Question

Calculati:
a) 0,(3)+1,(6)+5,1 (3)+1/2
b) 3/11+0,(1)+0,2 (32)
c) 1, (18)+0,41 (6)+0,25
d)1,1 (2)+2,2 (3)+3,3 (4)

Answer 1

a) 0,(3)+1,(6)+5,1(3)+1/2=1/3+5/3+77/15+1/2=(10+50+154+15)/15=
=229/30=7,6(3)
0,(3)=3/9=1/3
1,(6)=(16-1)/9=15/9=5/3
5,1(3)=(513-51)/90=462/90=77/15

b) 3/11+0,(1)+0,2 (32)=3/11+1/9+23/99=(27+11+23)/99=61/99=0,(61)
0,(1)=1/9
0,2 (32)=(232-2)/990=230/990=23/99


c) 1,(18)+0,41(6)+0,25=13/11+5/12+1/4=(156+55+33)/132=244/132=61/33=
=1,(84)
1,(18)=(118-1)/99=117/99=13/11
0,41(6)=(416-41)/900=375/900=5/12

d)1,1(2)+2,2(3)+3,3(4)=101/90+201/90+301/90=603/90=67/10=6,7
1,1(2)=(112-11)/90=101/90
2,2(3)=(223-22)/90=201/90
3,3(4)=(334-33)/90=301/90