Đề cương ôn tập cuối kì 2 Toán 6 Chân trời sáng tạo cấu trúc mới có đáp án - Tự luận

a) \(\frac{6}{{13}} + \frac{{ - 17}}{{39}} = \frac{{18}}{{39}} + \frac{{ - 17}}{{39}}\)

\( = \frac{{18 + \left( { - 17} \right)}}{{39}} = \frac{1}{{39}}.\)

c) \(\frac{{ - 15}}{{16}} \cdot \frac{8}{{ - 25}} = \frac{{ - 1 \cdot 3 \cdot 5 \cdot 8}}{{8 \cdot 2 \cdot \left( { - 1} \right) \cdot {5^2}}} = \frac{3}{{10}}.\)

e) \(\frac{2}{3} - \left( {\frac{{ - 5}}{7} + \frac{2}{3}} \right)\)\( = \frac{2}{3} + \frac{5}{7} - \frac{2}{3}\)

\( = \left( {\frac{2}{3} - \frac{2}{3}} \right) + \frac{5}{7}\)\( = 0 + \frac{5}{7}\)\( = \frac{5}{7}.\)

g) \(\frac{1}{4} + \frac{3}{4}:\left( { - \frac{6}{7}} \right) = \frac{1}{4} + \frac{3}{4} \cdot \frac{{ - 7}}{6}\)

\( = \frac{1}{4} + \frac{{ - 7}}{8} = \frac{2}{8} - \frac{7}{8} = \frac{{ - 5}}{8}.\)

i) \[12\frac{5}{{14}} - \left( {3\frac{5}{7} + 5\frac{5}{{14}}} \right)\]

\[ = 12\frac{5}{{14}} - 3\frac{5}{7} - 5\frac{5}{{14}}\]\( = \left( {12\frac{5}{{14}} - 5\frac{5}{{14}}} \right) - 3\frac{5}{7}\)

\( = 7 - 3\frac{5}{7} = \frac{{49}}{7} - \frac{{26}}{7} = \frac{{23}}{7}.\)

k) \[\frac{7}{{12}} \cdot \frac{2}{3} - \frac{5}{3} \cdot \frac{7}{{12}} + \frac{7}{{12}} \cdot 3\]

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

\( = \frac{7}{{12}} \cdot \left( {\frac{2}{3} - \frac{5}{3} + \frac{9}{3}} \right) = \frac{7}{{12}} \cdot 2 = \frac{7}{6}.\)

b) \( - 1,25 - 2\frac{1}{4} =  - 1,25 - 2,25 =  - 3,5.\)

d) \(\frac{5}{6}:\frac{{ - 7}}{{12}} = \frac{5}{6} \cdot \frac{{12}}{{ - 7}} = \frac{{10}}{{ - 7}} =  - \frac{{10}}{7}.\)

f) \(\frac{3}{4} - \frac{4}{5} + \frac{{ - 17}}{{20}} = \frac{{15}}{{20}} - \frac{{16}}{{20}} + \frac{{ - 17}}{{20}}\)

\( = \frac{{15 - 16 + \left( { - 17} \right)}}{{20}} = \frac{{ - 18}}{{20}} = \frac{{ - 9}}{{10}}.\)

h) \[\frac{9}{{11}} - \frac{7}{8} + \frac{{13}}{{11}} + \frac{{ - 1}}{8}\]

\[ = \left( {\frac{9}{{11}} + \frac{{13}}{{11}}} \right) + \left( { - \frac{7}{8} + \frac{{ - 1}}{8}} \right)\]\[ = \frac{{22}}{{11}} + \frac{{ - 8}}{8} = 2 - 1 = 1.\]

j) \(\left( {\frac{{ - 12}}{5} + \frac{5}{{12}} + \frac{1}{4}} \right) + \left( {\frac{7}{5} + \frac{{ - 19}}{{12}} + \frac{2}{{12}}} \right) - {2024^0}\)

\[ = \frac{{ - 12}}{5} + \frac{5}{{12}} + \frac{1}{4} + \frac{7}{5} + \frac{{ - 19}}{{12}} + \frac{2}{{12}} - 1\]

\[ = \left( {\frac{{ - 12}}{5} + \frac{7}{5}} \right) + \left( {\frac{5}{{12}} + \frac{{ - 19}}{{12}} + \frac{2}{{12}}} \right) - 1 + \frac{1}{4}\]

\[ = \frac{{ - 5}}{5} + \frac{{ - 12}}{{12}} - 1 + \frac{1}{4} =  - 1 + \left( { - 1} \right) - 1 + \frac{1}{4}\]

\[ =  - 3 + \frac{1}{4} = \frac{{ - 12}}{4} + \frac{1}{4} = \frac{{ - 11}}{4}.\]

l) \(\frac{2}{3}:\frac{4}{5} - \frac{5}{4} + \frac{1}{3}:\frac{4}{5}\)

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

\( = \frac{5}{4} \cdot \left( {\frac{2}{3} - 1 + \frac{1}{3}} \right) = \frac{5}{4} \cdot \left[ {\left( {\frac{2}{3} + \frac{1}{3}} \right) - 1} \right]\)

\( = \frac{5}{4} \cdot \left[ {\frac{3}{3} - 1} \right] = \frac{5}{4} \cdot \left( {1 - 1} \right) = \frac{5}{4} \cdot 0 = 0.\)

m) \(\frac{2}{5} \cdot \left( {\frac{{ - 5}}{{12}} + \frac{{ - 9}}{{13}}} \right) - \frac{2}{5} \cdot \left( {\frac{4}{{13}} - \frac{5}{{12}}} \right):2\)

\( = \frac{1}{5} \cdot 2 \cdot \left( {\frac{{ - 5}}{{12}} + \frac{{ - 9}}{{13}}} \right) - \frac{2}{5} \cdot \left( {\frac{4}{{13}} - \frac{5}{{12}}} \right) \cdot \frac{1}{2}\)

\( = \frac{1}{5} \cdot \left( {\frac{{ - 10}}{{12}} + \frac{{ - 18}}{{13}}} \right) - \frac{1}{5} \cdot \left( {\frac{4}{{13}} - \frac{5}{{12}}} \right)\)

\[ = \frac{1}{5} \cdot \left( {\frac{{ - 10}}{{12}} + \frac{{ - 18}}{{13}} - \frac{4}{{13}} + \frac{5}{{12}}} \right)\]

\[ = \frac{1}{5} \cdot \left[ {\left( {\frac{{ - 10}}{{12}} + \frac{5}{{12}}} \right) + \left( {\frac{{ - 18}}{{13}} - \frac{4}{{13}}} \right)} \right]\]

\[ = \frac{1}{5} \cdot \left( {\frac{{ - 5}}{{12}} + \frac{{ - 22}}{{13}}} \right) = \frac{1}{5} \cdot \left( {\frac{{ - 65}}{{156}} + \frac{{ - 264}}{{156}}} \right)\]

\[ = \frac{1}{5} \cdot \frac{{ - 329}}{{156}} = \frac{{ - 329}}{{780}}.\]

n) \(\frac{2}{{15}}.\frac{3}{8} - \left( {\frac{7}{{20}} - 75\% } \right):\frac{8}{5}\)

\( = \frac{1}{{20}} - \left( {\frac{7}{{20}} - \frac{{75}}{{100}}} \right):\frac{8}{5}\)

\( = \frac{1}{{20}} - \left( {\frac{{35}}{{100}} - \frac{{75}}{{100}}} \right):\frac{8}{5}\)

\( = \frac{1}{{20}} + \frac{{40}}{{100}}.\frac{5}{8}\)

\( = \frac{1}{{20}} + \frac{1}{4}\)

\( = \frac{6}{{20}} = \frac{3}{{10}}\).

p) \({\left( {\frac{{ - 2}}{5}} \right)^2} + \frac{1}{2} \cdot \left( {4,5 - 2} \right) - 25\% \)

\( = \frac{4}{{25}} + \frac{1}{2} \cdot \frac{5}{2} - \frac{1}{4}\)

\( = \frac{4}{{25}} + \frac{5}{4} - \frac{1}{4}\)

\( = \frac{4}{{25}} + 1 = \frac{{29}}{{25}}.\)