Punctul a)
[tex]\displaystyle{ 1 + \frac{1}{1 +\frac{2}{3}}+\frac{12}{25} : 2\frac{4}{5} = }[/tex]
[tex]\displaystyle{ = 1 + \frac{1}{\frac{3}{3} +\frac{2}{3}}+\frac{12}{25} : \frac{14}{5} }[/tex]
[tex]\displaystyle{ = 1 + \frac{1}{\frac{5}{3}}+\frac{12}{25} \cdot \frac{5}{14} }[/tex]
[tex]\displaystyle{ = 1 + \frac{1}{1} : \frac{5}{3} + \frac{ 60 }{350} }[/tex]
[tex]\displaystyle{ =1 + \frac{1}{1} \cdot \frac{3}{5} + \frac{6}{35} }[/tex]
[tex]\displaystyle{ = 1 + \frac{3}{5}+ \frac{6}{35} }[/tex]
[tex]\displaystyle{ = 1 + \frac{21}{35} + \frac{6}{35} }[/tex]
[tex]\displaystyle{ = 1 + \frac{27}{35} }[/tex]
[tex]\displaystyle{ =\frac{35}{35}+\frac{27}{35}}[/tex]
[tex]\boxed{=\frac{62}{35}}[/tex]
Punctul b)
[tex]\displaystyle{ \frac{ 2\frac{1}{3}+\frac{5}{2} : (3 + \frac{7}{20} \cdot \frac{10}{3})}{16: 1\frac{1}{5}+1\frac{1}{4}} = }[/tex]
[tex]\displaystyle{ =\frac{\frac{7}{3}+\frac{5}{2} : (3+\frac{70}{60})}{16:\frac{6}{5}+\frac{5}{4}} }[/tex]
[tex]\displaystyle{ =\frac{\frac{7}{3} + \frac{5}{2}:(\frac{3}{1}+\frac{7}{6})}{\frac{16}{1} :\frac{6}{5}+\frac{5}{4}} }[/tex]
[tex]\displaystyle{=\frac{\frac{7}{3} +\frac{5}{2}:(\frac{18}{6}+\frac{7}{6})}{\frac{16}{1} \cdot \frac{5}{6} + \frac{5}{4}} }[/tex]
[tex]\displaystyle{ =\frac{\frac{7}{3}+\frac{5}{2} : \frac{25}{6}}{\frac{80}{6}+\frac{5}{4}} }[/tex]
[tex]\displaystyle{ =\frac{\frac{7}{3} + \frac{5}{2} \cdot \frac{6}{25}}{\frac{40}{3}+\frac{5}{4}} }[/tex]
[tex]\displaystyle{ =\frac{\frac{7}{3}+\frac{30}{50}}{\frac{160}{12}+\frac{15}{12}} }[/tex]
[tex]\displaystyle{ =\frac{\frac{7}{3}+\frac{3}{5}}{\frac{175}{12}} }[/tex]
[tex]\displaystyle{ =\frac{\frac{35}{15}+\frac{9}{15}}{\frac{175}{12}} }[/tex]
[tex]\displaystyle{ =\frac{44}{15} : \frac{175}{12} }[/tex]
[tex]\displaystyle{ =\frac{44}{15} \cdot \frac{12}{175} }[/tex]
[tex]\displaystyle{ =\frac{528}{2625} }[/tex]
[tex]\boxed{=\frac{176}{875}}[/tex]
- Lumberjack25
