RS Aggarwal Class 6 Solutions Chapter 4 Integers Ex 4B
These Solutions are part of RS Aggarwal Solutions Class 6. Here we have given RS Aggarwal Solutions Class 6 Chapter 4 Integers Ex 4B.
Other Exercises
Question 1.
 Solution:
 (i) On the number line we start from 0 and move 9 steps to the right to reach a point A. Now, starting from A, we move 6 steps to the left to reach a point B, as shown below :
 
 Now, B represents the integer 3
 9 + ( – 6) = 3
 (ii) On the number line, we start from 0 and move 3 steps to the left to reach a point A. Now, starting from A, we move 7 steps to the right to reach a point B, as shown below :
 
 And B represents the integer 4
 ( – 3) + 7 = 4
 (iii) On the number line, we start from 0 and move 8 steps to the right to reach a point A. Now, starting from A, we move 8 steps to the left to reach a point B, as shown below :
 
 And, B represents the integer 0.
 8 + ( – 8) = 0
 (iv) On the number line, we start from 0 and move 1 step the left to reach a point A. Now, starting from point A, we move 3 steps to the left to reach g. point B, as shown below :
 
 And, B represents the integer – 4
 ( – 1) + ( – 3) = – 4.
 (v) On the number line, we start from 0 and move 4 steps to the left to reach a point A. Now, starting from point A, we move 7 steps to the left to reach a point B, as shown below :
 
 And, B represents the integer -11.
 ( – 4) + ( – 7) = – 11
 (vi) On the number line we start from 0 and move 2 steps to the left to reach a point A. Now, starting from A, we move 8 steps to the left to reach a point B, as shown below :
 
 And, B represents the integer – 10
 ( – 2) + ( – 8) = – 10
 (vii) On the number line we start from 0 and move 3 steps to the right to reach a point A. Now, starting from A, we move 2 steps to the left to reach a point B and again starting from left to reach a point B and again starting from B, we move 4 steps to the left to reach a point C, as shown below :
 
 And, C represents the integer – 3
 3 + ( – 2) + ( – 4) = – 3
 (viii) On the number line we start from 0 and move 1 step to the left to reach a point A. Now, starting from A, we move 2 steps to the left to reach a point B and again starting from B, we move 3 steps to the left to reach point C, as shown below :
 
 And, C represents the integer – 6
 ( – 1) + ( – 2) + ( – 3) = – 6.
 (ix) On the number line we start from 0 and move 5 steps to the right to reach a point A. Now, starting from A, we move 2 steps to the left to reach a point B and again starting from point B, we move 6 steps to the left to reach a point C, as shown below :
 
 And, C represents the integer – 3.
 5 + (- 2) + (- 6) = – 3
Question 2.
 Solution:
 (i) (- 3) + ( – 9) = – 12
 (Using the rule for addition of integers having like signs)
 (ii) ( – 7) + ( – 8) = – 15
 (Using the rule for addition of integers having like signs)
 (iii) ( – 9) + 16 = 7
 (Using the rule for addition of integers having unlike signs)
 (iv) ( – 13) + 25 = 12
 (Using the rule for addition of integers having unlike signs)
 (v) 8 + ( – 17) = – 9
 (Using the rule for addition of integers having unlike signs)
 (vi) 2 + ( – 12) = – 10
 (Using the rule for addition of integers having unlike signs)
Question 3.
 Solution:
 (i) Using the rule for addition of integers with like signs, we get:
 
 (ii) Using the rule for addition of integers with like signs, we get :
 
 (iii) Using the rule for addition of integers with like signs, we get :
 
 (iv) Using the rule for addition of integers with like signs, we get:
 
Question 4.
 Solution:
 (i) Using the rule for addition of integers with unlike signs, we get:
 
 (ii) Using the rule for addition of integers with unlike signs, we get:
 
 (iii) Using the rule for addition of integers with unlike signs, we have
 
 (iv) Using the rule for addition of integers with unlike signs, we have
 
Question 5.
 Solution:
 (i) Using the rule for addition of integers with unlike signs, we get :
 
 (ii) Using-the rule for addition of integers with unlike signs, we get
 
 (iii) Using the rule for addition of integers with unlike signs, we get :
 
 (iv) Using the rule for addition of integers with unlike signs, we get :
 
 (v) Using the rule for addition of integers with like signs, we get:
 
 (vi) Using the rule for addition of integers with unlike signs, we get :
 
 (vii) Using the rule for addition of integers with unlike signs, we get :
 
 (viii) We have, ( – 18) + 25 + ( – 37)
 = [( – 18) + 25] + ( – 37)
 = 7 + ( – 37)
 = – 30
 (ix) We have, – 312 + 39 + 192
 = ( – 312) + (39 + 192)
 = ( – 312) + 231
 = – 81
 (x) We have ( – 51) + ( – 203) + 36 + ( – 28)
 = [( – 51) + ( – 203)] + [36 + ( – 28)]
 = ( – 254) + 8
 = – 246
Question 6.
 Solution:
 (i) The additive inverse of – 57 is 57
 (ii) The additive inverse of 183 is – 183
 (iii) The additive inverse of 0 is 0
 (iv) The additive inverse of – 1001 is 1001
 (v) The additive inverse of 2054 is – 2054
Question 7.
 Solution:
 (i) Successor of 201 = 201 + 1 = 202
 (ii) Successor of 70 = 70 + 1 = 71
 (iii) Successor of – 5 = – 5 + 1 = – 4
 (iv) Successor of – 99 = – 99 + 1 = – 98
 (v) Successor of – 500 = – 500 + 1 = – 499 Ans.
Question 8.
 Solution:
 (i) Predecessor of 120 = 120 – 1 = 119
 (ii) Predecessor of 79 = 79 – 1 = 78
 (iii) Predecessor of – 8 = – 8 – 1 = – 9
 (iv) Predecessor of – 141 = – 141 – 1 = – 142
 (v) Predecessor of – 300 = – 300 – 1 = – 301 Ans.
Question 9.
 Solution:
 (i) ( – 7) + ( – 9) + 12 + ( – 16)
 = – 7 – 9 + 12 – 16
 = – 7 – 9 – 16 + 12
 = – 32 + 12
 = – 20
 (ii) 37 + ( – 23) + ( – 65) + 9 + ( – 12)
 = 37 – 23 – 65 + 9 – 12
 = 37 + 9 – 23 – 65 – 12
 = 46 – 100
 = – 54
 (iii) ( – 145) + 79 + ( – 265) + ( – 41) + 2
 = – 145 + 79 – 265 – 41 + 2
 = 79 + 2 – 145 – 265 – 41
 = 81 – 451
 = – 370
 (iv) 1056 + ( – 798) + ( – 38) + 44 + ( – 1)
 = 1056 – 798 – 38 + 44 – 1
 = 1056 + 44 – 798 – 38 – 1
 = 1100 – 837
 = 263 Ans.
Question 10.
 Solution:
 Distance travelled from Patna to its north = 60 km
 Distance travelled from that place to south of it = 90 km
 Distance of the final place to Patna = 60 – 90
 = – 30 km
 = 30 km south
 Ans.
Question 11.
 Solution:
 Total amount of pencils purchased = Rs. 30 + Rs. 25
 = Rs 55
 Total amount of pens purchased = Rs. 90
 Total cost price = Rs. 55 + Rs. 90
 = Rs. 145
 Total sale price of pencils and pens = Rs 20 + Rs. 70
 = Rs. 90
 Loss = cost price – selling price
 = Rs. 145 – Rs. 90
 = Rs. 55 Ans.
Question 12.
 Solution:
 (i) True.
 (ii) False : As if positive integer is greater then it will be positive.
 (iii) True : As ( – a + a = 0).
 (iv) False : As the sum of three integers can be zero or non-zero.
 (v) False : As | – 5 | = 5 and | – 3 | = 3 and 5 ≮ 3.
 (vi) False : | 8 – 5 | = | 3 | = 3 and | 8 | + | – 5 | = 8 + 5 = 13.
Question 13.
 Solution:
 (i) a + 6 = 0
 Subtracting 6 from both sides,
 a + 6 – 6 = 0 – 6
 => a = – 6
 a = – 6.
 (ii) 5 + a = 0
 Subtracting 5 from both sides,
 5 + a – 5 = 0 – 5
 => a = – 5
 a = – 5
 (iii) a + ( – 4) = 0
 Adding 4 to both sides,
 a + ( – 4) + 4 = 0 + 4
 => a = 4
 a = 4
 (iv) – 8 + a = 0
 Adding 8 to both sides,
 – 8 + a + 8 = 0 + 8
 => a – 8
 a = 8 Ans.
Hope given RS Aggarwal Solutions Class 6 Chapter 4 Integers Ex 4B are helpful to complete your math homework.
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