🌐 All Subjects 🔬 Science 🌍 Social Science 📐 Mathematics 📖 English 🪶 हिन्दी

🔢 Chapter 3: The World of Numbers • Exercise Set 3.2

Verified step-by-step solutions for your class notes.

Q1

Exercise Set 3.2

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?

  • Initial temperature = 4°C
  • Temperature drop = 15°C
  • Midnight temperature = 4 - 15 = -11°C
Q2

Exercise Set 3.2

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.

  • Integer Equation: (-850) + (+1200) + (-450)
  • Step 1: (-850) + 1200 = +350
  • Step 2: 350 + (-450) = -100
  • Final Financial Standing: He has a net debt of ₹100 (standing is -₹100).
Q3

Exercise Set 3.2

3. Calculate the following using Brahmagupta's laws:

(i) (-12) × 5      (ii) (-8) × (-7)      (iii) 0 - (-14)      (iv) (-20) ÷ 4

  • (i) (-12) × 5: Product of a debt and a fortune is a debt ⇒ -60
  • (ii) (-8) × (-7): Product of two debts is a fortune ⇒ 56
  • (iii) 0 - (-14): Subtracting a debt leaves a positive fortune ⇒ 0 + 14 = 14
  • (iv) (-20) ÷ 4: Dividing a debt by a positive quantity gives a debt ⇒ -5
Q4

Exercise Set 3.2

4. 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).

  • Suppose you have ₹10 in cash, but you also hold a formal debt (negative value) of ₹5 owed to a storekeeper.
  • If someone generously waives or removes that ₹5 debt for you, they are subtracting a debt of 5: -(-5).
  • Relieving you of that ₹5 obligation increases your financial net worth by ₹5. Therefore, removing a ₹5 debt is identical to being handed ₹5 in cash:
    10 - (-5) = 10 + 5 = 15.