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# Chapter 5: Negative Numbers and Integers – Exercise 5.4

## Negative Numbers and Integers – Exercise – 5.4 – Q.1

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

## Negative Numbers and Integers – Exercise – 5.4 – Q.2

Ans.

(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

## Negative Numbers and Integers – Exercise – 5.4 – Q.3

Ans.

The sum of 5020 and 2320 is – 5020 + 2320

= 2320 – 5020

= – 2700.

⟹ – ( – 2700) + ( – 709) = – 709 – (– 2700)

= – 709 + 2700

= 1991

## Negative Numbers and Integers – Exercise – 5.4 – Q.4

Ans.

sum of -1250 and 1138 = - 1250 + 1138

= 1138 - 1250

= -112

Sum of 1136 and -1272 = 1136 - 1272

= – 136

⟹ – 136 - (-112) = -136 + 112

= – 24

## Negative Numbers and Integers – Exercise – 5.4 – Q.5

Ans.

Sum of 233 and -147 = 233 -147

= 86.

⟹ 86 – (– 284) = 86 + 284

= 370.

## Negative Numbers and Integers – Exercise – 5.4 – Q.6

Ans.

Given that,

Sum of two integer's = 238.

one of the integer = -122

Required integer = -(-122) + 238

= 238 + 122

360.

## Negative Numbers and Integers – Exercise – 5.4 – Q.7

Ans.

Required integer = -223 - 172

= - 395.

## Negative Numbers and Integers – Exercise – 5.4 – Q.8

Ans.

(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.

## Negative Numbers and Integers – Exercise – 5.4 – Q.9

Ans.

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

## Negative Numbers and Integers – Exercise – 5.4 – Q.10

Ans.

(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

= 0

(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.