Question

Ex 11 subpunctul a)......dau coroana

Answer 1

1,1(6)=(116-11)/90=105/90=21/18=7/6
0,5=5/10=1/2
1intreg 1/4=(1x4+1)/4=5/4
0,(6)=6/9=2/3
2 intreg 1/4=(2x4+1)/4=9/4
ex.devine: 7/6-[(1/2-5/4)-(2/3-9/4)]=
7/6-[(2/4-5/4)-(6/4-9/4)]=
7/6-[(-3/4)-(-3/4)]=
7/6-(-3/4+3/4)=7/6-0=7/6=1,1(6)

ex.b
2,08(3)=(2083-208)/900=1875/900=375/180=75/36=25/12
3intreg5/6=23/6
3intreg3/4=15/4
2intreg1/8=17/8
2intreg1/6=13/6
[25/12-23/6]-(15/4-17/8-13/6)=
[(25-23x2)/12]-[(15x6-17x3-13x4)/24]=
[(25-46)/12]-[(90-51-52)/24]=
-21/12-(-13/24)=
-7/4+13/24=
(-7x6+13)/24=
(-42+13)/24=-29/24=-1,208(3)

ex.c
1,0(6)=(106-10)/90=96/90=48/45=16/15
2intreg1/6=13/6
0,(3)=3/9=1/3
7/15-[16/15-13/6-(7/10-1/3)]=
7/15-[16/15-13/6-7/10+1/3]=
7/15-16/15+13/6+7/10-1/3=
-9/15+13/6+7/10-1/3=
(-9x2+13x5+7x3-1x10)/30=
(-18+45+21-10)/30=38/30=19/15=1,2(6)

ex.d
0,(1)=1/9
2,0(6)=(206-20)/90=186/90=93/45=31/15
0,(3)=3/9=1/3
[4/5-1/9]-[31/15-1/3]-(-2/45)=
4/5-1/9-31/15+1/3+2/45=
(4x9-1x5-31x3+1x15+2)/45=
(36-5-93+15+2)/45=-45/45=-1

ex.e
3,25=325/100=65/20=13/4
1,1(6)=(116-11)/90=105/90=21/18=7/6
2,125=2125/1000=425/200=85/40=17/8
3,(25)=(325-3)/99=322/99
00,(14)=14/99
[13/4+7/6-17/8]-[322/99-14/99]=
13/4+7/6-17/8-308/99=
(13x198+7x132-17x99-308/792=
(2574+924-1683-308)/792=1507/792=1,902(7)