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Class 7 Maths: Operations with Integers, 8 practice questions with answers

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These are 8 practice questions on Chapter 2, Operations with Integers, of the new NCERT Class 7 Maths textbook, Ganita Prakash, Part 2. Each has a worked answer and the textbook page it comes from. They cover two integers from their product and sum, a bank balance, a tank that is losing water, points in a game, a falling reservoir level, dividing integers, choosing cards for the largest and smallest products, and the distributive property. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every number was re-computed by a test script and none of the chapter's own examples is reused, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Prakash, Grade 7, Part 2, Chapter 2, printed pages 24 to 46):

Sums, moves and tokens

Question 1. (a) Find two integers whose product is −24 and whose sum is −2. (b) Find two integers whose product is 18 and whose sum is −9.

Answer: (a) 4 and −6; (b) −3 and −6. (a) The product is negative, so one number is positive and the other negative. The sum is negative, so the negative one is the larger in size. Pairs that multiply to 24 are 1 and 24, 2 and 12, 3 and 8, 4 and 6; only 4 and 6 differ by 2, so the numbers are 4 and −6. Check: 4 × (−6) = −24 and 4 + (−6) = −2. (b) The product is positive, so both have the same sign; the sum is negative, so both are negative. Pairs that multiply to 18 are 1 and 18, 2 and 9, 3 and 6; only 3 and 6 add up to 9, so the numbers are −3 and −6. Check: (−3) × (−6) = 18 and (−3) + (−6) = −9. (Signs of products, pages 33 to 35.)

Question 2. A savings account starts at ₹0, and this bank lets the balance go below zero. Deposits are positive and withdrawals negative. (a) The entries are +600, −900, +400 and −800 rupees, in that order. What is the balance at the end? (b) Another account starts at ₹0, has a withdrawal of ₹300, then one more entry, and ends at ₹800. What was that entry?

Answer: (a) −₹700; (b) a deposit of ₹1100. (a) The balance is the sum of the entries: 600 + (−900) + 400 + (−800) = 1000 + (−1700) = −700, that is ₹700 below zero. (b) −300 + (second entry) = 800, so the second entry is 800 − (−300) = 800 + 300 = +1100, a deposit of ₹1100. (Adding and subtracting integers, pages 25 to 27.)

Question 3. A water tank is being emptied, and its water falls by 5 litres every minute. Take time from now as positive and time before now as negative, and the change in water as positive for a gain. (a) What is the change in the water over the next 3 minutes? (b) Compared with now, how much more water was in the tank 3 minutes ago? Write each as a product of integers.

Answer: (a) 3 × (−5) = −15 litres; (b) (−3) × (−5) = +15 litres. The rate of change is −5 litres a minute. (a) Over the next 3 minutes the change is 3 × (−5) = −15: 15 litres less than now. (b) Going back 3 minutes is a time of −3, so the change is (−3) × (−5) = +15: 3 minutes ago there were 15 litres more than now, which makes sense because the tank has been losing water since then. A negative times a negative is positive. (Multiplying integers, pages 31 to 35.)

Integers in real life

Question 4. In a game level there are 36 boxes, and Mira opens all of them. A box with a coin adds 3 points and a box with a trap takes away 1 point. She ends the level with 72 points. (a) How many coins did she find? (b) What are the lowest and highest scores anyone could get on this level?

Answer: (a) 27 coins and 9 traps; (b) −36 and 108. (a) If all 36 boxes had coins, the score would be 36 × 3 = 108. Each trap in place of a coin changes the score by 3 + 1 = 4 points (the 3 is lost and 1 is taken away). Mira scored 108 − 72 = 36 less, so 36 ÷ 4 = 9 boxes had traps and 27 had coins. Check: 27 × 3 + 9 × (−1) = 81 + (−9) = 72. (b) All traps: 36 × (−1) = −36. All coins: 36 × 3 = 108. (Multiplying integers, pages 31 to 35; dividing integers, pages 38 and 39.)

Question 5. The water level in a reservoir is measured against a mark on a pillar. It falls at a steady rate from 14 cm above the mark to 10 cm below it in 6 days. (a) Write the change per day as an integer. (b) If it keeps falling at the same rate, where will the level be 3 days after that?

Answer: (a) −4 cm a day; (b) 22 cm below the mark (−22). Take above the mark as positive. (a) The level goes from +14 to −10, a change of −10 − 14 = −24 cm in 6 days, so the change per day is (−24) ÷ 6 = −4. (b) In 3 more days it changes by 3 × (−4) = −12, so the level is −10 + (−12) = −22, that is 22 cm below the mark. (Dividing integers, pages 38 and 39; multiplying integers, pages 31 to 35.)

Division, long products and brackets

Question 6. Find (a) (−144) ÷ 16, (b) 154 ÷ (−11) and (c) (−195) ÷ (−13). (d) What number goes in the blank: (−7) × ___ = 91?

Answer: (a) −9; (b) −14; (c) 15; (d) −13. Turn each division into a multiplication. (a) 16 × ? = −144, and 16 × (−9) = −144, so the answer is −9. (b) (−11) × ? = 154, and (−11) × (−14) = 154, so −14. (c) (−13) × ? = −195, and (−13) × 15 = −195, so 15: a negative divided by a negative is positive. (d) 91 ÷ (−7) = −13; check: (−7) × (−13) = 91. (Division of integers, pages 38 and 39.)

Question 7. You have five cards: −5, −2, −1, 3 and 4. (a) Choose three cards whose product is as large as possible. (b) Choose three cards whose product is as small (as far below zero) as possible.

Answer: (a) −5, −2 and 4, with product 40; (b) −5, 3 and 4, with product −60. (a) A positive product needs an even number of negative cards. Only two cards (3 and 4) are positive, so any three cards include at least one negative, and a positive product needs exactly two negatives and one positive. The largest is (−5) × (−2) × 4 = 40 (compare (−5) × (−2) × 3 = 30). (b) For a product below zero we need an odd number of negative cards. With one negative, the best is (−5) × 3 × 4 = −60; with three negatives, (−5) × (−2) × (−1) = −10. So −60 is the smallest. (Multiplying several integers, page 40.)

Question 8. Find (−6) × (17 + (−7)) in two ways: first by working out the bracket, and then by using the distributive property. Show that both give the same answer.

Answer: −60 both ways. Bracket first: 17 + (−7) = 10, and (−6) × 10 = −60. Distributing: (−6) × 17 + (−6) × (−7) = −102 + 42 = −60. The two ways agree, as the distributive property a × (b + c) = a × b + a × c says they must, even when some of the numbers are negative. (The distributive property for integers, pages 40 and 41.)

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Sources

All opened and read on 1 November 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 23 for this chapter.

The rules are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.

Practise with the worksheet: Operations with Integers, Class 7 worksheet. Printable, in English, Hindi and Marathi, with an answer key.