by Thực hiện phép tính:
a. \(\frac{7}{{23}}.\left[ {\left( { – \frac{8}{6}} \right) – \frac{{45}}{{18}}} \right]\)
b. \(\left( {\frac{{ – 2}}{3} + \frac{3}{7}} \right):\frac{4}{5} + \left( {\frac{{ – 1}}{3} + \frac{4}{7}} \right):\frac{4}{5}\)
c. \( – \frac{8}{3} + \left( {\frac{2}{3} – 1 + \frac{1}{2}} \right) – \left( { – \frac{5}{4} + \frac{1}{2}} \right)\)
A. a) \(-\frac{7}{6}\)
b) \(0\)
c) \(-\frac{7}{4}\)
B. a) \( \frac{7}{6}\)
b) \(0\)
c) \(-\frac{7}{4}\)
C. a) \(-\frac{7}{6}\)
b) \(1\)
c) \(\frac{7}{4}\)
D. a) \(-\frac{7}{6}\)
b) \(\frac{4}{3}\)
c) \(-\frac{7}{4}\)
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Chọn đáp án là: A
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giải chi tiết
a. \(\frac{7}{{23}}.\left[ {\left( { – \frac{8}{6}} \right) – \frac{{45}}{{18}}} \right]\)
\(\begin{array}{l} = \frac{7}{{23}}\left[ {\frac{{ – 4}}{3} – \frac{5}{2}} \right]\\ = \frac{7}{{23}}\left( {\frac{{ – 8}}{6} – \frac{{15}}{6}} \right)\\ = \frac{7}{{23}}.\frac{{ – 23}}{6}\\ = \frac{{ – 7}}{6}\end{array}\)
b. \(\left( {\frac{{ – 2}}{3} + \frac{3}{7}} \right):\frac{4}{5} + \left( {\frac{{ – 1}}{3} + \frac{4}{7}} \right):\frac{4}{5}\)
\(\begin{array}{l} = \left( {\frac{{ – 2}}{3} + \frac{3}{7} + \frac{{ – 1}}{3} + \frac{4}{7}} \right):\frac{4}{5}\\ = \left[ {\left( {\frac{{ – 2}}{3} + \frac{{ – 1}}{3}} \right) + \left( {\frac{3}{7} + \frac{4}{7}} \right)} \right]:\frac{4}{5}\\ = \left( { – 1 + 1} \right):\frac{4}{5}\\ = 0:\frac{4}{5}\\ = 0\end{array}\)
c. \( – \frac{8}{3} + \left( {\frac{2}{3} – 1 + \frac{1}{2}} \right) – \left( { – \frac{5}{4} + \frac{1}{2}} \right)\)
\(\begin{array}{l} = – \frac{8}{3} + \frac{2}{3} – 1 + \frac{1}{2} + \frac{5}{4} – \frac{1}{2}\\ = \left( { – \frac{8}{3} + \frac{2}{3}} \right) – 1 + \left( {\frac{1}{2} – \frac{1}{2}} \right) + \frac{5}{4}\\ = – 2 – 1 + 0 + \frac{5}{4}\\ = – 3 + \frac{5}{4}\\ = – \frac{7}{4}\end{array}\)
