Đáp án:
$a) \dfrac{45}{2}\\
b)\dfrac{1}{24}\\
c) \dfrac{-48}{13}\\
d) \dfrac{1191}{100}$
Giải thích các bước giải:
$a) \left [ 6+\left ( \dfrac{1}{3} \right )^3-\left |-\dfrac{1}{2} \right | \right ]:\dfrac{3}{12}\\
=\left [ 6+\dfrac{1}{8}-\dfrac{1}{2} \right ].\dfrac{12}{3}\\
=\left [\dfrac{6.8}{8}+\dfrac{1}{8}-\dfrac{4}{8} \right ].4\\
=\dfrac{48+1-4}{8}.4\\
=\dfrac{45}{2}\\$
$b) \dfrac{18}{37}+\dfrac{8}{24}+\dfrac{19}{37}-1\dfrac{23}{24}+\dfrac{2}{3}\\
=\left ( \dfrac{18}{37}+\dfrac{19}{37} \right )+\left ( \dfrac{8}{24}-\dfrac{47}{24} \right )+\dfrac{2}{3}\\
=\dfrac{37}{37}-\dfrac{39}{24}+\dfrac{2}{3}\\
=1-\dfrac{39}{24}+\dfrac{2}{3}\\
=\dfrac{24}{24}-\dfrac{39}{24}+\dfrac{2.8}{24}\\
=\dfrac{24-39+16}{24}=\dfrac{1}{24}\\$
$c) (-2)^3\left ( \dfrac{3}{4}-0,25 \right ):\left ( 2\dfrac{1}{4}-1\dfrac{1}{6} \right )\\
=(-8).\left ( \dfrac{3}{4}-\dfrac{1}{4} \right ):\left ( \dfrac{9.3}{12}-\dfrac{7.2}{12} \right )\\
=(-8).\dfrac{2}{4}:\dfrac{13}{12}\\
=(-8).\dfrac{1}{2}.\dfrac{12}{13}\\
=\dfrac{-48}{13}\\
d) \left ( \dfrac{2}{5} \right )^2+5\dfrac{1}{2}\left ( 4,5-2 \right )+\dfrac{2^3}{-4}\\
=\dfrac{4}{25}+\dfrac{11}{2}.2,5-\dfrac{8}{4}\\
=\dfrac{4}{25}+\dfrac{11}{2}.\dfrac{5}{2}-2\\
=\dfrac{4}{25}+\dfrac{55}{4}-2\\
=\dfrac{16}{100}+\dfrac{55.25}{100}-\dfrac{200}{100}\\
=\dfrac{16+1375-200}{100}=\dfrac{1191}{100}$
