---
title: "NCERT Solutions for Class 9 Maths Chapter 3 Exercise 3.1"
url: https://www.swavid.com/maths/class/9/chapter/the-world-of-numbers/ncert-solutions/exercise-3-1
dateModified: 2026-10-07T15:46:03+00:00
---

# NCERT Solutions for Class 9 Maths Chapter 3 Exercise 3.1

Chapter 3: The World of Numbers. Every question from Exercise 3.1, with full working and the final answer.

Free PDF (22 pages): https://www.swavid.com/api/seo/pdf/ncert/maths/class-9/swavid-ncert-solutions-class-9-maths-chapter-3-the-world-of-numbers-521b6f38aa.pdf

## Exercise Set 3.1

### Question 1

*3 marks · Short answer*

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**

1. Given that for every 2 bags of spices, the merchant receives 15 copper ingots.
2. The number of pairs of 2 bags in 12 bags of spices is $\frac{12}{2} = 6$.
3. Therefore, the total number of copper ingots he will receive is $6 \times 15 = 90$ ingots.

**Answer:** 90 copper ingots

> Common mistake: Multiplying 15 by 12 directly instead of finding the number of batches of 2 bags.

### Question 2

*3 marks · Short answer*

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**

1. The given numbers are $11, 13, 17, 19$.
2. These numbers are prime numbers, specifically the prime numbers between 10 and 20.
3. The next three prime numbers following 19 are 23, 29, and 31.

**Answer:** They are prime numbers between 10 and 20. The next three numbers are 23, 29, and 31.

> Common mistake: Including composite odd numbers like 21, 25, or 27 in the sequence.

### Question 3

*3 marks · Short answer*

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**

1. Natural numbers are not closed under subtraction.
2. For example, taking two natural numbers 3 and 5, their difference $3 - 5 = -2$, which is an integer but not a natural number.
3. Similarly, $5 - 5 = 0$, and 0 is also not a natural number.

**Answer:** No, natural numbers are not closed under subtraction, as shown by $3 - 5 = -2$.

> Common mistake: Confusing natural numbers with integers.

### Question 4

*3 marks · Short answer*

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**

1. Each of the four fingers (excluding the thumb) has 3 phalanges or joints.
2. Using the thumb of the same hand to touch and count each joint gives $4 \times 3 = 12$ distinct counts on one hand.
3. This correspondence of counting 12 units on a single hand naturally provided the historical basis for base-12 (duodecimal) counting systems.

**Answer:** You can count 12 on one hand, which directly relates to the historical base-12 counting systems.

> Common mistake: Including the thumb itself as a finger to be counted instead of using it as the pointer.

## Related pages

- [All Chapter 3 NCERT solutions](https://www.swavid.com/maths/class/9/chapter/the-world-of-numbers/ncert-solutions)
- [Exercise 3.2](https://www.swavid.com/maths/class/9/chapter/the-world-of-numbers/ncert-solutions/exercise-3-2)
- [Exercise 3.3](https://www.swavid.com/maths/class/9/chapter/the-world-of-numbers/ncert-solutions/exercise-3-3)
- [Exercise 3.4](https://www.swavid.com/maths/class/9/chapter/the-world-of-numbers/ncert-solutions/exercise-3-4)
- [Exercise 3.5](https://www.swavid.com/maths/class/9/chapter/the-world-of-numbers/ncert-solutions/exercise-3-5)

Solutions written by SwaVid, a personal AI tutor for Class 6 to 10 Maths and Science. Practise this chapter free: https://www.swavid.com/start/student