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Overview

Step-by-step NCERT solutions for Operations with Integers (Chapter 10, NCERT Class 7 Mathematics) — the full working for every question, not just the final answer. You can also read the Operations with Integers textbook chapter.

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What these solutions cover

All 68 questions in Operations with Integers are solved in the PDF. Here's what's inside, exercise by exercise:

A Quick Recap of Integers — Sum and Difference Pairs

  1. Find the pair of numbers with: (a) Sum = 27, Difference = 9
  2. Find the pair of numbers with: (b) Sum = 4, Difference = 12
  3. Find the pair of numbers with: (c) Sum = 0, Difference = 10
  4. Find the pair of numbers with: (d) Sum = 0, Difference = –10
  5. Find the pair of numbers with: (e) Sum = –7, Difference = –1
  6. Find the pair of numbers with: (f) Sum = –7, Difference = –13

Multiplication of Integers — Token Model

  1. Using the token interpretation, find the values of: (a) 3 × (–2)
  2. Using the token interpretation, find the values of: (b) (–5) × (–2)
  3. Using the token interpretation, find the values of: (c) (–4) × (–1)
  4. Using the token interpretation, find the values of: (d) (–7) × 3
  5. If 123 × 456 = 56088, without calculating, find the value of: (a) (–123) × 456
  6. If 123 × 456 = 56088, without calculating, find the value of: (b) (–123) × (–456)
  7. If 123 × 456 = 56088, without calculating, find the value of: (c) (123) × (–456)

Patterns in Integer Multiplication — Find Products

  1. Find the following product: (a) 4 × (–3)
  2. Find the following product: (b) (–6) × (–3)
  3. Find the following product: (c) (–5) × (–1)
  4. Find the following product: (d) (–8) × 4
  5. Find the following product: (e) (–9) × 10
  6. Find the following product: (f) 10 × (–17)

Division of Integers

  1. Find the value of: (a) 14 × (–15)
  2. Find the value of: (b) –16 × (–5)
  3. Find the value of: (c) 36 ÷ (–18)
  4. Find the value of: (d) (–46) ÷ (–23)
  5. A freezing process requires that the room temperature be lowered from 32°C at the rate of 5°C every hour. What will be the room temperature 10 hours after the process begins?
  6. A cement company earns a profit of ₹8 per bag of white cement sold and a loss of ₹5 per bag of grey cement sold. The company sells 3,000 bags of white cement and 5,000 bags of grey cement in a month. What is its profit or loss?
  7. If the number of bags of grey cement sold is 6,400 bags, what is the number of bags of white cement the company must sell to have neither profit nor loss?
  8. Replace the blank with an integer to make a true statement: (a) (–3) × _____ = 27
  9. Replace the blank with an integer to make a true statement: (b) 5 × _____ = (–35)
  10. Replace the blank with an integer to make a true statement: (c) _____ × (–8) = (–56)
  11. Replace the blank with an integer to make a true statement: (d) _____ × (–12) = 132
  12. Replace the blank with an integer to make a true statement: (e) _____ ÷ (–8) = 7
  13. Replace the blank with an integer to make a true statement: (f) _____ ÷ 12 = –11

Expressions Using Integers — Properties and Applications

  1. Find the value of: (a) (–5) × (18 + (–3))
  2. Find the value of: (b) (–7) × 4 × (–1)
  3. Find the value of: (c) (–2) × (–1) × (–5) × (–3)
  4. Find the value of: (a) (–27) ÷ 9
  5. Find the value of: (b) 84 ÷ (–4)
  6. Find the value of: (c) (–56) ÷ (–2)
  7. Find the integer whose product with (–1) is: (a) 27
  8. Find the integer whose product with (–1) is: (b) –31
  9. Find the integer whose product with (–1) is: (c) –1
  10. Find the integer whose product with (–1) is: (d) 1
  11. Find the integer whose product with (–1) is: (e) 0
  12. If 47 – 56 + 14 – 8 + 2 – 8 + 5 = –4, then find the value of –47 + 56 – 14 + 8 – 2 + 8 – 5 without calculating the full expression.
  13. In a test, (+4) marks are given for every correct answer and (–2) marks for every incorrect answer. (a) Anita answered all the questions. She scored 40 marks even though 15 of her answers were correct. How many of her answers were incorrect? How many questions are in the test?
  14. In a test, (+4) marks are given for every correct answer and (–2) marks for every incorrect answer. (b) Anil scored (–10) marks even though he had 5 correct answers. How many of his answers were incorrect? Did he leave any questions unanswered?
  15. Pick the pattern — find the operations done by the machine shown. The machine takes 3 inputs (a, b, c) and gives outputs: (4, 8, –3) → 28; (6, 9, 6) → –48; (2, 3, –2) → 8; (–9, 5, –8) → 31; (7, –4, –6) → –17; (–16, –6, –9) → ?
  16. Imagine you're in a place where the temperature drops by 5°C each hour. If the temperature is currently at 8°C, write an expression which denotes the temperature after 4 hours.
  17. Find 3 consecutive numbers with a product of (a) –6
  18. Find 3 consecutive numbers with a product of (b) 120
  19. An alien society uses a peculiar currency called 'pibs' with two denominations — a +13 pibs coin and a –9 pibs coin. Using the two denominations, try to get the following totals: (a) +20
  20. Using +13 and –9 pib coins, get a total of: (b) +40
  21. Using +13 and –9 pib coins, get a total of: (c) –50
  22. Using +13 and –9 pib coins, get a total of: (d) +8
  23. Using +13 and –9 pib coins, get a total of: (e) +10
  24. Using +13 and –9 pib coins, get a total of: (f) –2
  25. Using +13 and –9 pib coins, get a total of: (g) +1
  26. Find the value of: (a) (32 × (–18)) ÷ (–36)
  27. Find the value of: (b) 32 ÷ ((–36) × (–18))
  28. Find the value of: (c) (25 × (–12)) ÷ ((45) × (–27))
  29. Find the value of: (d) (280 × (–7)) ÷ ((–8) × (–35))
  30. Arrange the expressions given below in increasing order:
    • (a) (–348) + (–1064),
    • (b) (–348) – (–1064),
    • (c) 348 – (–1064),
    • (d) (–348) × (–1064),
    • (e) 348 × (–1064),
    • (f) 348 × 964
  31. Given that (–548) × 972 = –532656, write the value of: (a) (–547) × 972
  32. Given that (–548) × 972 = –532656, write the value of: (b) (–548) × 971
  33. Given that (–548) × 972 = –532656, write the value of: (c) (–547) × 971
  34. Given that 207 × (–33 + 7) = –5382, write the value of –207 × (33 – 7).
  35. Use the numbers 3, –2, 5, –6 exactly once and the operations '+', '–', and '×' exactly once and brackets as necessary to write an expression such that (a) the result is the maximum possible.
  36. Use the numbers 3, –2, 5, –6 exactly once and the operations '+', '–', and '×' exactly once and brackets as necessary to write an expression such that (b) the result is the minimum possible.
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More solutions in Ganita Prakash

01Large Numbers Around Us02Arithmetic Expressions03A Peek Beyond the Point04Expressions using Letter Numbers05Parallel and Intersecting Lines06Number Play07A Tale of Three Intersecting Lines08Working with Fractions09Geometric Twins11Finding Common Ground12Another Peek Beyond the Point13Connecting the Dots14Constructions and Tilings15Finding the Unknown
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More NCERT Solutions for Class 7

Read the Operations with Integers textbook chapter / PDF, or browse all NCERT Class 7 Mathematics solutions.

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