II. PHẦN TỰ LUẬN

1. Thực hiện phép tính (tính nhanh nếu có thể):

a) \(\frac{{ - 2}}{5} - \frac{1}{3}\);                                                       b) \(\frac{5}{{13}} + \frac{{ - 5}}{7} + \frac{{ - 20}}{{41}} + \frac{8}{{13}} + \frac{{ - 21}}{{41}}\);

2. Tìm \[x\]:

a) \(x + \frac{2}{3} = \frac{{11}}{9}\);                                                  b) \(\left( {x - \frac{4}{{15}}} \right).\frac{4}{5} - \frac{2}{3} = \frac{2}{5}\).

1.

a) \(\frac{{ - 2}}{5} - \frac{1}{3} = \frac{{ - 6}}{{15}} - \frac{5}{{15}} = \frac{{ - 11}}{{15}}\);                                                       

b) \(\frac{5}{{13}} + \frac{{ - 5}}{7} + \frac{{ - 20}}{{41}} + \frac{8}{{13}} + \frac{{ - 21}}{{41}}\)

\( = \left( {\frac{5}{{13}} + \frac{8}{{13}}} \right) + \left( {\frac{{ - 20}}{{41}} + \frac{{ - 21}}{{41}}} \right) + \frac{{ - 5}}{7}\)

\( = 1 + \left( { - 1} \right) + \frac{{ - 5}}{7} = \frac{{ - 5}}{7}\).

2.

a) \(x + \frac{2}{3} = \frac{{11}}{9}\)          

\(x = \frac{{11}}{9} - \frac{2}{3}\)

\(x = \frac{5}{9}\).

Vậy \(x = \frac{5}{9}\).

b) \(\left( {x - \frac{4}{{15}}} \right).\frac{4}{5} - \frac{2}{3} = \frac{2}{5}\)

\(\left( {x - \frac{4}{{15}}} \right).\frac{4}{5} = \frac{2}{5} + \frac{2}{3}\)

\(\left( {x - \frac{4}{{15}}} \right)\,.\,\frac{4}{5} = \frac{{16}}{{15}}\)

\(x - \frac{4}{{15}} = \frac{{16}}{{15}}:\frac{4}{5}\)

\(x - \frac{4}{{15}} = \frac{4}{3}\)

\(x = \frac{4}{3} + \frac{4}{{15}}\)

\(x = \frac{8}{5}\).

Vậy \(x = \frac{8}{5}\).