Integers

Test Your Skill

Exercise 1. Arrange the following integers in the ascending order: –2, 1, 0, –3, +4, –5.

Exercise 2. Arrange the following integers in the descending order: –3, 0, –1, –4, –3, –6.

Exercise 3. Calculate: 1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 + 9 – 10

Exercise 4. Observe the following: 1 + 2 – 3 + 4 + 5 – 6 – 7 + 8 – 9 = –5. Change one – sign as + sign to get the sum 9.

Exercise 5. The sum of two integers is 47. If one of the integers is – 24, find the other.

Exercise 6. Write the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 in this order and insert ‘+ ‘or ‘–’ between them to get the result (a) 5 (b) –3 (c) 3.

Exercise 7. Write two integers whose sum is less than both the integers.

Exercise 8. Write two distinct integers whose sum is equal to one of the integers.

Exercise 9. The sum of two integers is 30. If one of the integers is –42, then find the other.

Exercise 10. Sum of two integers is –80. If one of the integers is –90, then find the other.

Exercise 11. Write the opposite of each of the following:

  • (a) Increase in class strength
  • (b) Going north
  • (c) A loss of Rs. 1000
  • (d) Decrease in size
  • (e) Failure
  • (f) Profit of Rs.10
  • (g) 1000 A.D.
  • (h) Rise in water level
  • (i) 60 km south
  • (j) 10 m above the danger mark of river Ganga
  • (k) 20 m below the danger mark of the river Brahmaputra
  • (l) Winning by a margin of 2000 votes
  • (m) Depositing Rs.100 in the Bank account
  • (n) 20°C rise in temperature.

Exercise 12. Represent the following using integers with proper sign:

  • (a) 25° above zero
  • (b) 5° below zero
  • (c) 300m above the sea level
  • (d) 250m below the sea level
  • (e) A profit of Rs. 2000
  • (f) 3 km above sea level
  • (g) A loss of Rs. 500

Exercise 13. If we denote the height of a place above sea level by a positive integer and depth below the sea level by a negative integer, write the following using integers with the appropriate signs:

  • (a) 200 m above sea level      
  • (b) 100 m below sea level
  • (c) 10 m above sea level        
  • (d) sea level

Exercise 14. How many integers are between:

  • (i) – 4 and 3    
  • (ii) 5 and 12    
  • (iii) –9 and –2

Exercise 15. Find the following products using number line:

  • (a) 4 × (– 8)
  • (b) 8 × (–2)
  • (c) 3 × (–7)
  • (d) 10 × (–1)

Exercise 16. Compute each of the following:

  • (a) 30 + (–25) + (–10)
  • (b) (–20) + (–5)
  • (c) 70 + (–20) + (–30)
  • (d) –50 + (–60) + 50
  • (e) 1 + (–2) + (– 3) + (– 4)
  • (f) 0 + (– 5) + (– 2)           
  • (g) 0 – (–6) – (+6)
  • (h) 0 – 2 – (–2)

Exercise 17. Evaluate each of the following:

  • (a) (–30) ÷ 10
  • (b) 50 ÷ (–5)
  • (c) (–36) ÷ (–9)
  • (d) (– 49) ÷ (49)
  • (e) 13 ÷ [(–2) + 1]
  • (f) 0 ÷ (–12)
  • (g) (–31) ÷ [(–30) + (–1)]
  • (h) [(–36) ÷ 12] ÷ 3
  • (i) [(– 6) + 5)] ÷ [(–2) + 1]

Exercise 18. Find each of the following products:

  • (i) (–18) × (–10) × 9         
  • (ii) (–20) × (–2) × (–5) × 7              
  • (iii) (–1) × (–5) × (– 4) × (– 6)

Exercise 19. Find the value of the following expressions, using suitable properties:

  • (a) 7 × (50 – 2)
  • (b) (– 41) × 102
  • (c) (–17) × (–29)
  • (d) 8 × 53 × (–125)
  • (e) 15 × (–25) × (– 4) × (–10)
  • (f) 26 × (– 48) + (– 48) × (–36)
  • (g) 625 × (–35) + (– 625) × 65
  • (h) (–57) × (–19) + 57
  • (i) 81265 × 169 – 81265 × 69
  • (j) 3845 × 5 × 782 + 769 × 25 × 218

Exercise 20. Verify the following results:

  • (a) 18 × [7 + (–3)] = [18 × 7] + [18 × (–3)]
  • (b) (–21) × [(– 4) + (– 6)] = [(–21) × (– 4)] + [(–21) × (– 6)]
  • (c) 10 × [(6 + (–2)] = 10 × 6 + 10 × (–2)
  • (d) 11 × (6 – (–2)] = 11 × 6 – 11 × (–2)
  • (e) (–15) × [(–7) + (–1)] = (–15) × (–7) + (–15) × (–1)
  • (f) (–16) × [(–7) – (–1)] = (–16) × (–7) – (–16) × (–1)
  • (g) (–30) × [13 + (–3)] = [(–30) × 13] + [(–30) × (–3)]

6 comments

  1. Sir , I am from class 8
    Maths was really easy
    I solved all in first attempt
    Plz upload more interesting maths for us , as I have shared the post with my friends

    Liked by 1 person

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