Explain, using a real-world example of debt, why subtracting a negative number is the same as adding a positive number (e.g., ).

Question

Homi · Accepted Answer

Understand the Question

Money you have represents a positive amount ( $+10$ ), while money you owe (debt) represents a negative amount ( $-5$ ).
Subtracting represents taking away or removing something.
Removing a debt frees up money and increases your overall net worth, which has the exact same effect as receiving (adding) positive money.

Step 1 · Represent Initial Amount and Debt

Let having $\text{₹}10$ represent a positive amount $(+10)$ and owing $\text{₹}5$ represent a debt, which is a negative amount $(-5)$ . Diagram 1

$\text{Initial Amount} = \text{₹}10$

Step 2 · Remove Debt and Simplify

In the expression $10 - (-5)$ , subtracting $(-5)$ corresponds to removing a debt of $\text{₹}5$ .

Taking away a debt increases your net worth by $\text{₹}5$ , which is equivalent to adding $+5$ :

\begin{aligned} 10 - (-5) &= 10 + 5 \\[0.6em] &= 15 \end{aligned}

Answer

Subtracting a negative number removes a debt, increasing net worth: $10 - (-5) = 10 + 5 = 15$

Common Mistakes

Confusing Adding Debt with Removing Debt: Adding a debt of $\text{₹}5$ decreases money ( $10 + (-5) = 5$ ), whereas removing/subtracting a debt increases money ( $10 - (-5) = 15$ ).
Sign Error: Treating $10 - (-5)$ as $10 - 5 = 5$ by dropping one of the negative signs.

Question 4