Question

[0.(5) +1,(75) + 0,3(6)] : (1 + 2 5 + 109 + 0,19(60)
_ _ _
4 13 156

Answer 1

0,(5)=5/9
1,(75)=(175-1)/99=174/99=58/33
0,3(6)=(36-3)/90=33/90=11/30
0,19(60)=(1960-19)/9900=1941/9900=647/3300

[0.(5) +1,(75) + 0,3(6)] : [(1/4 + 2 5/13 + 109/156 + 0,19(60)]=(5/9+58/33+11/30):(1/4+25/13+109/156+647/3300)=
[(5·110+58·30+11·33)/990]:[(1·10725+25·3300+109·275+647·13)/42900]=
[(550+1740+363)/990]:(10725+82500+29975+8411)/42900]=
2653/990:131611/42900=
2653/990·42900/131611= se simplifica tot ce se poate=prima data se taie 0=
2653/99x42900/131611= se simplifica cu 3=
2653/33x1430/131611=se simplifica cu 11=
2653/3·130/131611=344890/394833=