Bài 1: Tính bằng hai cách:

a) (\(\frac{6}{11}\)+ \(\frac{5}{11}\) ) x \(\frac{3}{7}\)  ;

b) \(\frac{3}{5}\) x \(\frac{7}{9}\)  - \(\frac{3}{5}\)  x \(\frac{2}{9}\)  ;

c) ( \(\frac{6}{7}\) - \(\frac{4}{7}\) ) : \(\frac{2}{5}\)  ;

d)  \(\frac{8}{15}\) : \(\frac{2}{11}\)  + \(\frac{7}{15}\)  : \(\frac{2}{11}\) 

Lời Giải:

Bài 1:

a) Cách 1 : (\(\frac{6}{11}\)+ \(\frac{5}{11}\) ) x \(\frac{3}{7}\) = \(\frac{11}{11 }\) x \(\frac{3}{7}\)  = \(\frac{3}{7}\) 

Cách 2: (\(\frac{6}{11}\)+ \(\frac{5}{11}\) ) x \(\frac{3}{7}\)  = \(\frac{6}{11}\) x \(\frac{3}{7}\) + \(\frac{5}{11}\) x \(\frac{3}{7}\)  = \(\frac{18}{77 }\) + \(\frac{15}{77 }\) =  \(\frac{33}{77 }\) = \(\frac{3}{7}\) 

b)Cách 1 : \(\frac{3}{5}\) x \(\frac{7}{9}\)  - \(\frac{3}{5}\)  x \(\frac{2}{9}\) = \(\frac{21}{45}\) - \(\frac{6}{45}\) =  \(\frac{15}{45}\) = \(\frac{1}{3}\)

Cách 2:  \(\frac{3}{5}\) x \(\frac{7}{9}\)  - \(\frac{3}{5}\)  x \(\frac{2}{9}\) = \(\frac{3}{5}\) x (\(\frac{7}{9}\) - \(\frac{2}{9}\)) = \(\frac{3}{5}\) x \(\frac{5}{9}\) = \(\frac{15}{45}\) = \(\frac{1}{3}\)

c) Cách 1:  ( \(\frac{6}{7}\) - \(\frac{4}{7}\) ) : \(\frac{2}{5}\) = \(\frac{2}{7}\) : \(\frac{2}{5}\)  =  \(\frac{2}{7}\)  x \(\frac{5}{2}\) = \(\frac{5}{7}\)

Cách 2:  ( \(\frac{6}{7}\) - \(\frac{4}{7}\) ) : \(\frac{2}{5}\) = \(\frac{6}{7}\) : \(\frac{2}{5}\) - \(\frac{4}{7}\) : \(\frac{2}{5}\) = \(\frac{6}{7}\) x \(\frac{5}{2}\) - \(\frac{4}{7}\)  x \(\frac{5}{2}\) = \(\frac{30}{14}\) - \(\frac{20}{14}\) = \(\frac{10}{14}\) = \(\frac{5}{7}\)

d)  \(\frac{8}{15}\) : \(\frac{2}{11}\)  + \(\frac{7}{15}\)  : \(\frac{2}{11}\) = \(\frac{8}{15}\) x \(\frac{11}{2}\) + \(\frac{7}{15}\) x \(\frac{11}{2}\) = \(\frac{88}{30}\) + \(\frac{77}{30}\) = \(\frac{165}{30}\) = \(\frac{11}{2}\)

Cách 2: \(\frac{8}{15}\) : \(\frac{2}{11}\)  + \(\frac{7}{15}\)  : \(\frac{2}{11}\) = (\(\frac{8}{15}\) + \(\frac{7}{15}\) ) : \(\frac{2}{11}\) = \(\frac{15}{15}\) : \(\frac{2}{11}\) = \(\frac{15}{15}\) x  \(\frac{11}{2}\) = \(\frac{11}{2}\)