CBSE Class 7 Mathematics Operations with Integers Practice Paper Assignment Set 03 with Answers

This page gives Class 7 Maths Ganita Prakash Part 2 Chapter 2 Operations with Integers Practice Paper 30 in full: 40 marks, 20 questions in Sections A to E, and a clear worked solution after each question. The paper covers choosing the least or greatest value among products and quotients, solving (−x) × 11 = 121, filling a missing factor in □ × (−16) = 192, matching (−18) × 5 to a real situation, and finding the third integer when a product of three is known. Applied questions on a cargo lift, a drone, an underwater tunnel platform and an export firm's daily losses and profits end with a net-change calculation.

Section A: Multiple Choice Questions (1 Mark Each)

Section B: Short Answer Questions (2 Marks Each)

Question 11. A drone descends 18 m per minute for 7 minutes.
(i) Write the integer expression.
(ii) Find the total vertical movement.
Answer:
Descending is a downward movement, so the rate is −18 m per minute.
(i) Expression: (−18) × 7.
(ii) (−18) × 7 = −126 m, that is, 126 m downward.
In simple words: Down 18 m each minute for 7 minutes is −126 m.

Teacher's Note:
1. The rate takes the sign; the time stays positive.
2. 18 × 7 = 126.

Question 12. The product of two integers is −840. One integer is 24.
(i) Write the division statement.
(ii) Find the other integer.
Answer:
(i) Other integer = (−840) ÷ 24.
(ii) 840 ÷ 24 = 35, and negative ÷ positive is negative.
So the other integer is −35. Check: 24 × (−35) = −840.
In simple words: Divide the product by the known integer: −840 ÷ 24 = −35.

Teacher's Note:
1. Every multiplication fact gives a matching division fact.
2. 24 × 35 = 24 × 30 + 24 × 5 = 720 + 120 = 840.

Question 13. Evaluate: (−144) ÷ 12 × (−5)
(i) First find the quotient.
(ii) Then find the final result.
Answer:
(i) Quotient: (−144) ÷ 12 = −12.
(ii) (−12) × (−5) = 60.
In simple words: −144 ÷ 12 = −12, and −12 × −5 = 60.

Teacher's Note:
1. Do ÷ and × from left to right.
2. Two negative numbers in the expression make the result positive.

Question 14. Find x if: x × (−14) ÷ 7 = −28
(i) Remove the division.
(ii) Find x.
Answer:
(i) Multiply both sides by 7: x × (−14) = −28 × 7 = −196.
(ii) x = −196 ÷ (−14) = 14.
Check: 14 × (−14) = −196 and −196 ÷ 7 = −28.
In simple words: Multiply by 7, then divide by −14: x = 14.

Teacher's Note:
1. Multiplying undoes dividing.
2. Negative ÷ negative = positive.

Section C: Short Answer Questions (3 Marks Each)

Question 15. Evaluate: (−9) × 8 ÷ (−6) × 5
Answer:
Left to right:
(−9) × 8 = −72.
−72 ÷ (−6) = 12.
12 × 5 = 60.
So the value is 60.
In simple words: Two negative numbers make the answer positive: 60.

Teacher's Note:
1. The expression has two negative numbers (an even count), so the answer is positive.
2. Keep the left-to-right order for × and ÷.

Question 16. The product of three integers is −960. Two of them are −16 and 5. Find the third integer.
Answer:
Product of the two known integers: (−16) × 5 = −80.
Third integer = (−960) ÷ (−80).
Negative ÷ negative is positive, and 960 ÷ 80 = 12.
So the third integer is 12.
Check: (−16) × 5 × 12 = −80 × 12 = −960.
In simple words: Multiply the two known integers, then divide the product by that: −960 ÷ (−80) = 12.

Teacher's Note:
1. Combine the known factors into one number first.
2. The product has one negative factor already, so the third must be positive to keep it negative.

Question 17. Find the value of: (−360) ÷ 9 ÷ (−4)
Answer:
Left to right:
(−360) ÷ 9 = −40.
−40 ÷ (−4) = 10.
So the value is 10.
In simple words: Two negative numbers give a positive answer: 10.

Teacher's Note:
1. Division must be done in order from left to right.
2. Dividing in a different order, like 9 ÷ (−4) first, gives a wrong answer.

Section D: Long Answer Question (5 Marks)

Question 18. A cargo lift moves inside a warehouse carrying boxes.
The lift moves:
Descends 25 m per minute for 6 minutes
Ascends 18 m per minute for 7 minutes
Descends 12 m per minute for 5 minutes
Solve the following steps:
(a) Represent each movement using integers (1 mark)
(b) Calculate total downward movement (1 mark)
(c) Calculate total upward movement (1 mark)
(d) Calculate net movement (1 mark)
(e) State the final position relative to the starting point (1 mark)
Answer:
(a) Downward: (−25) × 6 and (−12) × 5; upward: (+18) × 7.
(b) (−25) × 6 = −150 m and (−12) × 5 = −60 m.
Total downward movement = −150 + (−60) = −210 m.
(c) Total upward movement = 18 × 7 = +126 m.
(d) Net movement = −210 + 126 = −84 m.
(e) The lift is 84 m below its starting point.
In simple words: 210 m down and 126 m up leaves the lift 84 m below the start.

Teacher's Note:
1. Write each movement as rate × time with the right sign.
2. Net movement is the sum of all the signed movements.

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

Question 19. Case Study 1: Underwater Tunnel Construction
During the construction of an underwater tunnel, engineers monitor the vertical movement of a drilling platform. The platform descends at a rate of 20 meters per hour for 7 hours to reach the seabed. After inspection, it ascends at a rate of 14 meters per hour for 6 hours for equipment replacement. Engineers calculate the net vertical movement using integer operations to ensure accurate depth control and structural safety of the tunnel project.
Answer the following questions:
(a) What integer represents the downward movement per hour?
(b) What is the total downward movement?
(c) What is the total upward movement?
(d) What is the net movement of the platform?
Answer:
(a) Downward movement per hour = −20 m.
(b) Total downward movement = 7 × (−20) = −140 m.
(c) Total upward movement = 6 × 14 = +84 m.
(d) Net movement = −140 + 84 = −56 m (56 m below where it started).
In simple words: Down 140 m and up 84 m leaves the platform 56 m lower.

Teacher's Note:
1. Here the rate is per hour, so multiply by the number of hours.
2. The net movement is negative, so the platform ends below its start.

Question 20. Case Study 2: Export Business Transactions
An export company records daily financial changes. Due to shipping losses, the company loses ₹1,250 per day for 8 days. Later, successful exports generate a profit of ₹1,800 per day for 5 days. Accountants calculate the net financial change using integer multiplication and division to assess company performance and plan future strategies.
Answer the following questions:
(a) What integer represents the daily loss?
(b) What is the total loss over 8 days?
(c) What is the total profit over 5 days?
(d) What is the net financial outcome?
Answer:
(a) Daily loss = −1250 (₹).
(b) Total loss = 8 × (−1250) = −₹10,000.
(c) Total profit = 5 × 1800 = +₹9,000.
(d) Net outcome = −10,000 + 9,000 = −₹1,000, that is, an overall loss of ₹1,000.
In simple words: ₹10,000 lost and ₹9,000 earned means a net loss of ₹1,000.

Teacher's Note:
1. Losses are negative and profits are positive.
2. A negative net outcome means an overall loss.