The World of Numbers | Exercise 3.2

Question 1

The temperature in the high-altitude desert of Ladakh is recorded as 4∘C4^\circ\text{C} at noon. By midnight, it drops by 15∘C15^\circ\text{C}. What is the midnight temperature?

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Solution
Understand the Question
  • The temperature starts at 4∘C4^\circ\text{C} at noon.
  • A "drop" in temperature represents a decrease, so we subtract the temperature change (15∘C15^\circ\text{C}) from the initial temperature.
  • Final Temperature=Initial Temperature−Drop in Temperature\text{Final Temperature} = \text{Initial Temperature} - \text{Drop in Temperature}

Step 1 · Calculate Midnight Temperature

Given:

  • Temperature at noon=4∘C\text{Temperature at noon} = 4^\circ\text{C}
  • Temperature drop=15∘C\text{Temperature drop} = 15^\circ\text{C}Diagram 1
Midnight temperature=Initial temperature−Temperature drop=4−15=−11\begin{aligned} \text{Midnight temperature} &= \text{Initial temperature} - \text{Temperature drop} \\[0.6em] &= 4 - 15 \\[0.6em] &= -11 \end{aligned}
Answer

−11∘C-11^\circ\text{C}

Common Mistakes
  • Adding Instead of Subtracting: A temperature drop means subtracting 1515 from 44, not adding them (4+15=19∘C4 + 15 = 19^\circ\text{C}).
  • Sign Error in Subtraction: Subtracting the smaller number from the larger number (15−4=11∘C15 - 4 = 11^\circ\text{C}) instead of 4−15=−11∘C4 - 15 = -11^\circ\text{C}.

More questions in Exercise 3.2

Q1

The temperature in the high-altitude desert of Ladakh is recorded as 4∘C4^\circ\text{C} at noon. By midnight, it drops by 15∘C15^\circ\text{C}. What is the midnight temperature?

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.

Q3

Calculate the following using Brahmagupta's laws:

(i) (−12)×5(-12) \times 5

(ii) (−8)×(−7)(-8) \times (-7)

(iii) 0−(−14)0 - (-14)

(iv) (−20)÷4(-20) \div 4

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)=1510 - (-5) = 15).

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