Class 7 Maths Operations with Integers Worksheet with Answers

Q1. Find the two integers using their sum and difference. Difference means first number minus second number.

1. Sum = 27, Difference = 9
2. Sum = 4, Difference = 12
3. Sum = 0, Difference = 10
4. Sum = −7, Difference = −1

Q2. A carrom coin starts at position 0. It moves −4 units in the first strike and reaches position 5 after the second strike. Find the second movement.

Q3. A coin makes the following movements in order: 1, −2, 3, −4, 5, −6, 7, −8, 9, −10. Find its final position, starting from 0.

Q4. Write the additive inverse of each integer.

1. 18
2. −25
3. 0
4. −103

Q5. Using the token interpretation, find the following products.

1. 3 × (−2)
2. (−5) × (−2)
3. (−4) × (−1)
4. (−7) × 3

Q6. Explain how zero pairs help us calculate (−4) × 2 using the token model.

Q7. Explain how the token model represents (−4) × (−2). Why is the answer positive?

Q8. Use the fact that 123 × 456 = 56,088 to find the following without performing the full multiplication.

1. (−123) × 456
2. (−123) × (−456)
3. 123 × (−456)

Q9. Find the following products.

1. 4 × (−3)
2. (−6) × (−3)
3. (−5) × (−1)
4. (−8) × 4
5. (−9) × 10
6. 10 × (−17)

Q10. Find the following quotients.

1. 36 ÷ (−18)
2. (−46) ÷ (−23)
3. (−100) ÷ 25
4. (−100) ÷ (−4)
5. 50 ÷ (−25)
6. (−56) ÷ (−2)

Q11. Replace each blank with an integer to make the statement true.

1. (−3) × _____ = 27
2. 5 × _____ = −35
3. _____ × (−8) = −56
4. _____ × (−12) = 132
5. _____ ÷ (−8) = 7
6. _____ ÷ 12 = −11

Q12. Find the integer whose product with −1 is:

1. 27
2. −31
3. −1
4. 1
5. 0

Q13. State whether each statement is true or false. Give an example to support your answer.

1. Multiplication of integers is commutative.
2. Multiplication of integers is associative.
3. The product of two negative integers is negative.
4. The product of an integer and 0 is 0.

Q14. Find the values of the expressions.

1. (−5) × (18 + (−3))
2. (−7) × 4 × (−1)
3. (−2) × (−1) × (−5) × (−3)
4. (−27) ÷ 9
5. 84 ÷ (−4)
6. (−56) ÷ (−2)

Q15. Use the distributive property to calculate (−2) × (4 + (−3)). Verify your answer by calculating both sides separately.

Q16. Calculate 25 × (−6) × 12. Explain why grouping the factors differently does not change the product.

Q17. If 47 − 56 + 14 − 8 + 2 − 8 + 5 = −4, find the value of −47 + 56 − 14 + 8 − 2 + 8 − 5 without calculating the full expression again.

Q18. In a test, +4 marks are awarded for every correct answer and −2 marks for every incorrect answer.

1. Anita answered 15 questions correctly and scored 40 marks. How many answers were incorrect?
2. How many questions did Anita answer in total?

Q19. A lift in a mining shaft moves down at 3 metres per minute.

1. Starting from ground level, what is its position after 60 minutes?
2. If it starts 15 metres above ground level, what is its position after 45 minutes?

Q20. A freezing process lowers the room temperature from 32°C at a rate of 5°C per hour. What will the temperature be after 10 hours?

Q21. A cement company earns a profit of ₹8 per bag of white cement and a loss of ₹5 per bag of grey cement.

1. The company sells 3,000 bags of white cement and 5,000 bags of grey cement. Find the overall profit or loss.
2. If it sells 6,400 bags of grey cement, how many bags of white cement must it sell to make neither a profit nor a loss?

Q22. A place has a temperature of 8°C. The temperature drops by 5°C every hour. Write an integer expression and find the temperature after 4 hours.

Q23. Find three consecutive integers whose product is:

1. −6
2. 120

Q24. Find the values.

1. (32 × (−18)) ÷ (−36)
2. 32 ÷ ((−36) × (−18))
3. (25 × (−12)) ÷ (45 × (−27))
4. (280 × (−7)) ÷ ((−8) × (−35))

Q25. A number is multiplied by −1 five times in succession. If the starting number is −7, what is the final result? Explain how the number of negative factors affects the sign of a product.