Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 172

а) $$ \frac{2}{\frac{1}{3}+\frac{1}{5}}=\frac{2}{\frac{1 \cdot 5}{3 \cdot 5}+\frac{1 \cdot 3}{5 \cdot 3}}=\frac{2}{\frac{5}{15}+\frac{3}{15}}=\frac{2}{\frac{5+3}{15}}=\frac{2}{\frac{8}{15}} $$ = 2 : 8/15 = 2/1 ⋅ 15/8 = 30/8 = 30 : 2/8 : 2 = 15/4 = 3,75
б) $$ \frac{3}{\frac{1}{2}+\frac{1}{4}+\frac{1}{8}}=\frac{3}{\frac{1 \cdot 4}{2 \cdot 4}+\frac{1 \cdot 2}{4 \cdot 2}+\frac{1}{8}}=\frac{3}{\frac{4}{8}+\frac{2}{8}+\frac{1}{8}}=\frac{3}{\frac{4+2+1}{8}}=\frac{3}{\frac{7}{8}} $$ = 3 : 7/8 = 3/1 ⋅ 8/7 = 24/7 = 33/7
в) $$ \frac{4}{\frac{1}{5}+\frac{1}{10}+\frac{1}{15}+\frac{1}{20}}=\frac{4}{\frac{1 \cdot 12}{5 \cdot 12}+\frac{1 \cdot 6}{10 \cdot 6}+\frac{1 \cdot 4}{15 \cdot 4}+\frac{1 \cdot 3}{20 \cdot 3}}=\frac{4}{\frac{12}{60}+\frac{6}{60}+\frac{4}{60}+\frac{3}{60}}=\frac{4}{\frac{12+6+4+3}{60}}= $$ $$ \frac{\frac{4}{25}}{\frac{60}{60}} $$ = 4 : 25/60 = 4/1 ⋅ 60/25 = 4/1 ⋅ 60 : 5/25 : 5 = 48/5 = 9,6