Răspuns :
Răspuns:
Explicație pas cu pas:
a)
[tex] \frac{ {}^{4)} 5}{12} = \frac{20}{48} \\ [/tex]
[tex] \frac{ {}^{3)} 7}{16} = \frac{21}{48} \\ [/tex]
[tex] \frac{20}{48} < \frac{21}{48}\Longrightarrow \frac{5}{12} < \frac{7}{16} \\ [/tex]
b)
[tex] \frac{ {}^{11)} 5}{13} = \frac{55}{143} \\ [/tex]
[tex] \frac{ {}^{13)} 7}{11} = \frac{91}{143} \\ [/tex]
[tex] \frac{55}{143} < \frac{91}{143} \Longrightarrow \frac{5}{13} < \frac{7}{11} \\ [/tex]
c)
[tex] \frac{ {}^{17)} 11}{13} = \frac{187}{221} \\ [/tex]
[tex] \frac{ {}^{13)} 16}{17} = \frac{208}{221} \\ [/tex]
[tex] \frac{187}{221} < \frac{208}{221} \Longrightarrow \frac{11}{13} < \frac{16}{17} \\ [/tex]
d)
[tex] \frac{ {}^{2018)} 2016}{2017} = \frac{4068288}{4070306} \\ [/tex]
[tex] \frac{ {}^{2017)} 2017}{2018} = \frac{4068289}{4070306} \\ [/tex]
[tex] \frac{406828}{4070306} < \frac{4068289}{4070306} \Longrightarrow \frac{2016}{2017} < \frac{2017}{2018} \\ [/tex]
e)
[tex]\frac{ 1 }{2^{2} \times 3 } = \frac{1}{4 \times 3} =\frac{1}{12} \\[/tex]
[tex]\frac{1}{3 \times 5^{2} } =\frac{1}{3 \times 25} =\frac{1}{75} \\[/tex]
[tex] \frac{ {}^{25)} 1}{12} = \frac{25}{300} \\ [/tex]
[tex] \frac{ {}^{4)} 1}{75} = \frac{4}{300} \\ [/tex]
[tex] \frac{25}{300} > \frac{4}{300} \Longrightarrow \frac{1}{ {2}^{2} \times 3 } > \frac{1}{3 \times 5 {}^{2} } \\ [/tex]
f)
[tex] \frac{1}{2 {}^{3} \times {3}^{2} \times 5 {}^{1} } = \frac{1}{8 \times 9 \times 5} = \frac{1}{360} \\ [/tex]
[tex] \frac{1}{2 {}^{2} \times {3}^{1} \times {5}^{2} } = \frac{1}{4 \times 3 \times 25} = \frac{1}{300} \\ [/tex]
[tex] \frac{ {}^{5)} 1}{360} = \frac{5}{1800} \\ [/tex]
[tex] \frac{ {}^{6)} 1}{300} = \frac{6}{1800} \\ [/tex]
[tex] \frac{5}{1800} < \frac{6}{1800} \Longrightarrow \frac{1}{ {2}^{3} \times {3}^{2} \times 5 {}^{1} } < \frac{1}{ {2}^{2} \times {3}^{1} \times {5}^{2} } \\ [/tex]