Question

Va roooggg

Calculeaza

a) 1,(6) + 0,(12)
b) 10,05 + 1,(1)
c) 4,75 - 1,(05) - 1,3
d) 7 - 3,(17)

Answer 1

a) (16-1)/9+12/99=15/9+12/99=(15*11+12)/99=(165+12)/99=177/99=1,(78)

b) 1005/100+10/9=(9045+1000)/900=11,16(1)

c) 475/100-(105-1)/99-13/10=(47025-10400-12870)/9900=23755/990=2,3(98)

d) 7-(317-3)/99=7-314/99=(693-314)/99=379/99=3,(82)

Answer 2

a )

1,(6) + 0,(12) = ( 16 - 1) / 9 + 12 / 99 = 15 / 9 + 4 / 33 =

= 5 / 3 + 4 /33 = 55 / 33 + 4 / 33 =

= 59 / 33 = 1,(78)

______________________

b )

10,05 + 1,(1) = 1005 / 100 + ( 11 - 1) / 9 = 201 / 20 + 10 / 9 =

= ( 9 x 201 ) / 180 + ( 20 x 10 ) / 180 =

= 1 809 / 180 + 200 / 180 =

= 2 009 / 180 =

= 11,16(1)

_______________

c)

4,75 - 1,(05) - 1,3= 475 / 100 - ( 105 - 1) / 99 - 13 / 10 =

= 95/ 20 - 104 / 99 - 13 / 10 =

= 19 / 4 - 104 / 99 - 13 / 10 =

cmmmc al numitorilor ( 4; 10 si 99 ) = 4 x 5 x 99 = 1980

= ( 19 x 495 ) / 1 980 - ( 20 x 104 )/ 1980 - ( 13 x 198 ) / 1 980 =

= 9 405 / 1980 - 2 080 / 1 980 - 2 574 / 1980 =

= 4 751 / 1980 = 2,399(49)

_________________________

d)

7 - 3,(17 ) = 7 - ( 317 - 3 ) / 99 = ( 7 x 99 - 314 ) / 99 =

= ( 693 - 314 ) / 99 =

= 379 / 99 = 3,(82)