Question

1.transformand mai intai fractiile zecimale in fractii ordinare efectuati
a)0,02+0,(02)=
b)3,1+3,(1)=
c)2,(3)+1,(2)=
d)0,(14)+0,(41)=
e)0,(1)+0,(12)+0,(123)=
f)2,1(2)-1,2(1)=
g)2,0(1)+2,01(12)-1,2(102)=
h)1,1+1,(1)-1,1(1)=
i)1,2(3)+2,02(03)-3,1(012)=
j)0,(3)×1,2:2,1(6)=
k)2,(2):2,2×2,2(2)=
l)1,(5)+1,5-1,5(1):1,1(5)=
DAU COROANA!!!

Answer 1

a)0,02+0,(02)= 
=2/100+2/99 = 1/50+2/99=(99+100)/4950=199/4950

b)3,1+3,(1)= =31/10+(31-3)/9= 31/10+28/9=(279+280)/90=559/90

c)2,(3)+1,(2)=(23-2)/9+(12-1)/9=21/9+11/9=32/9

d)0,(14)+0,(41)=14/99+41/99=55/99=5/9

e)0,(1)+0,(12)+0,(123)=1/9+12/99+123/999=
=1/9+4/33+41/333=(407+444+451)/3663=1302/3663

f) 2,1(2)-1,2(1)=
=(212-21)/90-(121-12)/90=191/90-109/90=82/90=41/45

g)2,0(1)+2,01(12)-1,2(102)=
=(201-20)/90+(20112-201)/9900-(12102-12)/9990=
=181/90+19911/9900-12090/9990=
=181/90+6637/3300-4030/3330=
=(736670+736707-443300)/366300=
=1030077/366300
h)1,1+1,(1)-1,1(1)=
=11/10+(11-1)/9-(111-11)/90=
=11/10+10/9-100/90=
=11/10+10/9-10/9=11/10

i)1,2(3)+2,02(03)-3,1(012)=
=(23-2)/9+(20203-202)/9900-(31012-31)/9990=
=21/9+20001/9900-30981/9990=
=7/3+6667/3300-10327/3330=
=(854700+740037-1135970)/366300=
=458767/366300


j)0,(3)×1,2:2,1(6)=
=3/9 x 12/10 : (216-21)/90=
=1/3 x 12/10 x90/195 =
=36/195
k)2,(2):2,2×2,2(2)=
=(22-2)/9 : 22/10 x (222-22)/90=
=20/9 x10/22 x200/90=
=200/198 x20/9=4000/1782 =2000/891

l)1,(5)+1,5-1,5(1):1,1(5)=
=(15-1)/9+15/10-(151-15)/90 : (115-11)/90=
=14/9+3/2-136/90 x 90/104 =
=14/9+3/2-136/104=
=14/9+3/2-17/13=
=(364+351-306)/234=
=409/234