Question

Решите пример по действиям

Answer 1

$\displaystyle\bf\\1)\\\\0,5+\frac{1}{4} +0,1666...+0,125=\frac{1}{2} +\frac{1}{4} +0,1(6)+\frac{1}{8}=\frac{4+2+1}{8}+\frac{16-1}{90} =\\\\\\=\frac{7}{8} +\frac{15}{90} =\frac{7}{8} +\frac{1}{6} =\frac{7\cdot 3+4}{24}=\frac{25}{24} =1\frac{1}{24} \\\\\\2)\\\\0,(1)+0,4+\frac{14}{15} =\frac{1}{9} +\frac{2}{5} +\frac{14}{15} =\frac{5+2\cdot 9+14\cdot3}{45} =\frac{5+18+42}{45}=\\\\\\=\frac{65}{45} =\frac{13}{9} =1\frac{4}{9}$

$\displaystyle\bf\\3)\\\\1\frac{1}{24} :1\frac{4}{9} =\frac{25}{24} :\frac{13}{9} =\frac{25}{24} \cdot\frac{9}{13} =\frac{25\cdot 3}{8\cdot 13} =\frac{75}{104} \\\\\\4)\\\\0,1(6)+0,(3)=\frac{16-1}{90} +\frac{3}{9} =\frac{15}{90} +\frac{1}{3}=\frac{1}{6} +\frac{1}{3} =\frac{1+2}{6} =\frac{3}{6} =\frac{1}{2} \\\\\\5)\\\\0,(3)+1,1(6)=\frac{3}{9} +1\frac{16-1}{90} =\frac{1}{3} +1\frac{15}{90}=\frac{1}{3} +1\frac{1}{6} =\frac{2}{6} +1\frac{1}{6} =\\\\\\=1\frac{3}{6} =1\frac{1}{2}$

$\displaystyle\bf\\6)\\\\\frac{1}{2} :1\frac{1}{2} =\frac{1}{2}:\frac{3}{2} =\frac{1}{2}\cdot\frac{2}{3} =\frac{1}{3} \\\\\\7)\\\\\frac{75}{104} +\frac{1}{3} =\frac{75\cdot3+104}{104\cdot 3} =\frac{329}{312} =1\frac{17}{312}$