CBSE Class 7 Mathematics Operations with Integers Practice Paper Assignment Set 02 with Answers

Class 7 Maths Ganita Prakash Part 2 Chapter 2 Operations with Integers Practice Paper 28 is a 40-mark paper with 20 questions across Sections A to E, and each one is followed by a worked answer. The questions test how the number of negative factors decides the sign of a product, comparing negative products, finding a missing factor from a product such as −936, and evaluating mixed chains like (−360) ÷ (−9) × (−4) × 2. Real-life items on a robotic lift, a deep-sea drone, a mountain trek and loan repayments ask you to turn movements and money changes into signed numbers and find the net result.

Section A: Multiple Choice Questions (1 Mark Each)

Section B: Short Answer Questions (2 Marks Each)

Question 11. A deep-sea drone descends at 20 m/min for 7 minutes and then ascends at 12 m/min for 5 minutes.
(a) Find the total downward movement.
(b) Find the total upward movement.
Answer:
Downward is negative and upward is positive.
(a) Total downward movement = 7 × (−20) = −140 m.
(b) Total upward movement = 5 × 12 = +60 m.
(Net, the drone is −140 + 60 = −80 m, i.e. 80 m below its start.)
In simple words: Multiply each rate by its time: 140 m down and 60 m up.

Teacher's Note:
1. Attach the sign to the rate, then multiply by the time.
2. Time is always positive; the direction carries the sign.

Question 12. The product of two integers is −936. One of the integers is 36.
(a) Find the other integer.
(b) State the rule of signs used.
Answer:
(a) Other integer = (−936) ÷ 36.
936 ÷ 36 = 26, and negative ÷ positive is negative.
So the other integer is −26. Check: 36 × (−26) = −936.
(b) Rule: positive × negative = negative (so negative ÷ positive = negative).
In simple words: −936 ÷ 36 = −26, because unlike signs give a negative answer.

Teacher's Note:
1. 36 × 26 = 36 × 25 + 36 = 900 + 36 = 936.
2. A negative product needs one positive and one negative factor.

Question 13. Evaluate: (−144) × (−5) ÷ (−12)
Answer:
Work from left to right.
(−144) × (−5) = 720 (negative × negative = positive).
720 ÷ (−12) = −60 (positive ÷ negative = negative).
So the value is −60.
In simple words: Three negative numbers give a negative answer: −60.

Teacher's Note:
1. You may also divide first: (−144) ÷ (−12) = 12, then 12 × (−5) = −60.
2. Both orders give the same answer here because there is no remainder.

Question 14. Find x if x × (−16) ÷ 4 = −64
Answer:
Undo the division: x × (−16) = −64 × 4 = −256.
Undo the multiplication: x = −256 ÷ (−16) = 16.
Check: 16 × (−16) = −256 and −256 ÷ 4 = −64.
So x = 16.
In simple words: Multiply −64 by 4, then divide by −16: x = 16.

Teacher's Note:
1. Reverse the operations in the opposite order.
2. Negative ÷ negative gives a positive value.

Section C: Short Answer Questions (3 Marks Each)

Question 15. Determine the sign and value of: (−14) × 9 ÷ (−6) × (−2)
Answer:
Sign: there are three negative numbers (−14, −6, −2), an odd count, so the result is negative.
Value, left to right:
(−14) × 9 = −126.
−126 ÷ (−6) = 21.
21 × (−2) = −42.
So the sign is negative and the value is −42.
In simple words: Three negatives make it negative; the value is −42.

Teacher's Note:
1. Predict the sign first, then calculate the value.
2. Work strictly from left to right with × and ÷.

Question 16. Evaluate: (−360) ÷ (−9) × (−4) × 2
Answer:
Left to right:
(−360) ÷ (−9) = 40.
40 × (−4) = −160.
−160 × 2 = −320.
So the value is −320.
In simple words: Three negative numbers give a negative answer: −320.

Teacher's Note:
1. Count the negative numbers to check the sign: three, so negative.
2. 360 ÷ 9 = 40 because 9 × 40 = 360.

Question 17. If x × (−20) ÷ (−5) × 3 = 96, find x.
Answer:
Simplify the known numbers: (−20) ÷ (−5) = 4, and 4 × 3 = 12.
So x × 12 = 96.
x = 96 ÷ 12 = 8.
Check: 8 × (−20) = −160; −160 ÷ (−5) = 32; 32 × 3 = 96.
So x = 8.
In simple words: The numbers after x combine to 12, so x = 96 ÷ 12 = 8.

Teacher's Note:
1. Group the known numbers into one multiplier before solving.
2. Substitute back to confirm the answer.

Section D: Long Answer Question (5 Marks)

Question 18. A robotic lift descends 18 m/min for 9 minutes, ascends 12 m/min for 6 minutes, and then descends again 7 m/min for 5 minutes.
(a) Represent each movement using integers.
(b) Calculate the total downward movement.
(c) Calculate the total upward movement.
(d) Find the net movement.
(e) State the final position relative to the starting point.
Answer:
(a) First descent −18 m/min, ascent +12 m/min, second descent −7 m/min.
(b) First descent: 9 × (−18) = −162 m. Second descent: 5 × (−7) = −35 m.
Total downward movement = −162 + (−35) = −197 m.
(c) Total upward movement = 6 × 12 = +72 m.
(d) Net movement = −197 + 72 = −125 m.
(e) The lift is 125 m below its starting point.
In simple words: Down 197 m and up 72 m leaves the lift 125 m below the start.

Teacher's Note:
1. Keep the two descents separate at first, then add them.
2. A negative net movement means below the starting point.

Section E: Case Study Based Questions (4 Marks Each)

Question 19. Case Study 1: Mountain Expedition
A mountain trekking team is climbing and descending a steep trail. During one stage, the team descends at 18 meters per minute for 7 minutes due to a steep slope. Later, they climb upward at 12 meters per minute for 5 minutes. The team leader records these movements carefully to determine their net vertical position and plan rest breaks accordingly. Accurate calculation using integers is essential to track the team’s altitude and ensure safety during the expedition.
Answer the following questions:
(a) What integer represents the downward movement per minute?
(b) What is the total downward movement?
(c) What is the total upward movement?
(d) What is the net vertical movement of the team?
Answer:
(a) Downward movement per minute = −18 m.
(b) Total downward movement = 7 × (−18) = −126 m.
(c) Total upward movement = 5 × 12 = +60 m.
(d) Net vertical movement = −126 + 60 = −66 m (66 m lower than where the stage began).
In simple words: The team went down 126 m and up 60 m, ending 66 m lower.

Teacher's Note:
1. Going down reduces altitude, so it is negative.
2. Net movement = total down + total up, with signs.

Question 20. Case Study 2: Bank Loan Transactions
A bank customer takes a loan and makes regular repayments. The loan amount reduces by ₹450 every month for 8 months. Later, due to additional borrowing, the loan increases by ₹720 per month for 5 months. The bank manager needs to calculate the net change in the loan balance using integer operations to maintain accurate financial records.
Answer the following questions:
(a) What integer represents the monthly loan repayment?
(b) What is the total reduction in the loan over 8 months?
(c) What is the total increase in the loan over 5 months?
(d) What is the net change in the loan balance?
Answer:
Treat a fall in the loan balance as negative and a rise as positive.
(a) Each repayment lowers the loan by ₹450, so it is −450.
(b) Total reduction = 8 × (−450) = −₹3600.
(c) Total increase = 5 × 720 = +₹3600.
(d) Net change = −3600 + 3600 = 0. The loan balance is back where it started.
In simple words: ₹3600 was repaid and ₹3600 was borrowed again, so the loan did not change.

Teacher's Note:
1. A number and its opposite add up to zero: −3600 + 3600 = 0.
2. The sign shows the direction of change in the balance, not who pays.