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Ans.
(i) Using the rule for sub traction, we have – 5 –12 = – 17.
(ii) In order to subtract -12 from 8, 8 – ( –12) = 8 + 12 = 20.
(iii) -135 – ( – 225) = 225 –135 = 90
(iv) 101 – 1001 = – 900
(v) 3126 – ( – 812)6 = 3126 + 812 = 3938.
(vi) – 8-7560 = – 7568
(vii) – 4109 – ( – 3978) = – 4109 + 3978 = – 131
(viii) –1005 – 0 = –1005
(i) – 27 – ( – 23) = – 27 + 12
= 23 – 27
= – 4
(ii) – 17 –18 – ( – 35) = – 35 + 35
= 0
(iii) –12 – (– 5) – (– 125) + 270 = – 12 + 5 + 125 + 270
= 400 – 12
= 388.
(iv) 373 + ( – 245) + (– 373) + 145 + 3000 = 373 - 245 - 373 + 3145
= 3145 + 373 - 373 - 245
= 3145 - 245
= 2900.
(v) 1 - 475 - 475 - 475 + 1900 = 1 - 950 - 950 + 1900
= 1900 + 1 - 1900 = 1.
(vi) (-1) + (– 304) + 304 + 304 + (– 304) + 1 = -1 + 1 - 304 + 304 - 304 + 304 = 0
The sum of 5020 and 2320 is – 5020 + 2320
= 2320 – 5020
= – 2700.
⟹ – ( – 2700) + ( – 709) = – 709 – (– 2700)
= – 709 + 2700
= 1991
sum of -1250 and 1138 = - 1250 + 1138
= 1138 - 1250
= -112
Sum of 1136 and -1272 = 1136 - 1272
= – 136
⟹ – 136 - (-112) = -136 + 112
= – 24
Sum of 233 and -147 = 233 -147
= 86.
⟹ 86 – (– 284) = 86 + 284
= 370.
Given that,
Sum of two integer's = 238.
one of the integer = -122
Required integer = -(-122) + 238
= 238 + 122
360.
Required integer = -223 - 172
= - 395.
(i) – 8 - 24 + 31- 26 - 28 + 7 + 19 - 18 - 8 + 33
= – 8 -24 - 26 - 28 - 18-8 + 31+ 7 + 19 + 33
= – 32 - 26 - 28 - 26 + 38 + 19 + 33
= 38 - 32 - 26 - 28 + 33 - 26 + 19.
= 6 - 26 - 28 + 7 + 19
= 6 - 28 - 26 + 26
= 6 - 28
= -22.
(ii) – 26 - 20 + 33 - (-33) + 21 + 24 - (-25) - 26 - 14 - 34
= - 46 + 33 + 33 + 21 + 24 + 25 - 26 - 14 - 34
= - 46 + 66 + 21 + 24 + 25+ -74
= – 46 + 66 + 70 - 74
= – 46 - 4 + 66
= – 50 + 66
= 66 - 50
= 16.
1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10 + 11 - 12 + 13 - 14 + 15 - 16 = -1 -1 -1 -1 -1 -1 -1 -1
= – 8
(i) If the number of term is 10
5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5)
= 5 - 5 + 5 - 5 + 5 - 5 + 5 -5
(ii) If the number of terms is 11.
5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5) + 5
= 5 - 5 + 5 - 5 + 5 - 5 + 5 -5 + 5 - 5 + 5
= 5.
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Chapter 5: Negative Numbers and Integers –...