Page No.5.17, Negative Numbers And Integers, Class 6, Maths RD Sharma Solutions | RD Sharma Solutions for Class 6 Mathematics PDF Download

PAGE NO 5.17:

Question 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

ANSWER:

(i) −27 − (−23)
= −27 + 23
= −4
(ii) −17 −18 − (−35)
= −17 − 18 + 35
= −35 + 35
= 0
(iii) −12 − (−5) − (−125) + 270
= −12 + (5 + 125 + 270)
= −12 + 400
= 388
(iv) 373 + (−245) + (−373) + 145 + 3000
= 373 − 245 − 373 + (145 + 3000)
= 128 − 373 + 3145
= −245 + 3145
= 2900
(v) 1 + (−475) + (−475) + (−475) + (−475) + 1900
= 1 (−475 − 475 − 475 − 475 ) + 1900
= 1 − 1900 + 1900
= 1
(vi) (−1) + (−304) + 304 + 304 + (−304) + 1
= −1 + (−304 + 304) + ( 304 − 304) + 1
= −1 + 0 + 0 + 1
= 0

Question 3 : Subtract the sum of −5020 and 2320 from −709.
ANSWER: We have to subtract the sum of −5020 and 2320 from −709.

Sum:

−5020 + 2320 = −2700

Now,

−709 − (−2700) = −709 + 2700 = 1991

Question 4: Subtract the sum of −1250 and 1138 from the sum of 1136 and −1272.

ANSWER: Sum of −1250 and 1138 = (−1250) + 1138 = −112

Sum of 1136 and −1272 = 1136 + (−1272) = −136

Now,

−136 − (−112) = −136 + 112 = −24

Question 5:From the sum of 233 and −147, subtract −284.

ANSWER: We have to subtract −284 from the sum of 233 and −147.

Sum of 233 and (−147) = 233 + (−147) = 233 − 147 = 86

Now, we will subtract −284 from 86.

86 − (−284) = 86 + 284 = 370

Question 6: The sum of two integers is 238. If one of the integers is −122, determine the other.

ANSWER: Let x and y be two integers such that x + y =  238.

Given: x = −122

Now,

x + y = 238

⇒ −122 + y = 238

⇒  y = 238 + 122 = 360

So, the other integer is 360.

Question 7: The sum of two integers is −233. If one of the integers is 172, find the other.
ANSWER: Let  x and y be two integers such that x + y = −223.

Given: x = 172

Now,

x + y = −223

⇒ 172 + y = −223

⇒ y = −223 − 172

⇒ y = −395

Question 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

ANSWER:

(i) −8 − 24 + 31 − 26 − 28 + 7 + 19 − 18 − 8 + 33
  = (−8 − 24) + (31 − 26) + (−28 + 7) + (19 − 18) + (−8 + 33)
  = (−32 + 5 − 21) + (1 + 25)
  = −48 + 26
  = −22

(ii) −26 − 20 + 33 − (−33) + 21 + 24 − (−25) − 26 − 14 − 34
    = (−26 − 20) + (33 + 33) + (21 + 24) + (25 − 26) + (−14 − 34)
    = (−46 + 66) + (45 − 1 − 48)
    = 20 − 4
    = 16