Question

aratati ca rezultatul calculului ( aveti poza ) este nr natural .

Answer 1

   
[tex]\displaystyle\\ \left[\left(\frac{1}{15}-\frac{1}{18}\right):\frac{1}{45}+\frac{1}{60}:\left(\frac{1}{12}-\frac{1}{15}\right)\right]:1\frac{1}{2}=\\\\\\ =\left[\left(\frac{1\times 6}{15\times 6}-\frac{1\times 5}{18\times 5}\right):\frac{1}{45}+\frac{1}{60}:\left(\frac{1\times 5}{12\times 5}-\frac{1\times 4}{15\times 4}\right)\right]:1\frac{1}{2}= [/tex]

[tex]\displaystyle\\ =\left[\left(\frac{6}{90}-\frac{5}{90}\right):\frac{1}{45}+\frac{1}{60}:\left(\frac{5}{60}-\frac{4}{60}\right)\right]:1\frac{1}{2}=\\\\\\ =\left[\frac{1}{90}:\frac{1}{45}+\frac{1}{60}:\frac{1}{60}\right]:1\frac{1}{2}=\\\\\\ =\left[\frac{1}{90}\times\frac{45}{1}+\frac{1}{60}\times\frac{60}{1}\right]:1\frac{1}{2}=\\\\\\ =\left[\frac{45}{90}+\frac{60}{60}\right]:1\frac{1}{2}=\\\\\\ =\left[\frac{1}{2}+1\right]:1\frac{1}{2}=[/tex]

[tex]\displaystyle\\ =\frac{1\times 2 +1}{2} : \frac{1\times 2 +1}{2} = \frac{3}{2}:\frac{3}{2} =\frac{3}{2}\times \frac{2}{3} = \frac{3\times 2}{2\times 3}=\frac{6}{6}=\boxed{\bf 1 \in N}[/tex]