Integer questions for practice with solutions are provided here for students to help them in their examinations. All questions are important from the exam point of view, these questions are in accordance with the latest CBSE/ICSE syllabus for class 6 and 7 maths. It is recommended for all students to attempt these questions for a final touch-up for their preparations for examination.
For more resources: Integers Worksheets for Classes 6 and 7
Integers are a set of positive and negative whole numbers along with zero. The set of integers is denoted by Z.
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Properties of Integers |
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Closure Property: For any a and b integers, a * b is also an integer, where * represents arithmetic operations ( +, –, × ) For example:
Hence, integers are not closed with respect to division. |
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Associativity: For any integers a, b and c, a*(b*c) = (a*b)*c, where * represents arithmetic operations (+ and ×) For example:
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Distributive Property: For any integers a, b and c, a × ( b + c) = (a × b) + (a × c), this is known as distributive property of multiplication over addition. |
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Commutativity: For any integers a and b, a*b = b*a, where * represents the arithmetic operations ( + and ×). For example:
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Additive Identity: 0 is the additive identity for integers, as for any integer a, a + 0 = a = 0 + a. |
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Additive Inverse: For any integer a, there exist an integer –a such that a + (–a) = 0 = (–a) + a.Thus –a is the additive inverse of a. |
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Multiplicative Identity: 1 is the multiplicative identity for integers, as for any integer a, a × 1 = a = 1 × a. |
Learn more about Integers.
Integers Questions with Solutions
Practice these questions on integers to improve your understanding, skill and speed of solving questions.
Question 1: Evaluate the following:
(i) 22 – ( –87)
(ii) 198 + ( –12)
(iii) –16.87 – 30
(iv) – 19 + 34 – 34
Solution:
(i) 22 – ( –87) = 22 + 87 = 109
(ii) 198 + ( –12) = 198 – 12 = 186
(iii) –16.87 – 30 = – (16.87 + 30) = – 46.87
(iv) – 19 + 34 – 34 = –19 + 0 = –19
Question 2: Find the additive inverse of the following:
(i) 23
(ii) 108
(iii) 476
(iv) –39
Solution:
(i) 23
Additive inverse of 23 is –23 such that;
23 + (–23) = 0 = (–23) + 23
(ii) 108
Additive inverse of 108 is –108 such that;
108 + (–108) = 0 = (–108) + 108
(iii) 476
Additive inverse of 476 is –476 such that;
476 + (–476) = 0 = (–476) + 476
(iv) –39
Additive inverse of –39 is –(–39) = 39 such that;
–39 + 39 = 0 = 39 + (–39)
Question 3: Verify a + (b + c) = (a + b) + c for the following:
(i) a = 2, b = 0, c = –9
(ii) a = 34, b = 90, c = –1
Solution:
(i) a = 2, b = 0, c = –9
L.H.S = a + (b + c) = 2 + (0 + 9)
= 2 + 9 = 11
R.H.S = (a + b) + c = (2 + 0) + 9
= 2 + 9 = 11
∴ L.H.S = R.H.S
(ii) a = 34, b = 90, c = –1
L.H.S = a + (b + c) = 34 + {90 + (–1)}
34 + {90 – 1}
= 34 + 89 = 123
R.H.S = (a + b) + c = (34 + 90) + (–1)
= 124 + (–1)
= 124 – 1 = 123
∴ L.H.S = R.H.S
Also Read:
Question 4: Evaluate using properties:
(i) 89 – 58 + 28 – (–32)
(ii) 193 + 208 – {29 – (367)}
(iii) 56 – 34 + 235 – (123)
(iv) (84 – 34) × (84 + 45)
Solution:
(i) 89 – 58 + 28 – (–32)
= 89 – 58 + 28 + 32
= 89 – 58 + (28 + 32) {associativity}
= 89 – 58 + 60
= (89 + 60) – 58 {commutativity and associativity}
= 149 – 58 = 91
(ii) 193 + 208 – {29 – (367)}
= 193 + 208 – {29 – 367}
= 193 + 208 – (–338)
= 193 + 208 + 338
= (193 + 208) + 338 {associativity}
= 401 + 338 = 739.
(iii) 56 – 34 + 235 – (123)
= 56 – 34 + 235 – 123
= (56 + 235) – (34 + 123) {commutativity and associativity}
= 291 – 157
= 134
(iv) (84 – 34) × (84 + 45)
= {84 + (–34)} × (84 + 45)
= 84 × (–34 + 45) {distributivity of multiplication over addition}
= 84 × 11
= 924
Question 5: Write ‘true’ or ‘false’ for the following:
(i) Zero is the smallest integer.
(ii) –10 is smaller than –7.
(iii) 1 is the smallest positive integer.
(iv) –1 is the smallest negative integer.
(v) Sum of two negative integers is a positive integer.
Solution:
(i) Zero is the smallest integer. (False)
(ii) –10 is smaller than –7. (True)
(iii) 1 is the smallest positive integer. (True)
(iv) –1 is the smallest negative integer. (False)
(v) Sum of two negative integers is a positive integer. (False)
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Important Results:
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Question 6: Evaluate:
(i) (–4) × (–15) × (–33)
(ii) (–1) × (–1) × (–1) × … 100 times
(iii) (–7) × (–4) × 5
Solution:
(i) (–4) × (–15) × (–33)
= – (4 × 15 × 33)
= – 1980.
(ii) (–1) × (–1) × (–1) × … 100 times
= (– 1)100
= 1 {∵ 100 is an even number}
(iii) (–7) × (–4) × 5
= (7 × 4) × 5
= 28 × 5
= 140
Question 7: In a class test containing 20 questions, 5 marks are awarded for each correct answer and 2 marks is deducted for each wrong answer. If Riya get 15 correct answers out of all the questions attempted. What is her total score?
Solution:
Number of questions = 20
Marks awarded for corrected answer = 5
Marks awarded for wrong answer = –2
Number questions attempted correctly = 15
Number questions not attempted correctly = 5
Her total score = (15 × 5) + (–2 × 5) = 75 – 10 = 65
Question 8: An elevator descends at the rate of 4 m/min. If the elevator start descending 25 m above the ground level, how long will it take to cover –450 m? ‘
Solution:
Given, the elevator is at 25 m above the ground level and have to reach 450 m below the ground level.
Distance have to be covered = 25 – (–450) = 475 m
Speed of the elevator = 4 m/min
Time taken = 475/4 = 118.75 min.
Question 9: What number should be added to the sum of 345 and 67 to make it equal to the smallest 3-digit number?
Solution:
Smallest 3-digit number = 100
Now, 345 + 67 = 412
412 – 100 = 312
Thus, 412 + (–312) = 100
Question 10: During summer, the temperature within a room is 37o C. If an air conditioner cools the room by 5o C/min. What will be the temperature of the room after 5 minutes of switching on the air conditioner?
Solution:
Temperature of the room before switching on the air conditioner = 37oC
Rate of cooling = –5o c/min
Temperature of the room after switching on the air conditioner for 5 min = 37 – (5 × 5)
= 37 – 25 = 12oC.
Video Lesson on Number Sytem
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Practice Questions on Integers
1. Evaluate the following:
(i) 34 – 56 + (–18)
(ii) [32 – 17] × [32 + 90]
(iii) 12 – 25 + (–35) + 2.9
(iv) 34 – 56 + 13 – ( –37)
2. A dishonest shopekeeper uses a weighing machine which 900 g as 1kg. If cost of per kg sugar is ₹ 40. How more money did the shopekeeper earned by selling 3 kg sugar to the customer.
3. An air conditioner cools a room by 4oC/min. If the temperature of the room is 45oC before switching on the air conditioner. Find temperature of the room after switching on the air contioner for 6 min.
4. Write true or fallse for the following statements:
(i) Zero is a positive integer.
(ii) –1 is greatest negative integer.
(iii) Sum of a positive integer and a negative integer is always a positive integer.
(iv) Division of integers is always an integer.
(v) Multiplication of a positive integer and a negative integer is always a negative integer.
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