6.113 Найдите корень уравнения: a) 4/7 + x = 5/7; б) m ⋅ 2/9 = 5/9; в) 13/15 - z = 7/45; г) n : 3/4 = 8/9

a) \(\frac{4}{7} + x = \frac{5}{7}\)

\[x = \frac{5}{7} - \frac{4}{7} = \frac{5-4}{7} = \frac{1}{7}\]

б) \(m \cdot \frac{2}{9} = \frac{5}{9}\)

\[m = \frac{5}{9} : \frac{2}{9} = \frac{5}{9} \cdot \frac{9}{2} = \frac{5 \cdot 9}{9 \cdot 2} = \frac{5}{2} = 2.5\]

в) \(\frac{13}{15} - z = \frac{7}{45}\)

\[z = \frac{13}{15} - \frac{7}{45} = \frac{13 \cdot 3}{15 \cdot 3} - \frac{7}{45} = \frac{39}{45} - \frac{7}{45} = \frac{39-7}{45} = \frac{32}{45}\]

г) \(n : \frac{3}{4} = \frac{8}{9}\)

\[n = \frac{8}{9} \cdot \frac{3}{4} = \frac{8 \cdot 3}{9 \cdot 4} = \frac{24}{36} = \frac{2}{3}\]

Ответ: a) \(\frac{1}{7}\); б) 2.5; в) \(\frac{32}{45}\); г) \(\frac{2}{3}\)