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:
\(Temperature at noon = 4^\circC\)
\(Drop in temperature = 15^\circC\)
\(Midnight temperature = 4 - 15\)
\(= -11^\circC\)
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:
\((i) (-12) \times 5\)
A negative number multiplied by a positive number gives a negative number.
\((-12) \times 5 = -60\)
Answer: -60
\((ii) (-8) \times (-7)\)
A negative number multiplied by a negative number gives a positive number.
\((-8) \times (-7) = 56\)
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
\((iv) (-20) \div 4\)
A negative number divided by a positive number gives a negative number.
\((-20) \div 4 = -5\)
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.