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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