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Page 1 Exercise 5.3 page: 5.11 1. Find the additive inverse of each of the following integers: (i) 52 (ii) – 176 (iii) 0 (iv) 1 Solution: (i) The additive inverse of 52 is – 52. (ii) The additive inverse of – 176 is 176. (iii) The additive inverse of 0 is 0. (iv) The additive inverse of 1 is – 1. 2. Find the successor of each of the following integers: (i) – 42 (ii) 1 (iii) 0 (iv) – 200 (v) 99 Solution: (i) The successor of – 42 is  42 + 1 =  41 (ii) The successor of – 1 is 1 + 1 = 0 (iii) The successor of 0 is 0 + 1 = 1 (iv) The successor of – 200 is 200 + 1 =  199 (v) The successor of – 99 is  99 + 1 =  98 3. Find the predecessor of each of the following integers: (i) 0 (ii) 1 (iii) – 1 (iv) – 125 (v) 1000 Solution: (i) The predecessor of 0 is 0 – 1 =  1 Page 2 Exercise 5.3 page: 5.11 1. Find the additive inverse of each of the following integers: (i) 52 (ii) – 176 (iii) 0 (iv) 1 Solution: (i) The additive inverse of 52 is – 52. (ii) The additive inverse of – 176 is 176. (iii) The additive inverse of 0 is 0. (iv) The additive inverse of 1 is – 1. 2. Find the successor of each of the following integers: (i) – 42 (ii) 1 (iii) 0 (iv) – 200 (v) 99 Solution: (i) The successor of – 42 is  42 + 1 =  41 (ii) The successor of – 1 is 1 + 1 = 0 (iii) The successor of 0 is 0 + 1 = 1 (iv) The successor of – 200 is 200 + 1 =  199 (v) The successor of – 99 is  99 + 1 =  98 3. Find the predecessor of each of the following integers: (i) 0 (ii) 1 (iii) – 1 (iv) – 125 (v) 1000 Solution: (i) The predecessor of 0 is 0 – 1 =  1 (ii) The predecessor of 1 is 1 – 1 = 0 (iii) The predecessor of 1 is 1 – 1 = 2 (iv) The predecessor of – 125 is 125 – 1 =  126 (v) The predecessor of 1000 is 1000 – 1 = 999 4. Which of the following statements are true? (i) The sum of a number and its opposite is zero. (ii) The sum of two negative integers is a positive integer. (iii) The sum of a negative integer and a positive integer is always a negative integer. (iv) The successor of – 1 is 1. (v) The sum of three different integers can never be zero. Solution: (i) True. 1 – 1 = 0 (ii) False. 1 – 1 = 2 (iii) False. – 2 + 3 = 1 (iv) False. The successor of – 1 is 0. (v) False. 1 + 2 – 3 = 0 5. Write all integers whose absolute values are less than 5. Solution: The integers whose absolute values are less than 5 are 4,  3,  2,  1, 0, 1, 2, 3, 4 6. Which of the following is false: (i) 4 + 2 = 4 + 2 (ii) 2 – 4 = 2 + 4 (iii) 4 – 2 = 4  2 (iv) (2) + (4) = 2 + 4 Solution: (i) True. (ii) False. (iii) True. (iv) True. Page 3 Exercise 5.3 page: 5.11 1. Find the additive inverse of each of the following integers: (i) 52 (ii) – 176 (iii) 0 (iv) 1 Solution: (i) The additive inverse of 52 is – 52. (ii) The additive inverse of – 176 is 176. (iii) The additive inverse of 0 is 0. (iv) The additive inverse of 1 is – 1. 2. Find the successor of each of the following integers: (i) – 42 (ii) 1 (iii) 0 (iv) – 200 (v) 99 Solution: (i) The successor of – 42 is  42 + 1 =  41 (ii) The successor of – 1 is 1 + 1 = 0 (iii) The successor of 0 is 0 + 1 = 1 (iv) The successor of – 200 is 200 + 1 =  199 (v) The successor of – 99 is  99 + 1 =  98 3. Find the predecessor of each of the following integers: (i) 0 (ii) 1 (iii) – 1 (iv) – 125 (v) 1000 Solution: (i) The predecessor of 0 is 0 – 1 =  1 (ii) The predecessor of 1 is 1 – 1 = 0 (iii) The predecessor of 1 is 1 – 1 = 2 (iv) The predecessor of – 125 is 125 – 1 =  126 (v) The predecessor of 1000 is 1000 – 1 = 999 4. Which of the following statements are true? (i) The sum of a number and its opposite is zero. (ii) The sum of two negative integers is a positive integer. (iii) The sum of a negative integer and a positive integer is always a negative integer. (iv) The successor of – 1 is 1. (v) The sum of three different integers can never be zero. Solution: (i) True. 1 – 1 = 0 (ii) False. 1 – 1 = 2 (iii) False. – 2 + 3 = 1 (iv) False. The successor of – 1 is 0. (v) False. 1 + 2 – 3 = 0 5. Write all integers whose absolute values are less than 5. Solution: The integers whose absolute values are less than 5 are 4,  3,  2,  1, 0, 1, 2, 3, 4 6. Which of the following is false: (i) 4 + 2 = 4 + 2 (ii) 2 – 4 = 2 + 4 (iii) 4 – 2 = 4  2 (iv) (2) + (4) = 2 + 4 Solution: (i) True. (ii) False. (iii) True. (iv) True. 7. Complete the following table: From the above table: (i) Write all the pairs of integers whose sum is 0. (ii) Is (4) + (2) = (2) + (4)? (iii) Is 0 + (6) = 6? Solution: (i) The pairs of integers whose sum is 0 are (6, 6), (4,  4), (2,  2), (0, 0) (ii) Yes. By using commutativity of addition (4) + (2) = (2) + (4) (iii) Yes. By using additive identity 0 + (6) = 6. 8. Find an integer x such that (i) x + 1 = 0 (ii) x + 5 = 0 (iii) – 3 + x = 0 (iv) x + (8) = 0 (v) 7 + x = 0 (vi) x + 0 = 0 Solution: (i) x + 1 = 0 Subtracting 1 on both sides x + 1 – 1 = 0 – 1 Page 4 Exercise 5.3 page: 5.11 1. Find the additive inverse of each of the following integers: (i) 52 (ii) – 176 (iii) 0 (iv) 1 Solution: (i) The additive inverse of 52 is – 52. (ii) The additive inverse of – 176 is 176. (iii) The additive inverse of 0 is 0. (iv) The additive inverse of 1 is – 1. 2. Find the successor of each of the following integers: (i) – 42 (ii) 1 (iii) 0 (iv) – 200 (v) 99 Solution: (i) The successor of – 42 is  42 + 1 =  41 (ii) The successor of – 1 is 1 + 1 = 0 (iii) The successor of 0 is 0 + 1 = 1 (iv) The successor of – 200 is 200 + 1 =  199 (v) The successor of – 99 is  99 + 1 =  98 3. Find the predecessor of each of the following integers: (i) 0 (ii) 1 (iii) – 1 (iv) – 125 (v) 1000 Solution: (i) The predecessor of 0 is 0 – 1 =  1 (ii) The predecessor of 1 is 1 – 1 = 0 (iii) The predecessor of 1 is 1 – 1 = 2 (iv) The predecessor of – 125 is 125 – 1 =  126 (v) The predecessor of 1000 is 1000 – 1 = 999 4. Which of the following statements are true? (i) The sum of a number and its opposite is zero. (ii) The sum of two negative integers is a positive integer. (iii) The sum of a negative integer and a positive integer is always a negative integer. (iv) The successor of – 1 is 1. (v) The sum of three different integers can never be zero. Solution: (i) True. 1 – 1 = 0 (ii) False. 1 – 1 = 2 (iii) False. – 2 + 3 = 1 (iv) False. The successor of – 1 is 0. (v) False. 1 + 2 – 3 = 0 5. Write all integers whose absolute values are less than 5. Solution: The integers whose absolute values are less than 5 are 4,  3,  2,  1, 0, 1, 2, 3, 4 6. Which of the following is false: (i) 4 + 2 = 4 + 2 (ii) 2 – 4 = 2 + 4 (iii) 4 – 2 = 4  2 (iv) (2) + (4) = 2 + 4 Solution: (i) True. (ii) False. (iii) True. (iv) True. 7. Complete the following table: From the above table: (i) Write all the pairs of integers whose sum is 0. (ii) Is (4) + (2) = (2) + (4)? (iii) Is 0 + (6) = 6? Solution: (i) The pairs of integers whose sum is 0 are (6, 6), (4,  4), (2,  2), (0, 0) (ii) Yes. By using commutativity of addition (4) + (2) = (2) + (4) (iii) Yes. By using additive identity 0 + (6) = 6. 8. Find an integer x such that (i) x + 1 = 0 (ii) x + 5 = 0 (iii) – 3 + x = 0 (iv) x + (8) = 0 (v) 7 + x = 0 (vi) x + 0 = 0 Solution: (i) x + 1 = 0 Subtracting 1 on both sides x + 1 – 1 = 0 – 1 We get x = 1 (ii) x + 5 = 0 By subtracting 5 on both sides x + 5 – 5 = 0 – 5 So we get x = 5 (iii) – 3 + x = 0 By adding 3 on both sides 3 + x + 3 = 0 + 3 So we get x = 3 (iv) x + (8) = 0 By adding 8 on both sides x – 8 + 8 = 0 + 8 So we get x = 8 (v) 7 + x = 0 By subtracting 7 on both sides 7 + x – 7 = 0 – 7 So we get x =  7 (vi) x + 0 = 0 So we get x = 0Read More
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