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?

Answer:

Solution:

Temperature at noon = 4°C

Drop in temperature = 15°C

Midnight temperature = 4 − 15 = −11°C

Answer: −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.

Answer:

Solution:

Debt = −850

Profit = +1200

Loss = −450

Final standing = −850 + 1200 − 450

= 350 − 450

= −100

Answer: The trader's final financial standing is a debt of ₹100, represented as −100.

Q3. Calculate the following using Brahmagupta's laws: (i) (−12) × 5 (ii) (−8) × (−7) (iii) 0 − (−14) (iv) (−20) ÷ 4

Answer:

Solution:

(i) (−12) × 5 = −60 (debt × fortune = debt)

(ii) (−8) × (−7) = 56 (debt × debt = fortune)

(iii) 0 − (−14) = 0 + 14 = 14

(iv) (−20) ÷ 4 = −5

Answer: (i) −60, (ii) 56, (iii) 14, (iv) −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).

Answer:

Solution:

Let's use a debt example. Suppose you have ₹10 (positive). If someone removes (subtracts) a debt of ₹5 from you, that means they are taking away your obligation to pay ₹5. This makes you ₹5 richer, so your effective money becomes ₹10 + ₹5 = ₹15.

Thus, subtracting a negative number (removing a debt) is equivalent to adding a positive number.

Answer: Removing a debt increases your wealth, so 10 − (−5) = 10 + 5 = 15.