Question

va rog frumos repede dau coroana!!
la exercitiul 7 doar b și c!​

Answer 1

$\displaystyle b)~ \frac{\Bigg(\cfrac{^{3)}11}{24}+\cfrac{^{2)}11}{36}\Bigg):\cfrac{11}{6}}{\Bigg(\cfrac{^{3)}11}{6}-\cfrac{^{2)}5}{9} \Bigg):\cfrac{23}{5} } =\frac{\cfrac{33+22}{72} :\cfrac{11}{6} }{\cfrac{33-10}{18} :\cfrac{23}{5} } =\frac{\cfrac{55}{72} \cdot \cfrac{6}{11} }{\cfrac{23}{18}\cdot \cfrac{5}{23} } =\frac{\cfrac{5}{12} }{\cfrac{5}{18} }=\frac{5}{12}\cdot \frac{18}{5} =\frac{18}{12} ^{(6}=\frac{3}{2}$

$\displaystyle c)~\frac{\Bigg(3\cfrac{1}{4}+2\cfrac{1}{6}\Bigg):\cfrac{5}{6}}{\Bigg(2\cfrac{5}{8}-1\cfrac{3}{4}\Bigg) \cdot \cfrac{13}{7} } =\frac{\Bigg(\cfrac{3\cdot 4+1}{4}+\cfrac{2\cdot 6+1}{6}\Bigg):\cfrac{5}{6}}{\Bigg(\cfrac{2\cdot 8+5}{8} -\cfrac{1\cdot4+3}{4}\Bigg) \cdot \cfrac{13}{7} } =\frac{\Bigg(\cfrac{^{3)}13}{4} +\cfrac{^{2)}13}{6} \Bigg):\cfrac{5}{6} }{\Bigg(\cfrac{^{2)}21}{8}-\cfrac{^{4)}7}{4} \Bigg)\cdot \cfrac{13}{7} } =$

$\displaystyle =\frac{\cfrac{39+26}{12} :\cfrac{5}{6} }{\cfrac{42-28}{16} \cdot \cfrac{13}{7} } =\frac{\cfrac{65}{12}\cdot \cfrac{6}{5} }{\cfrac{14}{16} \cdot \cfrac{13}{7} } =\frac{\cfrac{13}{2} }{\cfrac{2}{16}\cdot 13 } =\frac{\cfrac{13}{2} }{\cfrac{26}{16} } =\frac{13}{2} \cdot \frac{16}{26} =\frac{8}{2} =4$

$\displaystyle 8)~~\Bigg[\Bigg(\frac{^{6)}1}{15} -\frac{^{5)}1}{18} \Bigg):\frac{1}{45} +\frac{1}{60}:\Bigg(\frac{^{5)}1}{12}-\frac{^{4)}1}{15}\Bigg)\Bigg]:1\frac{1}{2} = \\\\\\=\Bigg(\frac{6-5}{90} :\frac{1}{45} +\frac{1}{60} :\frac{5-4}{60} \Bigg):\frac{1\cdot 2+1}{2} =\Bigg(\frac{1}{90} \cdot 45+\frac{1}{60} \cdot 60\Bigg):\frac{3}{2} =\\\\\\=\Bigg(\frac{1}{2} +^{2)}1\Bigg):\frac{3}{2} =\frac{1+2}{2} :\frac{3}{2} =\frac{3}{2} \cdot \frac{2}{3} =1 \in \mathbb{N}$