Question

172 5/6 - 170 1/3 + 3 5/12 / 0,8 • 0,25

Answer 1

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1.

$\bf \displaystyle 172\dfrac{5}{6}-170\dfrac{1}{3}+\dfrac{3\dfrac{5}{12}}{0,8}\,\cdot 0,25=3\dfrac{109}{192}\\\\\\1)\ \ 172\dfrac{5}{6}-170\dfrac{1}{3}=172\frac{5}{6}-170\frac{2}{6}=\Big(172-170\Big)+\Big(\frac{5}{6}-\frac{2}{6}\Big)=\\\\\\=2+\frac{5-2}{6}=2+\frac{3}{6}=2\frac{1}{2}=\frac{5}{2}$

$\bf \displaystyle 2)\ \ \frac{3\dfrac{5}{12}}{0,8}\cdot 0,25=\frac{\dfrac{41}{12}}{\dfrac{8}{10}}\cdot \frac{25}{100}=\frac{41\cdot 10}{12\cdot 8}\cdot \frac{1}{4}=\frac{41\cdot 5}{12\cdot 4}\cdot \frac{1}{4}=\frac{205}{192}=1\frac{13}{192}$        

$\bf 3)\ \ \dfrac{5}{2}+\dfrac{205}{192}=\dfrac{5\cdot 96+205}{192}=\dfrac{685}{192}=3\dfrac{109}{192}$                        

Или  2.

$\bf \displaystyle \dfrac{172\dfrac{5}{6}-170\dfrac{1}{3}+3\dfrac{5}{12}}{0,8\cdot 0,25}=29\frac{7}{12}\\\\\\1)\ \ 172\dfrac{5}{6}-170\dfrac{1}{3}+3\dfrac{5}{12}}=172\frac{10}{12}-170\frac{4}{12}+3\frac{5}{12}=\\\\\\=\Big(172-170+3\Big)+\Big(\frac{10}{12}-\frac{4}{12}+\frac{5}{12}\Big)=5+\frac{10-4+5}{12}=5+\frac{11}{12}=5\frac{11}{12}$  

$\bf \displaystyle 2)\ \ 0,8\cdot 0,25=\frac{8}{10}\cdot \frac{25}{100}=\frac{4}{5}\cdot \frac{1}{4}=\frac{1}{5}$  

$\bf \displaystyle 3)\ \ 5\frac{11}{12}\ :\ \frac{1}{5}=\frac{5\cdot 12+11}{12}\ :\ \frac{1}{5}=\frac{71}{12}\cdot \frac{5}{1}=\frac{355}{12}=29\frac{7}{12}$      

Или  3.

$\bf \displaystyle \Big(\dfrac{172\dfrac{5}{6}-170\dfrac{1}{3}+3\dfrac{5}{12}}{0,8}\, \Big)\cdot 0,25}=1\frac{11}{60}\\\\\\1)\ \ 172\dfrac{5}{6}-170\dfrac{1}{3}+3\dfrac{5}{12}}=172\frac{10}{12}-170\frac{4}{12}+3\frac{5}{12}=\\\\\\=\Big(172-170+3\Big)+\Big(\frac{10}{12}-\frac{4}{12}+\frac{5}{12}\Big)=5+\frac{10-4+5}{12}=5+\frac{11}{12}=5\frac{11}{12}$  

$\bf \displaystyle 2)\ \ 5\frac{11}{12}\ :\ 0,8=\frac{5\cdot 12+11}{12}\ :\ \frac{8}{10}=\frac{71}{12}\cdot \frac{4}{5}=\frac{71}{3\cdot 5}=\frac{71}{15}=4\frac{11}{15}\\\\\\3)\ \ \frac{71}{15}\cdot 0,25=\frac{71}{15}\cdot \frac{1}{4}=\frac{71}{60}=1\frac{11}{60}$        

Answer 2

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