2.53

2.53. Найдите значение выражения

а)
\[ \frac49+\frac79-\frac19=\frac{4+7-1}{9}=\frac{10}{9}=1\frac19. \]

б)
\[ \frac67-\left(\frac57-\frac17\right) =\frac67-\frac47=\frac27. \]

в)
\[ 5\frac{6}{39}+4\frac{7}{78} =5\frac{12}{78}+4\frac{7}{78} =9\frac{19}{78}. \]

г)
\[ 7\frac{13}{15}-3\frac{11}{30} =7\frac{26}{30}-3\frac{11}{30} =4\frac{15}{30}=4\frac12. \]

д)
\[ \frac78\cdot\frac4{35}\cdot\frac{10}{9} =\frac1{10}\cdot\frac{10}{9} =\frac19. \]

е)
\[ \left(\frac12:\frac34-\frac49\right)\cdot\frac53 =\left(\frac23-\frac49\right)\cdot\frac53 =\frac29\cdot\frac53 =\frac{10}{27}. \]

Ответ:
\[ \boxed{\text{а) }1\frac19;\quad \text{б) }\frac27;\quad \text{в) }9\frac{19}{78};\quad \text{г) }4\frac12;\quad \text{д) }\frac19;\quad \text{е) }\frac{10}{27}.} \]