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NCERT Solutions for Class 9 Maths Chapter 3 Exercise 3.2 2026-27

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

Exercise 3.2 gives you a chance to look at numbers from a different angle and apply the ideas introduced in The World of Numbers. The questions encourage you to work out patterns, use number properties, and explain your reasoning. 

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The Class 9 Maths Chapter 3 Exercise 3.2 solutions present these ideas simply, so you can understand the method rather than just note the answer.


When a question feels difficult, going through the NCERT solutions for Class 9 Maths Chapter 3 Exercise 3.2 can help you see where to begin and how the solution develops. Try each question first, then use the NCERT Maths solutions for Class 9, Chapter 3, Exercise 3.2 to check your approach and strengthen your understanding.

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Exercise Set 3.2: Class 9 Maths Solutions

Question 1: The temperature in the high-altitude desert of Ladakh is recorded as 4 °C at noon. By midnight, it drops by 15 °C. What is the midnight temperature?

Solution:

The noon temperature is 4 °C.

By midnight, the temperature drops by 15 °C.

A drop in temperature means we subtract.

So, the midnight temperature is:

4 - 15 = -11

Therefore, the temperature at midnight is -11 °C.

Final Answer:

The midnight temperature is -11 °C.


Question 2: A spice trader takes a loan (debt) of ₹850. The next day, he makes a profit (fortune) of ₹1,200. The following week, he incurs a loss of ₹450. Write this sequence as an equation using integers and calculate his final financial standing.

Solution:

A loan is treated as debt, so it is represented by a negative integer.

Loan of ₹850 = -850

A profit is represented by a positive integer.

Profit of ₹1,200 = +1200

A loss is represented by a negative integer.

Loss of ₹450 = -450

So, the sequence can be written as:

-850 + 1200 - 450

Now, calculate step by step.

First:

-850 + 1200 = 350

Now subtract the loss:

350 - 450 = -100

The final result is -100.

This means the trader is still in debt of ₹100.

Final Answer:

The equation is:

-850 + 1200 - 450 = -100

The trader’s final financial standing is -₹100, which means he has a debt of ₹100.


Question 3: Calculate the following using Brahmagupta’s laws:

(i) (-12) × 5

Solution:

We have:

(-12) × 5

Here, -12 represents a debt, and 5 represents a fortune.

According to Brahmagupta’s laws, the product of a debt and a fortune is a debt.

So, the answer will be negative.

12 × 5 = 60

Therefore:

(-12) × 5 = -60

Final Answer: -60


(ii) (-8) × (-7)

Solution:

We have:

(-8) × (-7)

Here, both numbers are negative.

According to Brahmagupta’s laws, the product of two debts is a fortune.

This means the product of two negative numbers is positive.

8 × 7 = 56

Therefore:

(-8) × (-7) = 56

Final Answer: 56


(iii) 0 - (-14)

Solution:

We have:

0 - (-14)

Subtracting a negative number is the same as adding the corresponding positive number.

So:

0 - (-14) = 0 + 14

0 + 14 = 14

Therefore, the answer is 14.

Final Answer: 14


(iv) (-20) ÷ 4

Solution:

We have:

(-20) ÷ 4

Here, -20 is negative, and 4 is positive.

According to Brahmagupta’s laws, a debt divided by a fortune gives a debt.

So, the answer will be negative.

20 ÷ 4 = 5

Therefore:

(-20) ÷ 4 = -5

Final Answer: -5


Question 4: Explain, using a real-world example of debt, why subtracting a negative number is the same as adding a positive number, for example, 10 - (-5) = 15.

Solution:

Suppose you have ₹10.

Now imagine that you also have a debt of ₹5.

A debt of ₹5 is represented as -5.

If this debt is removed, your financial condition improves.

Removing a debt of ₹5 is the same as gaining ₹5.

So:

10 - (-5)

means you are starting with ₹10 and removing a debt of ₹5.

This becomes:

10 + 5 = 15

Therefore:

10 - (-5) = 15

This shows that subtracting a negative number is the same as adding a positive number.

Final Answer:

Subtracting a negative means removing a debt. Removing a debt increases the value, so 10 - (-5) becomes 10 + 5 = 15.


Think and Reflect (NCERT Textbook Page No. 46)

1. Why does a negative times a negative equal a positive? Think of it in terms of action and debt. If a negative number represents a debt, then multiplying by a negative number represents removing that debt. (Hint: If someone takes away (-) four of your debts that are each worth ₹ 3 (that is, -3), you are effectively ₹ 12 richer! Therefore, (-3) × (-4) = +12.)

Solution:

Think of a negative number as a debt and multiplication as an action being repeated.

Suppose you have a debt of ₹ 3. This is written as -3.

Now, if someone removes this debt, what happens?

You are no longer required to pay ₹ 3, so your position improves.

Mathematically, you go from -3 to 0, which is an increase of ₹ 3.

That is why removing a debt is the same as gaining money.

Now apply this idea to: (-3) × (-4)


Here, -3 represents a debt of ₹ 3, and -4 represents the action of removing this debt 4 times.


So the expression means: “Remove four debts of ₹ 3 each.”


Each time you remove a debt of ₹ 3, you gain ₹ 3. Repeating this action four times:

  • After removing one debt → gain ₹ 3

  • After removing two debts → gain ₹ 6

  • After removing three debts → gain ₹ 9

  • After removing four debts → gain ₹ 12


So, after removing all debts, you are ₹ 12 better off.


Therefore, (-3) × (-4) = +12

In this way, a negative times a negative becomes positive.


Key Concepts to Pick Up from  Chapter 3 Maths Class 9

Exercise 3.2

  • Relate integers to everyday situations such as temperature, debt, profit, and loss.

  • Strengthen your understanding of integer addition and subtraction.

  • Learn how Brahmagupta’s laws explain operations with positive and negative numbers.

  • Understand the logic behind multiplying or dividing two negative numbers.

  • See why subtracting a negative integer changes into addition.

  • Improve accuracy while working with signs in integer calculations.


Access Exercise-wise NCERT Solutions for Chapter 3 Maths Class 9


Other Study Material for CBSE Class 9 Maths Chapter 3

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Important Links for Chapter 3: The World of Numbers

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Class 9 The World of Numbers Important Questions

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Class 9 The World of Numbers Revision Notes

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Class 9 The World of Numbers Important Formulas

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Class 9 The World of Numbers NCERT Exemplar Solution

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Class 9 The World of Numbers RD Sharma Solutions

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Class 9 The World of Numbers RS Aggarwal Solutions


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FAQs on NCERT Solutions for Class 9 Maths Chapter 3 Exercise 3.2 2026-27

1. How do you solve a temperature drop of 15°C from 4°C?

Represent the drop by −15 and calculate 4 + (−15). Therefore, the midnight temperature is −11°C.

2. How is a loan represented using integers in Exercise 3.2?

A loan or debt is represented by a negative integer. For example, a loan of ₹850 is written as −850.

3. What is the final financial standing of the spice trader in Question 2?

The calculation is −850 + 1200 − 450 = −100. Thus, the trader remains ₹100 in debt.

4. What happens when a negative number is multiplied by a positive number?

The result is negative. For example, (−12) × 5 = −60.

5. Why is the product of two negative numbers positive?

Using the debt-and-removal idea in the exercise, removing a debt increases your financial position. Hence, (−3) × (−4) = +12.

6. How do you calculate 0 − (−14)?

Subtracting a negative number is equivalent to adding its positive value: 0 − (−14) = 0 + 14 = 14.

7. What is the answer to (−20) ÷ 4 in Class 9 Maths Chapter 3 Exercise 3.2?

A negative number divided by a positive number gives a negative result. Therefore, (−20) ÷ 4 = −5.

8. Why does 10 − (−5) become 10 + 5?

The exercise explains a negative value as a debt. Removing a debt of ₹5 improves the position by ₹5, so 10 − (−5) = 15.

9. What are Brahmagupta’s laws used for in Exercise 3.2?

They help determine the signs and results when performing multiplication and division with positive and negative numbers.

10. What should students remember when solving integer questions in Chapter 3?

Pay close attention to the signs before operating. A positive or negative sign can change the meaning and final result of the calculation.

11. How do the Class 9 Maths Chapter 3 solutions exercise 3.2 explain integer operations?

They explain addition, subtraction, multiplication, and division of integers using examples involving temperature, debt, profit, and loss.

12. Where can I find Class 9 Maths Chapter 3 Exercise 3.2 question answers?

Vedantu provides the Class 9 Maths Chapter 3 Exercise 3.2 question answers with step-by-step explanations for the exercise and the Think and Reflect activity.

13. Why are Chapter 3 maths class 9 exercise 3.2 solutions useful for revision?

They bring together the key calculations and concepts from Exercise 3.2, making it easier to review integer operations and sign rules before a test.

14. What is the main idea behind the debt example in Exercise 3.2?

It shows that a negative number can represent a debt and that removing a debt can be understood as adding a positive amount.