. Therefore, natural numbers are not closed under subtraction.
4. What does “closed under subtraction” actually mean?
It means that subtracting any two numbers from a given set should always produce another number belonging to the same set. Exercise 3.1 shows that natural numbers do not satisfy this condition.
5. How does the merchant get 90 copper ingots in Question 1?
The exchange rate is 15 ingots for every 2 bags. Since 12 bags make 6 groups of 2, the merchant receives 6 × 15 = 90 ingots.
6. Why is the number 12 connected with counting on one hand?
The four fingers have three joints each. Using the thumb to count these joints gives 4 × 3 = 12, which explains the connection with base-12 counting.
7. What is the connection between the Ishango bone and prime numbers?
The sequence 11, 13, 17 and 19 mentioned in the exercise consists of prime numbers. The question uses this historical example to help students recognise a number pattern.
8. Does 5 − 3 prove that natural numbers are closed under subtraction?
No. One successful example is not enough to prove closure. Since 3 − 5 = −2 is not a natural number, subtraction does not always remain within the set of natural numbers.
9. How can I quickly check whether a number is prime for Exercise 3.1?
Check whether the number has any factor other than 1 and itself. If it has no other factor, it is prime.
10. Why does Exercise 3.1 include examples from ancient counting methods?
The examples show that mathematical ideas such as numbers, factors, and counting methods have practical and historical connections, making the concepts easier to relate to real situations.
11. How can Class 9 maths NCERT solutions chapter 3 exercise 3.1 help with difficult questions?
They show the reasoning behind each answer, making it easier to identify the mathematical concept used and compare it with your own method.
12. What should I write if a question asks me to justify whether natural numbers are closed under subtraction?
Give one example where the result is a natural number and another where it is not. For instance, 5 − 3 = 2, but 3 − 5 = −2. This clearly shows why natural numbers are not closed under subtraction.
13. Are the questions in Class 9 Maths Chapter 3 Exercise 3.1 based only on prime numbers?
No. The exercise also includes an exchange problem, closure of natural numbers under subtraction, and the finger-joint method of counting.
14. Where do the Class 9 maths chapter 3 exercise 3.1 solutions help most?
They are particularly useful for checking the reasoning behind questions involving prime numbers, closure, counting, and number patterns rather than just checking the final answer.
15. Is this exercise important for understanding Chapter 3 – The World of Numbers?
Yes. Exercise 3.1 introduces students to different ways of looking at numbers through patterns, properties, operations, and real-life or historical examples. It builds the basic thinking needed for the rest of the chapter.
