ГДЗ по Математике 6 Класс Номер 855 Мерзляк, Полонский — Подробные Ответы

1. \[
\frac{1}{3}x + \frac{1}{5}x + \frac{1}{6}x = \frac{21}{40}
\]

2. \[
\frac{1}{4}x + \frac{1}{6}x + \frac{1}{8}x = \frac{39}{56}
\]

1)
\[
\frac{1}{3}x + \frac{1}{5}x + \frac{1}{6}x = \frac{21}{40}
\]
\[
\frac{1}{3} \cdot 10x + \frac{1}{5} \cdot 6x + \frac{1}{6} \cdot 5x = \frac{21}{40}
\]
\[
\frac{10}{30}x + \frac{6}{30}x + \frac{5}{30}x = \frac{21}{40}
\]
\[
\frac{21}{30}x = \frac{21}{40}
\]
\[
x = \frac{21}{30} \cdot \frac{40}{21}
\]
\[
x = \frac{(21 \div 21) \cdot (30 \div 10)}{(40 \div 10) \cdot (21 \div 21)} = \frac{3}{4}
\]

2)
\[
\frac{1}{4}x + \frac{1}{6}x + \frac{1}{8}x = \frac{39}{56}
\]
\[
\frac{1}{4} \cdot 6x + \frac{1}{6} \cdot 4x + \frac{1}{8} \cdot 3x = \frac{39}{56}
\]
\[
\frac{6}{24}x + \frac{4}{24}x + \frac{3}{24}x = \frac{39}{56}
\]
\[
\frac{13}{24}x = \frac{39}{56}
\]
\[
x = \frac{39}{56} \cdot \frac{24}{13}
\]
\[
x = \frac{(39 \div 13) \cdot (24 \div 8)}{(56 \div 8) \cdot (13 \div 13)}
\]
\[
x = \frac{3 \cdot 3}{7} = 1 \frac{2}{7}
\]