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NCERT Class 9 Mathematics Exercise Set 3.2 Solutions: The World of Numbers
AI-written, checked on 23 Oct 2026
Solutions written by Shishya, checked — not the board's official answers
Step-by-step working for every question of Exercise Set 3.2 in NCERT's Class 9 Mathematics book, chapter “The World of Numbers”, written by Shishya. Each question is in our own short words; open the NCERT chapter for the exact wording and figures.
How these were checked: the solutions were drafted with AI and then read and corrected on 23 Oct 2026. Every numerical final answer is recomputed from the question's own numbers by a calculator check that runs before each release; proofs and explanations were read, not machine-checked. The NCERT textbook is the authority — if something here disagrees with it, follow the book.
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Ex 3.2 Q1
Ladakh: 4 °C at noon, the temperature falls by 15 °C by midnight. Find the midnight temperature.
- The temperature at noon is 4 °C.
- The temperature falls by 15 °C, so we subtract 15 from 4.
- Midnight temperature = 4 − 15.
- 4 − 15 = −11.
Answer: −11 °C
Ex 3.2 Q2
A trader borrows ₹850, then makes a profit of ₹1,200, then a loss of ₹450. Write this as one integer equation and find where he stands.
- Borrowing ₹850 is represented as −850.
- Profit of ₹1200 is represented as +1200.
- Loss of ₹450 is represented as −450.
- The equation is −850 + 1200 − 450.
- Calculate −850 + 1200 to get 350.
- Calculate 350 − 450 to get −100.
- The final position is −100.
Answer: −850 + 1200 − 450 = −100: he ends with a debt of ₹100.
Ex 3.2 Q3
Using Brahmagupta's rules find (i) (−12) × 5, (ii) (−8) × (−7), (iii) 0 − (−14), (iv) (−20) ÷ 4.
- (i) Multiply −12 by 5 using the rule that a negative times a positive is negative.
- (i) The product is −60.
- (ii) Multiply −8 by −7 using the rule that a negative times a negative is positive.
- (ii) The product is 56.
- (iii) Subtract −14 from 0, which is equivalent to adding 14.
- (iii) The result is 14.
- (iv) Divide −20 by 4 using the rule that a negative divided by a positive is negative.
- (iv) The quotient is −5.
Answer: (i) −60; (ii) 56; (iii) 14; (iv) −5
Ex 3.2 Q4
With a real-life debt example, explain why subtracting a negative number is the same as adding a positive one (for example 10 − (−5) = 15).
- Think of your net worth: money you own counts as positive, a debt counts as negative.
- Suppose your net worth is ₹10 and a debt of ₹5, that is −5, is part of your record.
- If that debt is cancelled, the −5 is taken away from your record: the new net worth is 10 − (−5).
- Cancelling a ₹5 debt makes you better off by exactly ₹5, the same as being handed ₹5.
- So 10 − (−5) = 10 + 5 = 15: subtracting a negative number gives the same result as adding the positive number.
Answer: Removing a debt of ₹5 raises your worth by ₹5, so 10 − (−5) = 10 + 5 = 15.
Other exercises in this chapter
- Exercise Set 3.1 — 4 questions
- Exercise Set 3.3 — 8 questions
- Exercise Set 3.4 — 6 questions
- Exercise Set 3.5 — 5 questions
- End-of-chapter exercises — 16 questions
← The World of Numbers: notes, practice and all exercises
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