Mathematics solution NCERT
Class 9 - Chapter 3: The World of Numbers
Q1: 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:
Temperature at noon = 4°C
Drop in temperature = 15°C
Midnight temperature = 4 − 15
= -11°C
Answer: The midnight temperature is -11°C.
Q2: 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:
Represent the amounts using integers:
- Debt of ₹850 = -850
- Profit of ₹1200 = +1200
- Loss of ₹450 = -450
Required equation:
(-850) + 1200 + (-450)
= 350 - 450
= -100
Answer: Final financial standing = -₹100.
This means the trader is still in debt by ₹100.
Q3: Calculate the following using Brahmagupta's laws:
(i) (-12) × 5
A negative number multiplied by a positive number gives a negative number.
(-12) × 5 = -60
Answer: -60
(ii) (-8) × (-7)
A negative number multiplied by a negative number gives a positive number.
(-8) × (-7) = 56
Answer: 56
(iii) 0 − (-14)
Subtracting a negative number is the same as adding the corresponding positive number.
0 - (-14)
= 0 + 14
= 14
Answer: 14
(iv) (-20) ÷ 4
A negative number divided by a positive number gives a negative number.
(-20) ÷ 4 = -5
Answer: -5
Q4: Explain, using a real-world example of debt, why subtracting a negative number is the same as adding a positive number (e.g., 10 − (−5) = 15).
Solution:
Consider a person who has ₹10.
Suppose he also has a debt of ₹5.
The debt can be represented as -₹5.
If someone cancels or removes that debt, we are subtracting a negative amount:
10 - (-5)
Removing a debt of ₹5 is actually a gain of ₹5.
Therefore:
10 - (-5)
= 10 + 5
= 15
Real-Life Interpretation:
If a bank forgives a debt of ₹5, your financial position improves by ₹5.
That is why subtracting a negative number gives the same result as adding a positive number.
| Situation | Value |
|---|---|
| Money Available | ₹10 |
| Debt | -₹5 |
| Debt Removed | -(-₹5) |
| Final Amount | ₹15 |
Answer: Subtracting a negative number is equivalent to adding the corresponding positive number because removing a loss or debt increases the value.