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  Negative Numbers and Integers - Exercise 5.4 Class 6 Notes | EduRev
  
  Class 6 : Negative Numbers and Integers - Exercise 5.4 Class 6 Notes | EduRev
  
  ``` 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)
  ```
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  Mathematics (Maths) Class 6
  
  191 videos|224 docs|43 tests
  
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  Negative Numbers and Integers - Exercise 5.4 Class 6 Notes | EduRev
  
  Class 6 : Negative Numbers and Integers - Exercise 5.4 Class 6 Notes | EduRev
  
  ``` 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)
  ```
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  Mathematics (Maths) Class 6
  
  191 videos|224 docs|43 tests
  
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distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is a set of exercises and solutions for a math class, specifically dealing with operations involving negative numbers and integers. The document contains multiple questions and their corresponding answers.
  
  Label: multiple-question-and-answer