II. PHẦN TỰ LUẬN

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

a) \(\frac{{ - 2}}{5} - \frac{1}{3}\);                                                            b) \(\frac{1}{2}\,.\,\frac{3}{7} + \frac{1}{2}\,.\,\frac{4}{7}\);

c) \(\frac{5}{6} - \left( {\frac{1}{3} + \frac{1}{2}} \right):20\% \);     d) \(\frac{3}{{17}} \cdot \frac{6}{{29}} - \frac{3}{{17}} \cdot \frac{{35}}{{29}} + 2022\frac{3}{{17}}\).

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

b) \(\frac{1}{2}\,.\,\frac{3}{7} + \frac{1}{2}\,.\,\frac{4}{7}\)\( = \frac{1}{2}\,.\,\left( {\frac{3}{7} + \frac{4}{7}} \right)\)\( = \frac{1}{2}\,.\,\,1\)\( = \frac{1}{2}\);

c) \(\frac{5}{6} - \left( {\frac{1}{3} + \frac{1}{2}} \right):20\% \)\( = \frac{5}{6} - \left( {\frac{2}{6} + \frac{3}{6}} \right) \cdot 20\% \) 

\( = \frac{5}{6} - \frac{5}{6} \cdot \frac{1}{5}\)\( = \frac{5}{6} - \frac{1}{6}\)\( = \frac{4}{6} = \frac{2}{3}\);

d) \(\frac{3}{{17}}.\frac{6}{{29}} - \frac{3}{{17}}.\frac{{35}}{{29}} + 2022\frac{3}{{17}}\)\( = \frac{3}{{17}} \cdot \left( {\frac{6}{{29}} - \frac{{35}}{{29}}} \right) + 2022\frac{3}{{17}}\)

\( = \frac{3}{{17}} \cdot \left( {\frac{{ - 29}}{{29}}} \right) + 2022\frac{3}{{17}}\)\( = \frac{3}{{17}} \cdot \left( { - 1} \right) + 2022\frac{3}{{17}}\)

\( = \frac{{ - 3}}{{17}} + 2022\frac{3}{{17}} = 2022\).