[tex]\boxed{\bold{1.}} \\ \bold{a)} \ \frac{x}{2} = \frac{y}{4} =\frac{z}{8}; \ Presupunem \ ca \ x=5, \ atunci \ y=\frac{5 \cdot 4}{2}=\frac{20}{2}=10; \\ y=10; \ z=\frac{10 \cdot 8}{4}=\frac{80}{4}=20; \ Deci, \boxed{\bold{\frac{5}{2}=\frac{10}{4}=\frac{20}{8}}}; \\ \bold{b)} \ Exact \ acelasi \ lucru \ faci \ si \ aici, \ doar \ ca \ alte \ cifre, \ care \\ se \ potrivesc \ si \ in \ rezultat \ se \ obtine \ o \ proportionalitate;[/tex]
[tex]\bold{c)} \ \frac{x}{0,(3)}=\frac{y}{0,5}=\frac{z}{4}; \ Presupunem \ ca \ x=6, \ atunci \ \frac{6}{0,(3)}=18; \\ Atunci \ y= \frac{6 \cdot 0,5}{0,(3)} = \frac{3}{0,(3)} =9; \ z=\frac{9 \cdot 4 }{0,5}=\frac{36}{0,5}=72; \\ \boxed{\bold{2.}} \ \bold{a)} \ \frac{3}{x}= \frac{8}{y} =\frac{9}{12} ; \ x=\frac{3 \cdot 12}{9}=4; \ y=\frac{12 \cdot 8}{9}=10,(6); \\ \bold{b)} \ \frac{5}{8} = \frac{x}{4} = \frac{y}{10} = \frac{0,5}{z} ; \ x=\frac{5 \cdot 4}{8}=2,5; \ y=\frac{2,5 \cdot 10}{4}=6,25; [/tex]
[tex]\\ z=\frac{10 \cdot 0,5}{6,25} =\frac{5}{6,25}=0,8; \\ \bold{c)} \ \frac{0,(4)}{x} = \frac{y}{1,5} = \frac{0,1(2)}{z} = \frac{8}{3} ; \
\ x=\frac{0,(4) \cdot 3}{8}=0,1(6); \\ y=\frac{1,5 \cdot 8}{3}=\frac{12}{3}=4; \ z=\frac{3 \cdot 0,1(2)}{8}=0,0458(3).[/tex]
