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).

Step-by-step solution

Idea: A negative number is a debt. Subtracting means taking something away. Taking away a debt leaves you richer by the same amount, exactly as if you had been given that money.

1. Suppose you hold ₹15 in cash but owe a friend ₹5. Your worth is 15 + (−5) = ₹10.½ mark
2. Your friend cancels the debt: the debt of ₹5 is taken away. In symbols this is ‘subtract −5’: 10 − (−5).½ mark
3. Now you hold ₹15 and owe nothing, so your worth is ₹15. It has gone up by ₹5, exactly as if someone had given you ₹5.½ mark
4. So removing a debt of 5 has the same effect as adding 5: 10 − (−5) = 10 + 5 = 15.½ mark

Check: Number line: the gap from −5 up to 10 is 15 steps, and 10 − (−5) measures exactly that gap ✓.

Answer to write in the exam

Common mistakes that cost marks

• Writing 10 − (−5) = 5 by ignoring the second minus sign.
• Explaining with an example that adds a debt instead of removing one; adding a debt is 10 + (−5) = 5.
• Giving only the rule ‘two minuses make a plus’ with no real-world explanation, which the question asks for.

How this can come in the exam

Try one yourself

Explain with a debt example why 20 − (−8) = 28.

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