ML Aggarwal Class 8 Chapter 1 Rational Numbers Exercise 1.2

Exercise 1.2

Question 1

Sol :
(i) 223=2×3+23=83

=223(37)

=83(37)

=83+37

=(8×7)+(3×3)21  LCM of 3,7=21

=56+921

=6521

49(358)

49(298)

49298

4×8(29×9)72 LCM of 9,18=72

29372


(ii) 315(479)

165(439)

165+439

(16×9)+(43×5)45 LCM OF 9,15=45

144+21545

7145


Question 3

Sol :
Let the Unknown number as x.

 511+x=78x=78(511)=78+511    

=(7×11)+(8×5)88 LCM Of 11,8=88

=77+4588

x=3288

x=411


(ii)   let the unknown number as x.  

27+x=35x=35(27)x=35+27=(3×7)+(2×5)35=21+1035x=3135


Question 4

Sol :
Let the Unknown number be x

435x=312

235x=72

235=72+xx=235+72=(23×2)+(7×5)10      LCM OF 5,2=10 

46+3510

x⇒1110


Question 5

Sol :

[57+(83)][52+(1112)]

[(5×3)+(8×7)21][5×6+(11×1)12]

2841338441784=13928=13928


Question 6

Sol :

x=49;y=712

Consider

x-y =  49(712)

=49+712

(4×4)+(7×3)36               (∴LCM OF 9,12= 36)

16+2136

xy=3736

Consider     

y-x = 712(49)

    

71249

(7×3)(4×4)36         LCM of  9, 12=36

211636

y-x ⇒3736

ஃx-y ≠ y-x


Question 7

Sol :

x=49;y=712;z=23

Consider

x(yz)=49(712(23))

=49(712+23)

49((7×1)+(2×4)12)

49(7+812)

49112

(4×4)(1×3)36

=16336

x(yz)  =1336 

       Consider       ( x-y)-z  =[49(712)](23)

=[49+712]+23

=[(4×4)+(7×3)36]+23

=16+2136+23

=3736+23

=(37×1)+(2×12)36

37+2436

(xy)z=6136

x(yz)(xy)z


Question 8

Sol :

(i) ⇒2345

(2×5)(4×3)15     LCM = 3,5 = 15

101215

25   It is a Rational Number

So. given statement is False


(ii)true

57+57=0                              

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