The World of Numbers | Exercise 3.2

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

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Solution

We will use money to understand subtracting a negative number.

Step 1 — Understanding Debt

Let's think about money. Having money is a positive amount. Owing money is a negative amount. If you have ₹10, that is positive. If you owe ₹5, that is -₹5. This is your debt. We start with ₹10. Our initial amount is ₹10.

1010

Initial Amount=10\boxed{\text{Initial Amount} = \text{₹}10}

Diagram 1

Step 2 — Removing Debt

Now, let's consider 10(5)10 - (-5). The -₹5 means you owe ₹5. Subtracting a negative number means removing this debt. Removing a debt of ₹5 makes you richer. Your money increases by ₹5. So, 10(5)10 - (-5) means 10+510 + 5.

10(5)10 - (-5)

=10+5= 10 + 5

15\boxed{15}

This shows subtracting a negative is adding a positive.

Answer

Subtracting a negative number, like removing a debt, increases your net worth, which is equivalent to adding a positive number.

More questions in Exercise 3.2

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?

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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