Page 1 Exercise 5.4 page: 5.17 1. Subtract the first integer from the second in each of the following: (i) 12, -5 (ii) – 12, 8 (iii) – 225, - 135 (iv) 1001, 101 (v) – 812, 3126 (vi) 7560, - 8 (vii) – 3978, - 4109 (viii) 0, - 1005 Solution: (i) 12, -5 So by subtracting the first integer from the second -5 – 12 = - 17 (ii) – 12, 8 So by subtracting the first integer from the second 8 – (-12) = 8 + 12 = 20 (iii) – 225, - 135 So by subtracting the first integer from the second -135 – (-225) = 225 – 135 = 90 (iv) 1001, 101 So by subtracting the first integer from the second 101 – 1001 = - 900 (v) – 812, 3126 So by subtracting the first integer from the second 3126 – (-812) = 3126 + 812 = 3938 (vi) 7560, - 8 So by subtracting the first integer from the second -8 – 7560 = - 7568 (vii) – 3978, - 4109 So by subtracting the first integer from the second -4109 – (-3978) = - 4109 + 3978 = -131 (viii) 0, - 1005 So by subtracting the first integer from the second -1005 – 0 = - 1005 2. Find the value of: (i) – 27 – (- 23) (ii) – 17 – 18 – (-35) (iii) – 12 – (-5) – (-125) + 270 (iv) 373 + (-245) + (-373) + 145 + 3000 Page 2 Exercise 5.4 page: 5.17 1. Subtract the first integer from the second in each of the following: (i) 12, -5 (ii) – 12, 8 (iii) – 225, - 135 (iv) 1001, 101 (v) – 812, 3126 (vi) 7560, - 8 (vii) – 3978, - 4109 (viii) 0, - 1005 Solution: (i) 12, -5 So by subtracting the first integer from the second -5 – 12 = - 17 (ii) – 12, 8 So by subtracting the first integer from the second 8 – (-12) = 8 + 12 = 20 (iii) – 225, - 135 So by subtracting the first integer from the second -135 – (-225) = 225 – 135 = 90 (iv) 1001, 101 So by subtracting the first integer from the second 101 – 1001 = - 900 (v) – 812, 3126 So by subtracting the first integer from the second 3126 – (-812) = 3126 + 812 = 3938 (vi) 7560, - 8 So by subtracting the first integer from the second -8 – 7560 = - 7568 (vii) – 3978, - 4109 So by subtracting the first integer from the second -4109 – (-3978) = - 4109 + 3978 = -131 (viii) 0, - 1005 So by subtracting the first integer from the second -1005 – 0 = - 1005 2. Find the value of: (i) – 27 – (- 23) (ii) – 17 – 18 – (-35) (iii) – 12 – (-5) – (-125) + 270 (iv) 373 + (-245) + (-373) + 145 + 3000 (v) 1 + (-475) + (-475) + (-475) + (-475) + 1900 (vi) (-1) + (-304) + 304 + 304 + (-304) + 1 Solution: (i) – 27 – (- 23) So we get = - 27 + 23 On further calculation = 23 – 27 We get = - 4 (ii) – 17 – 18 – (-35) So we get = - 35 + 35 On further calculation = 0 (iii) – 12 – (-5) – (-125) + 270 So we get = - 12 + 5 + 125 + 270 On further calculation = 400 – 12 We get = 388 (iv) 373 + (-245) + (-373) + 145 + 3000 So we get = 373 – 245 – 373 + 145 + 3000 On further calculation = 3145 + 373 – 373 – 245 We get = 3145 – 245 By subtraction = 2900 (v) 1 + (-475) + (-475) + (-475) + (-475) + 1900 So we get = 1 – 950 – 950 + 1900 On further calculation = 1900 + 1 – 1900 We get = 1 (vi) (-1) + (-304) + 304 + 304 + (-304) + 1 So we get = - 1 + 1 – 304 + 304 – 304 + 304 On further calculation = 0 Page 3 Exercise 5.4 page: 5.17 1. Subtract the first integer from the second in each of the following: (i) 12, -5 (ii) – 12, 8 (iii) – 225, - 135 (iv) 1001, 101 (v) – 812, 3126 (vi) 7560, - 8 (vii) – 3978, - 4109 (viii) 0, - 1005 Solution: (i) 12, -5 So by subtracting the first integer from the second -5 – 12 = - 17 (ii) – 12, 8 So by subtracting the first integer from the second 8 – (-12) = 8 + 12 = 20 (iii) – 225, - 135 So by subtracting the first integer from the second -135 – (-225) = 225 – 135 = 90 (iv) 1001, 101 So by subtracting the first integer from the second 101 – 1001 = - 900 (v) – 812, 3126 So by subtracting the first integer from the second 3126 – (-812) = 3126 + 812 = 3938 (vi) 7560, - 8 So by subtracting the first integer from the second -8 – 7560 = - 7568 (vii) – 3978, - 4109 So by subtracting the first integer from the second -4109 – (-3978) = - 4109 + 3978 = -131 (viii) 0, - 1005 So by subtracting the first integer from the second -1005 – 0 = - 1005 2. Find the value of: (i) – 27 – (- 23) (ii) – 17 – 18 – (-35) (iii) – 12 – (-5) – (-125) + 270 (iv) 373 + (-245) + (-373) + 145 + 3000 (v) 1 + (-475) + (-475) + (-475) + (-475) + 1900 (vi) (-1) + (-304) + 304 + 304 + (-304) + 1 Solution: (i) – 27 – (- 23) So we get = - 27 + 23 On further calculation = 23 – 27 We get = - 4 (ii) – 17 – 18 – (-35) So we get = - 35 + 35 On further calculation = 0 (iii) – 12 – (-5) – (-125) + 270 So we get = - 12 + 5 + 125 + 270 On further calculation = 400 – 12 We get = 388 (iv) 373 + (-245) + (-373) + 145 + 3000 So we get = 373 – 245 – 373 + 145 + 3000 On further calculation = 3145 + 373 – 373 – 245 We get = 3145 – 245 By subtraction = 2900 (v) 1 + (-475) + (-475) + (-475) + (-475) + 1900 So we get = 1 – 950 – 950 + 1900 On further calculation = 1900 + 1 – 1900 We get = 1 (vi) (-1) + (-304) + 304 + 304 + (-304) + 1 So we get = - 1 + 1 – 304 + 304 – 304 + 304 On further calculation = 0 3. Subtract the sum of – 5020 and 2320 from – 709. Solution: We know that the sum of -5020 and 2320 is -5020 + 2320 It can be written as = 2320 – 5020 So we get = - 2700 Subtracting from – 709 we get = - 709 – (-2700) We get = - 709 + 2700 By subtraction = 1991 4. Subtract the sum of – 1250 and 1138 from the sum of 1136 and - 1272. Solution: We know that the sum of – 1250 and 1138 is -1250 + 1138 It can be written as = 1138 – 1250 So we get = - 112 We know that the sum of 1136 and – 1272 is 1136 – 1272 = - 136 So we get -136 – (-112) = - 136 + 112 = -24 5. From the sum of 233 and – 147, subtract – 284. Solution: We know that the sum of 233 and – 147 is 233 – 147 = 86 Subtracting – 284 we get 86 – (-284) = 86 + 284 = 370 6. The sum of two integers is 238. If one of the integers is – 122, determine the other. Solution: It is given that Sum of two integers = 238 One of the integers = - 122 So the other integer = - (-122) + 238 On further calculation Other integer = 238 + 122 = 360 7. The sum of two integers is – 223. If one of the integers is 172, find the other. Page 4 Exercise 5.4 page: 5.17 1. Subtract the first integer from the second in each of the following: (i) 12, -5 (ii) – 12, 8 (iii) – 225, - 135 (iv) 1001, 101 (v) – 812, 3126 (vi) 7560, - 8 (vii) – 3978, - 4109 (viii) 0, - 1005 Solution: (i) 12, -5 So by subtracting the first integer from the second -5 – 12 = - 17 (ii) – 12, 8 So by subtracting the first integer from the second 8 – (-12) = 8 + 12 = 20 (iii) – 225, - 135 So by subtracting the first integer from the second -135 – (-225) = 225 – 135 = 90 (iv) 1001, 101 So by subtracting the first integer from the second 101 – 1001 = - 900 (v) – 812, 3126 So by subtracting the first integer from the second 3126 – (-812) = 3126 + 812 = 3938 (vi) 7560, - 8 So by subtracting the first integer from the second -8 – 7560 = - 7568 (vii) – 3978, - 4109 So by subtracting the first integer from the second -4109 – (-3978) = - 4109 + 3978 = -131 (viii) 0, - 1005 So by subtracting the first integer from the second -1005 – 0 = - 1005 2. Find the value of: (i) – 27 – (- 23) (ii) – 17 – 18 – (-35) (iii) – 12 – (-5) – (-125) + 270 (iv) 373 + (-245) + (-373) + 145 + 3000 (v) 1 + (-475) + (-475) + (-475) + (-475) + 1900 (vi) (-1) + (-304) + 304 + 304 + (-304) + 1 Solution: (i) – 27 – (- 23) So we get = - 27 + 23 On further calculation = 23 – 27 We get = - 4 (ii) – 17 – 18 – (-35) So we get = - 35 + 35 On further calculation = 0 (iii) – 12 – (-5) – (-125) + 270 So we get = - 12 + 5 + 125 + 270 On further calculation = 400 – 12 We get = 388 (iv) 373 + (-245) + (-373) + 145 + 3000 So we get = 373 – 245 – 373 + 145 + 3000 On further calculation = 3145 + 373 – 373 – 245 We get = 3145 – 245 By subtraction = 2900 (v) 1 + (-475) + (-475) + (-475) + (-475) + 1900 So we get = 1 – 950 – 950 + 1900 On further calculation = 1900 + 1 – 1900 We get = 1 (vi) (-1) + (-304) + 304 + 304 + (-304) + 1 So we get = - 1 + 1 – 304 + 304 – 304 + 304 On further calculation = 0 3. Subtract the sum of – 5020 and 2320 from – 709. Solution: We know that the sum of -5020 and 2320 is -5020 + 2320 It can be written as = 2320 – 5020 So we get = - 2700 Subtracting from – 709 we get = - 709 – (-2700) We get = - 709 + 2700 By subtraction = 1991 4. Subtract the sum of – 1250 and 1138 from the sum of 1136 and - 1272. Solution: We know that the sum of – 1250 and 1138 is -1250 + 1138 It can be written as = 1138 – 1250 So we get = - 112 We know that the sum of 1136 and – 1272 is 1136 – 1272 = - 136 So we get -136 – (-112) = - 136 + 112 = -24 5. From the sum of 233 and – 147, subtract – 284. Solution: We know that the sum of 233 and – 147 is 233 – 147 = 86 Subtracting – 284 we get 86 – (-284) = 86 + 284 = 370 6. The sum of two integers is 238. If one of the integers is – 122, determine the other. Solution: It is given that Sum of two integers = 238 One of the integers = - 122 So the other integer = - (-122) + 238 On further calculation Other integer = 238 + 122 = 360 7. The sum of two integers is – 223. If one of the integers is 172, find the other. Solution: It is given that Sum of two integers = - 223 One of the integers = 172 So the other integer = - 223 – 172 = - 395 8. Evaluate the following: (i) – 8 – 24 + 31 – 26 – 28 + 7 + 19 – 18 – 8 + 33 (ii) – 26 – 20 + 33 – (-33) + 21 + 24 – (-25) – 26 – 14 – 34 Solution: (i) – 8 – 24 + 31 – 26 – 28 + 7 + 19 – 18 – 8 + 33 We get = - 8 – 24 – 26 – 28 – 18 – 8 + 31 + 7 + 19 + 33 On further calculation = - 32 – 26 – 28 – 26 + 38 + 19 + 33 It can be written as = 38 – 32 – 26 – 28 + 33 – 26 + 19 So we get = 6 – 26 – 28 + 7 + 19 By calculation = 6 – 28 – 26 + 26 = 6 – 28 By subtraction = - 22 (ii) – 26 – 20 + 33 – (-33) + 21 + 24 – (-25) – 26 – 14 – 34 We get = - 46 + 33 + 33 + 21 + 24 + 25 – 26 – 14 – 34 On further calculation = - 46 + 66 + 21 + 24 + 25 + (-74) It can be written as = - 46 + 66 + 70 – 74 So we get = - 46 – 4 + 66 By calculation = - 50 + 66 = 66 – 50 By subtraction = 16 9. Calculate 1 – 2 + 3 – 4 + 5 – 6 + ……… + 15 – 16 Solution: It can be written as 1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 + 9 – 10 + 11 – 12 + 13 – 14 + 15 – 16 We get = - 1 – 1 – 1 – 1 – 1 – 1 – 1 – 1 Page 5 Exercise 5.4 page: 5.17 1. Subtract the first integer from the second in each of the following: (i) 12, -5 (ii) – 12, 8 (iii) – 225, - 135 (iv) 1001, 101 (v) – 812, 3126 (vi) 7560, - 8 (vii) – 3978, - 4109 (viii) 0, - 1005 Solution: (i) 12, -5 So by subtracting the first integer from the second -5 – 12 = - 17 (ii) – 12, 8 So by subtracting the first integer from the second 8 – (-12) = 8 + 12 = 20 (iii) – 225, - 135 So by subtracting the first integer from the second -135 – (-225) = 225 – 135 = 90 (iv) 1001, 101 So by subtracting the first integer from the second 101 – 1001 = - 900 (v) – 812, 3126 So by subtracting the first integer from the second 3126 – (-812) = 3126 + 812 = 3938 (vi) 7560, - 8 So by subtracting the first integer from the second -8 – 7560 = - 7568 (vii) – 3978, - 4109 So by subtracting the first integer from the second -4109 – (-3978) = - 4109 + 3978 = -131 (viii) 0, - 1005 So by subtracting the first integer from the second -1005 – 0 = - 1005 2. Find the value of: (i) – 27 – (- 23) (ii) – 17 – 18 – (-35) (iii) – 12 – (-5) – (-125) + 270 (iv) 373 + (-245) + (-373) + 145 + 3000 (v) 1 + (-475) + (-475) + (-475) + (-475) + 1900 (vi) (-1) + (-304) + 304 + 304 + (-304) + 1 Solution: (i) – 27 – (- 23) So we get = - 27 + 23 On further calculation = 23 – 27 We get = - 4 (ii) – 17 – 18 – (-35) So we get = - 35 + 35 On further calculation = 0 (iii) – 12 – (-5) – (-125) + 270 So we get = - 12 + 5 + 125 + 270 On further calculation = 400 – 12 We get = 388 (iv) 373 + (-245) + (-373) + 145 + 3000 So we get = 373 – 245 – 373 + 145 + 3000 On further calculation = 3145 + 373 – 373 – 245 We get = 3145 – 245 By subtraction = 2900 (v) 1 + (-475) + (-475) + (-475) + (-475) + 1900 So we get = 1 – 950 – 950 + 1900 On further calculation = 1900 + 1 – 1900 We get = 1 (vi) (-1) + (-304) + 304 + 304 + (-304) + 1 So we get = - 1 + 1 – 304 + 304 – 304 + 304 On further calculation = 0 3. Subtract the sum of – 5020 and 2320 from – 709. Solution: We know that the sum of -5020 and 2320 is -5020 + 2320 It can be written as = 2320 – 5020 So we get = - 2700 Subtracting from – 709 we get = - 709 – (-2700) We get = - 709 + 2700 By subtraction = 1991 4. Subtract the sum of – 1250 and 1138 from the sum of 1136 and - 1272. Solution: We know that the sum of – 1250 and 1138 is -1250 + 1138 It can be written as = 1138 – 1250 So we get = - 112 We know that the sum of 1136 and – 1272 is 1136 – 1272 = - 136 So we get -136 – (-112) = - 136 + 112 = -24 5. From the sum of 233 and – 147, subtract – 284. Solution: We know that the sum of 233 and – 147 is 233 – 147 = 86 Subtracting – 284 we get 86 – (-284) = 86 + 284 = 370 6. The sum of two integers is 238. If one of the integers is – 122, determine the other. Solution: It is given that Sum of two integers = 238 One of the integers = - 122 So the other integer = - (-122) + 238 On further calculation Other integer = 238 + 122 = 360 7. The sum of two integers is – 223. If one of the integers is 172, find the other. Solution: It is given that Sum of two integers = - 223 One of the integers = 172 So the other integer = - 223 – 172 = - 395 8. Evaluate the following: (i) – 8 – 24 + 31 – 26 – 28 + 7 + 19 – 18 – 8 + 33 (ii) – 26 – 20 + 33 – (-33) + 21 + 24 – (-25) – 26 – 14 – 34 Solution: (i) – 8 – 24 + 31 – 26 – 28 + 7 + 19 – 18 – 8 + 33 We get = - 8 – 24 – 26 – 28 – 18 – 8 + 31 + 7 + 19 + 33 On further calculation = - 32 – 26 – 28 – 26 + 38 + 19 + 33 It can be written as = 38 – 32 – 26 – 28 + 33 – 26 + 19 So we get = 6 – 26 – 28 + 7 + 19 By calculation = 6 – 28 – 26 + 26 = 6 – 28 By subtraction = - 22 (ii) – 26 – 20 + 33 – (-33) + 21 + 24 – (-25) – 26 – 14 – 34 We get = - 46 + 33 + 33 + 21 + 24 + 25 – 26 – 14 – 34 On further calculation = - 46 + 66 + 21 + 24 + 25 + (-74) It can be written as = - 46 + 66 + 70 – 74 So we get = - 46 – 4 + 66 By calculation = - 50 + 66 = 66 – 50 By subtraction = 16 9. Calculate 1 – 2 + 3 – 4 + 5 – 6 + ……… + 15 – 16 Solution: It can be written as 1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 + 9 – 10 + 11 – 12 + 13 – 14 + 15 – 16 We get = - 1 – 1 – 1 – 1 – 1 – 1 – 1 – 1 By calculation = - 8 10. Calculate the sum: 5 + (-5) + 5 + (-5) + ….. (i) if the number of terms is 10. (ii) if the number of terms is 11. Solution: (i) if the number of terms is 10 We get 5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5) On further calculation = 5 – 5 + 5 – 5 + 5 – 5 + 5 – 5 + 5 – 5 = 0 (ii) if the number of terms is 11 We get 5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5) + 5 On further calculation = 5 – 5 + 5 – 5 + 5 – 5 + 5 – 5 + 5 – 5 + 5 = 5 11. Replace * by < or > in each of the following to make the statement true: (i) (-6) + (-9) * (-6) – (-9) (ii) (-12) – (-12) * (-12) + (-12) (iii) (-20) – (-20) * 20 - (65) (iv) 28 – (-10) * (-16) – (-76) Solution: (i) (-6) + (-9) < (-6) – (-9) (ii) (-12) – (-12) > (-12) + (-12) (iii) (-20) – (-20) > 20 - (65) (iv) 28 – (-10) < (-16) – (-76) 12. If ? is an operation on integers such that a ? b = - a + b – (-2) for all integers a, b. Find the value of (i) 4 ? 3 (ii) (-2) ? (-3) (iii) 6 ? (-5) (iv) (-5) ? 6 Solution: (i) 4 ? 3 By substituting values in a ? b = - a + b – (-2) We get 4 ? 3 = - 4 + 3 – (-2) = 1 (ii) (-2) ? (-3) By substituting values in a ? b = - a + b – (-2)Read More

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