1. tính
\(a,\frac{-1}{2}+\frac{5}{-7}+\frac{15}{35}-\frac{4}{5}-\frac{1}{6}\)|
\(b,\frac{-3}{11}.\frac{-7}{19}+\frac{3}{-11}.\frac{12}{-19}-\frac{2}{11}\)
\(c,4^2.\left(2^3+4^2\right):\left(2^5+4^3\right)\)
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1. a) \(\frac{-2}{7}+\frac{15}{23}+\frac{\left(-15\right)}{17}+\frac{4}{19}+\frac{8}{23}\)
\(=\left(\frac{-2}{7}+\frac{-5}{7}\right)+\left(\frac{15}{23}+\frac{8}{23}\right)+\frac{4}{19}\)
\(=\left(-1\right)+1+\frac{4}{19}\)
\(=0+\frac{4}{19}=\frac{4}{19}\)
b) \(\frac{7}{19}\cdot\frac{8}{11}+\frac{7}{19}\cdot\frac{3}{11}+\frac{12}{19}\)
\(=\frac{7}{19}\cdot\left(\frac{8}{11}+\frac{3}{11}\right)+\frac{12}{19}\)
\(=\frac{7}{19}\cdot1+\frac{12}{19}\)
\(=\frac{7}{19}+\frac{12}{19}=\frac{19}{19}=1\)
2. a) \(\frac{1}{3}+\frac{\left(-2\right)}{16}-\frac{7}{14}\)
\(=\frac{5}{24}-\frac{1}{2}\)
\(=-\frac{7}{24}\)
b) \(11\frac{3}{13}-2\frac{4}{7}+5\frac{3}{13}\)
\(=\left(11-2+5\right)+\frac{3}{13}-\frac{4}{7}+\frac{3}{13}\)
\(=14+\left(-\frac{10}{91}\right)\)
\(=-14\frac{10}{91}\)
c) \(0,7\cdot2\frac{2}{3}\cdot20\cdot0,375\cdot\frac{5}{28}\)
\(=\frac{7}{10}\cdot\frac{8}{3}\cdot20\cdot\frac{3}{8}\cdot\frac{5}{28}\)
\(=\left(\frac{7}{10}\cdot\frac{5}{28}\right)\cdot\left(\frac{8}{3}\cdot\frac{3}{8}\right)\cdot20\)
\(=\frac{1}{8}\cdot1\cdot20\)
\(=\frac{20}{8}=\frac{5}{2}\)
d) \(\frac{6}{7}+\frac{5}{7}:5-\frac{8}{9}\)
\(=\frac{6}{7}+\frac{1}{7}-\frac{8}{9}\)
\(=1-\frac{8}{9}\)
\(=\frac{1}{9}\)
~Học tốt~
[\(\frac{-75}{59}\).\(\frac{-107}{93}\)]\(\frac{31}{50}\)=\(\frac{2675}{1829}\).\(\frac{31}{50}\)=\(\frac{107}{118}\)
\(\left[\frac{1\frac{11}{31}\cdot4\frac{3}{7}-\left(15-6\frac{1}{3}\cdot\frac{2}{19}\right)}{4\frac{5}{6}+\frac{1}{6}\left(12-5\frac{1}{3}\right)}\cdot\left(-1\frac{14}{93}\right)\right]\cdot\frac{31}{50}\)
\(=\left[\frac{\frac{42}{31}\cdot\frac{31}{7}-\left(15-\frac{19}{3}\cdot\frac{2}{19}\right)}{4\frac{5}{6}+\frac{1}{6}\left(12-\frac{16}{3}\right)}\cdot\left(-\frac{107}{93}\right)\right]\cdot\frac{31}{50}\)
\(=\left[\frac{6-\left(15-\frac{2}{3}\right)}{\frac{29}{6}+\frac{1}{6}\cdot\frac{20}{3}}\cdot\left(-\frac{107}{93}\right)\right]\cdot\frac{31}{50}\)
\(=\left[\frac{6-15+\frac{2}{3}}{\frac{29}{6}+\frac{10}{9}}\cdot\left(-\frac{107}{93}\right)\right]\cdot\frac{31}{50}\)
\(=\left[\frac{-\frac{25}{3}}{\frac{107}{18}}\cdot\left(-\frac{107}{93}\right)\right]\cdot\frac{31}{50}\)
\(=\left[\left(-\frac{150}{107}\right)\cdot\left(-\frac{107}{93}\right)\right]\cdot\frac{31}{50}=\frac{50}{31}\cdot\frac{31}{50}=1\)
a/ \(\frac{2}{3}-4.\left(\frac{1}{2}+\frac{3}{4}\right)\)
= \(\frac{2}{3}-2-3\)
=\(\frac{2}{3}-5\)
=\(\frac{2}{3}-\frac{15}{3}\)
=\(\frac{-13}{3}\)
b/\(\left(-\frac{1}{3}+\frac{5}{6}\right).11-7\)
=\(\frac{-11}{3}+\frac{55}{6}-7\)
=\(\frac{-22}{6}+\frac{55}{6}-7\)
= \(\frac{11}{2}-\frac{14}{2}\)
=\(\frac{-3}{2}\)
c/\(\frac{3}{11}.\frac{4}{15}+\frac{19}{15}.\frac{-3}{11}\)
=\(\frac{4}{55}\)\(-\frac{19}{55}\)
=\(\frac{-3}{11}\)
a) \(\frac{2}{3}-4.\left(\frac{1}{2}+\frac{3}{4}\right)=\frac{2}{3}-4.\left(\frac{2}{4}+\frac{3}{4}\right)\)
\(=\frac{2}{3}-4.\frac{5}{4}=\frac{2}{3}-5=\frac{-13}{3}\)
b) \(\left(-\frac{1}{3}+\frac{5}{6}\right).11-7\)
\(=\frac{3}{6}.11-7=\frac{1}{2}.11-7\)
\(=\frac{11}{2}-7=-\frac{3}{2}\)
c) \(\frac{3}{11}.\frac{4}{15}+\frac{19}{15}.\frac{-3}{11}\)
\(=\frac{3}{11}.\left(\frac{4}{15}-\frac{19}{15}\right)\)
\(=\frac{3}{11}.\left(-1\right)=-\frac{3}{11}\)
Chúc bạn học tốt nhé !