Class 9 Maths Ganita Manjari Chapter 3 Exercise 3.2 Solutions: The World of Numbers

Integers become easier to understand when positive and negative numbers are connected with real situations. Class 9 Maths Ganita Manjari Chapter 3 Exercise 3.2 Solutions focus on temperature change, profit-loss, debt, fortune and integer operations Class 9. This exercise from The World of Numbers helps students see why negative numbers are needed beyond natural numbers.

In Ganita Manjari Class 9 Chapter 3 Exercise 3.2, students use integers Class 9 concepts to solve questions based on Ladakh temperature, a spice trader’s loan and profit, and debt and fortune integers. These Class 9 Maths Chapter 3 Exercise 3.2 Solutions also explain Brahmagupta rules for zero and integers through simple examples such as subtracting a negative number, multiplying negative numbers and dividing integers.

Key Takeaways

Integers: Positive numbers, negative numbers and zero form integers.
Negative Numbers: Debt, loss and temperature drop are represented by negative integers.
Brahmagupta’s Rules: Debt and fortune ideas explain integer operations.
Subtracting Negative: Removing a debt works like adding a positive number.

Class 9 Maths Ganita Manjari Chapter 3 Exercise 3.2 Solutions Structure 2026

Class 9 Maths Ganita Manjari Chapter 3 Exercise 3.2 Solutions

Exercise Set 3.2 belongs to the section “Integers: Expanding the Horizon” in Chapter 3, The World of Numbers. The chapter explains how zero and negative numbers Class 9 ideas expanded the natural number system. Brahmagupta described positive numbers as Dhana, or fortune, and negative numbers as Ṛiṇa, or debt.

These Class 9 Maths integers exercise answers follow the textbook order and use the debt-fortune model wherever needed. The questions are simple, but they are important because they prepare students for later parts of the chapter, including rational numbers, number lines, irrational numbers and real numbers. This makes Exercise 3.2 an important part of Class 9 Ganita Manjari number system solutions.

Exercise 3.1 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:

The merchant receives 15 copper ingots for every 2 bags of spices.

So, for 2 bags:

2 bags = 15 ingots

Now, 12 bags can be grouped as:

12 / 2 = 6 groups

Each group gives 15 ingots.

So,

Total ingots = 6 × 15

Total ingots = 90

Answer: The merchant will leave with 90 copper ingots.

Exercise 3.1 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 are:

11, 13, 17, 19

All these numbers are prime numbers.

A prime number is a natural number greater than 1 that has exactly two factors: 1 and itself.

The prime numbers after 19 are:

23, 29, 31

Answer: The numbers 11, 13, 17 and 19 are prime numbers. The next three numbers in the pattern are 23, 29 and 31.

Exercise 3.1 Question 3

We know that Natural Numbers are closed under addition. Are they closed under subtraction? Provide a couple of examples to justify your answer.

Solution:

Natural numbers are:

N = {1, 2, 3, 4, …}

A set is closed under an operation if the result of that operation always remains inside the same set.

Natural numbers are closed under addition because adding any two natural numbers always gives a natural number.

Example:

3 + 5 = 8

Here, 8 is a natural number.

But natural numbers are not closed under subtraction because subtracting one natural number from another may give 0 or a negative number, which are not natural numbers.

Examples:

5 − 8 = −3

Here, −3 is not a natural number.

4 − 4 = 0

Here, 0 is also not a natural number in the set N = {1, 2, 3, 4, …}.

Answer: No, natural numbers are not closed under subtraction. For example, 5 − 8 = −3 and 4 − 4 = 0, and neither result is a natural number.

Exercise 3.1 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:

On one hand, the thumb is used to count the joints of the four fingers.

Each finger has 3 joints.

There are 4 fingers to count.

So,

Total joints = 4 × 3

Total joints = 12

Therefore, one hand can be used to count up to 12 using finger joints.

This relates to the ancient base-12 counting system because 12 becomes one full counting cycle. A base-12 system groups numbers in sets of 12, just as the finger-joint method lets a person count 12 positions on one hand.

Answer: We can count 12 on one hand. This relates to the base-12 counting system because one full hand-count gives a group of 12.

Final Answers for Exercise 3.1

Concept Used in The World of Numbers Exercise 3.2

The World of Numbers Exercise 3.2 is based on integers and their operations. The main idea is that numbers can represent not only counting quantities but also real-life gains and losses.

Important concepts include:

• Integers Class 9: positive numbers, negative numbers and zero.
• Negative numbers Class 9: numbers used to show debt, loss, fall in temperature or movement below zero.
• Debt and fortune integers: debt is represented by a negative integer, while fortune or gain is represented by a positive integer.
• Brahmagupta rules for zero: zero helps separate positive and negative values and allows operations such as adding, subtracting and multiplying with zero.
• Integer operations Class 9: addition, subtraction, multiplication and division of integers using sign rules.
• Subtracting a negative: removing a debt is the same as adding a positive value.

These ideas are central to Class 9 Maths Ganita Manjari Chapter 3 Solutions because the chapter builds the number system step by step, from natural numbers to integers, rational numbers, irrational numbers and real numbers.

About Class 9 Maths Ganita Manjari Chapter 3 Exercise 3.2

Ganita Manjari Class 9 Chapter 3 Exercise 3.2 comes after Exercise 3.1, where students study natural numbers, one-to-one correspondence, prime numbers and closure properties. Exercise 3.2 moves the discussion forward by introducing integers through Brahmagupta’s debt and fortune model.

These Class 9 Maths Chapter 3 Exercise 3.2 Solutions help students practise:

• writing temperature drops as integer subtraction,
• representing loans, profits and losses using positive and negative integers,
• applying sign rules in multiplication and division,
• understanding why 0 − (−14) = 14,
• explaining negative numbers Class 9 through real-life examples.

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 3