Negative Numbers and Integers - Exercise 5.4 Class 6 Notes | EduRev

Mathematics (Maths) Class 6

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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