1. [tex] \frac{a}{b}= \frac{15}{90} = \frac{1}{6} => \frac{5a}{b}= \frac{5}{6}=> \frac{5a+b}{b} = \frac{11}{6}; [/tex]
[tex] \frac{a}{b} = \frac{1}{6} => \frac{8a}{4b}= \frac{8}{24}= \frac{1}{3}=> \frac{8a-4b}{4b}= \frac{-2}{3} => \frac{8a-4b}{b} = \frac{-8}{3} [/tex]
Din cele doua fractii rezulta:
[tex] \frac{5a+b}{8a-4b} = \frac{ \frac{11}{6}}{ \frac{-8}{3}}=- \frac{11}{6}* \frac{3}{8} =- \frac{11}{16} [/tex]
2. In numerele de la 1 la 45 cifra 3 apare in 14 dintre ele: 3, 13, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43. Probabilitatea ca o bila extrasa sa contina cifra 3 este [tex] \frac{14}{45} [/tex].
3. a) scara 1:42 ⇒ D=4,7·42 cm
b) d/D=1/500 ⇒ d/12m=1/500 ⇒ d=1200cm/500=2,4 cm
c) l/L=1,2 cm/6m=1,2cm/600cm ⇒ scara desenului este 0,002=1:500;
l O2/L O2=1,6cm/L O2=1/500 ⇒ L O2 =500·1,6cm=800cm=8m