II. Tự luận

Thực hiện phép tính

a) $(\frac{9}{16}-\frac{5}{8}+\frac{3}{4}):\frac{11}{32}$

b) \(\frac{5}{9}.\frac{7}{{13}} + \frac{5}{9}.\frac{9}{{13}} + \frac{3}{{13}}.\frac{{ - 5}}{9}\)

c) \(\frac{{ - 3}}{7} + \frac{{ - 22}}{{26}} + \left( {\frac{2}{{ - 13}} + \frac{3}{7} + {{2021}^0}} \right)\)

a) \(\left( {\frac{9}{{16}} - \frac{5}{8} + \frac{3}{4}} \right):\frac{{11}}{{32}}\)

\( = \left( {\frac{9}{{16}} - \frac{{10}}{{16}} + \frac{{12}}{{16}}} \right):\frac{{11}}{{32}}\)

\( = \left( {\frac{{9 - 10 + 12}}{{16}}} \right):\frac{{11}}{{32}}\)

\( = \frac{{11}}{{16}}:\frac{{11}}{{32}}\)

\( = \frac{{11}}{{16}}.\frac{{32}}{{11}}\)

\( = \frac{{11.32}}{{16.11}}\)

\( = \frac{{11.16.2}}{{16.11}} = 2\)

b) \(\frac{5}{9}.\frac{7}{{13}} + \frac{5}{9}.\frac{9}{{13}} + \frac{3}{{13}}.\frac{{ - 5}}{9}\)

\( = \frac{5}{9}.\frac{7}{{13}} + \frac{5}{9}.\frac{9}{{13}} - \frac{5}{9}.\frac{3}{{13}}\)

\( = \frac{5}{9}.\left( {\frac{7}{{13}} + \frac{9}{{13}} - \frac{3}{{13}}} \right)\)

\( = \frac{5}{9}.\left( {\frac{{7 + 9 - 3}}{{13}}} \right)\)

\( = \frac{5}{9}.\frac{{13}}{{13}} = \frac{5}{9}.1 = \frac{5}{9}\)

c) \(\frac{{ - 3}}{7} + \frac{{ - 22}}{{26}} + \left( {\frac{2}{{ - 13}} + \frac{3}{7} + {{2021}^0}} \right)\)

\( = \frac{{ - 3}}{7} + \frac{{ - 22}}{{26}} + \left( {\frac{2}{{ - 13}} + \frac{3}{7} + 1} \right)\)

\( = \frac{{ - 3}}{7} + \frac{{ - 22}}{{26}} + \frac{2}{{ - 13}} + \frac{3}{7} + 1\)

\( = \left( {\frac{{ - 3}}{7} + \frac{3}{7}} \right) + \left( {\frac{{ - 22}}{{26}} + \frac{2}{{ - 13}}} \right) + 1\)

\( = \left( {\frac{{ - 3 + 3}}{7}} \right) + \left( {\frac{{ - 22}}{{26}} + \frac{{ - 4}}{{26}}} \right) + 1\)

\( = \frac{0}{7} + \frac{{\left( { - 22} \right) + \left( { - 4} \right)}}{{26}} + 1\)

\( = 0 + \frac{{ - 26}}{{26}} + 1\)

\( = 0 + ( - 1) + 1 = 0\)