\(\frac{1}{2}\)\(+\)\(\left(\frac{16}{21}+\frac{27}{13}\right)\)\(-\)\(\left(\frac{14}{13}-\frac{5}{21}\right)\)

\(=\)\(\frac{1}{2}\)\(+\)\(\frac{16}{21}\)\(+\)\(\frac{27}{13}\)\(-\)\(\frac{14}{13}\)\(+\)\(\frac{5}{21}\)

\(=\)\(\frac{1}{2}\)\(+\)\(\left(\frac{16}{21}+\frac{5}{21}\right)\)\(+\)\(\left(\frac{27}{13}-\frac{14}{13}\right)\)

\(=\)\(\frac{1}{2}\)\(+\)\(\frac{21}{21}\)\(+\)\(\frac{13}{13}\)

\(=\)\(\frac{1}{2}\)\(+\)\(1\)\(+\)\(1\)

\(=\)\(\frac{5}{2}\)

\(\frac{7}{2}\)\(-\)\(\left(\frac{-1}{5}\right)\)\(-\)\(\frac{5}{6}\)\(+\)\(\frac{2}{3}\)\(+\)\(\left(\frac{-1}{5}\right)\)

\(=\)\(\frac{7}{2}\)\(+\)\(\frac{1}{5}\)\(-\)\(\frac{5}{6}\)\(+\)\(\frac{2}{3}\)\(-\)\(\frac{1}{5}\)

\(=\)\(\left(\frac{7}{12}-\frac{5}{6}+\frac{2}{3}\right)\)\(+\)\(\left(\frac{1}{5}-\frac{1}{5}\right)\)

\(=\)\(\frac{7}{2}\)\(-\)\(\frac{5}{6}\)\(+\)\(\frac{2}{3}\)\(+\)\(0\)

\(=\)\(\frac{5}{12}\)\(+\)\(0\)

\(=\)\(\frac{5}{12}\)

Gọi học sinh 4 khối 6;7;8;9 lần lượt là a;b;c;d 

Ta có b - d = 70

Lại có \(\frac{a}{9}=\frac{b}{8}=\frac{c}{7}=\frac{d}{6}\)

Áp dụng dãy tỉ số bằng nhau ta được 

\(\frac{a}{9}=\frac{b}{8}=\frac{c}{7}=\frac{d}{6}=\frac{b-d}{8-6}=\frac{70}{2}=35\)

=> a = 9.35 = 315 ; 

b = 35.8 = 280 

c = 35.7 = 245

d = 35.6 = 210 

Vậy khối 6 có 210 học sinh ; khối 7 có 245 học sinh ; khối 8 có 280 học sinh ; khối 9 có 315 học sinh