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a , \(\frac{7}{8}:\frac{1}{6}+\frac{7}{8}.\frac{-7}{18}\)
= \(\frac{21}{4}+\frac{-49}{144}=\frac{707}{144}\)
b, -1 : (-5) + \(\frac{1}{15}-\frac{-1}{15}\)
= \(\frac{1}{5}+0=\frac{1}{5}\)
c, \(\frac{9}{10}-\frac{1}{10.9}-\frac{1}{9.8}-\frac{1}{8.7}-\frac{1}{7.6}-\frac{1}{6.5}-\frac{1}{5.4}-\frac{1}{4.3}-\frac{1}{3.2}-\frac{1}{2.1}\)
= \(\frac{9}{10}-\frac{10-9}{10.9}-\frac{9-8}{9.8}-\frac{8-7}{8.7}-\frac{7-6}{7.6}-\frac{6-5}{6.5}-\frac{5-4}{5.4}-\frac{4-3}{4.3}-\frac{3-2}{3.2}.\frac{2-1}{2.1}\)
= \(\frac{9}{10}-1-\frac{1}{10}-1-\frac{1}{9}-1-\frac{1}{8}-1-\frac{1}{7}-1-\frac{1}{6}-1-\frac{1}{5}-1-\frac{1}{4}-1-\frac{1}{3}-1-\frac{1}{2}\)
= \(\frac{9}{10}-\left(1+1+1+1+1+1+1+1+1\right)-\left(\frac{1}{10}+\frac{1}{9}+\frac{1}{8}+...+\frac{1}{2}\right)\)
= \(\frac{9}{10}-9-1,928=\frac{9}{10}-7,071=-6.171\)
1/9 - 0,3 . 5/9 + 1/3 + 5
= 1/9 - 3/10 . 5/9 + 1/3 + 5
= 1/9 - 1/6 + 16/3
= -1/18 + 16/3
= 95/18
b: \(\dfrac{4^5\cdot9^4-2\cdot6^9}{2^{10}\cdot3^8+6^8\cdot20}\)
\(=\dfrac{2^{10}\cdot3^8-2^{10}\cdot3^9}{2^{10}\cdot3^8+3^8\cdot2^{10}\cdot5}\)
\(=\dfrac{2^{10}\cdot3^8\left(1-3\right)}{2^{11}\cdot3^9}\)
\(=\dfrac{1}{2}\cdot\dfrac{-2}{3}=\dfrac{-1}{3}\)
\(\left(-\dfrac{2}{3}\right).0,75+1\dfrac{2}{3}:\left(-\dfrac{4}{9}\right)+\left(-\dfrac{1}{2}\right)^2\)
\(=\left(-\dfrac{2}{3}\right).\dfrac{3}{4}+\dfrac{5}{3}:\left(-\dfrac{4}{9}\right)+\dfrac{1}{4}\)
\(=\left(-\dfrac{1}{2}\right)+\left(-\dfrac{15}{4}\right)+\dfrac{1}{4}\)
\(=-\dfrac{16}{4}=-4\)
\(\sqrt{0,36}-\left|-0,75\right|:\left(-1\dfrac{3}{4}\right)\\ =0,6-0,75:\dfrac{-7}{4}\\ =\dfrac{3}{5}-\dfrac{3}{4}\cdot\dfrac{-4}{7}\\ =\dfrac{3}{5}-\dfrac{-12}{28}\\ =\dfrac{3}{5}+\dfrac{3}{7}\\ =\dfrac{36}{35}\)
\(1-\left(\dfrac{5}{9}-\dfrac{2}{3}\right)^2:\dfrac{4}{27}\\ =1-\left(\dfrac{5}{9}-\dfrac{6}{9}\right)^2\cdot\dfrac{27}{4}\\ =1-\left(-\dfrac{1}{9}\right)^2\cdot\dfrac{27}{4}\\ =1-\dfrac{1}{81}\cdot\dfrac{27}{4}\\ =1-\dfrac{1}{12}\\ =\dfrac{11}{12}\)
\(=\left(-\dfrac{2}{3}\right).\dfrac{3}{4}+\dfrac{5}{3}.\left(-\dfrac{9}{4}\right)+\dfrac{1}{4}=-\dfrac{1}{2}-\dfrac{15}{4}+\dfrac{1}{4}=-\dfrac{7}{2}-\dfrac{1}{2}=-4\)