Câu hỏi của Gia Huy To

Question

HT.Phong (9A5) · Accepted Answer

a) $\dfrac{8}{9}-\dfrac{1}{72}-\dfrac{1}{56}-\dfrac{1}{42}-\dfrac{1}{30}-\dfrac{1}{20}-\dfrac{1}{12}-\dfrac{1}{6}-\dfrac{1}{2}\
=\dfrac{8}{9}-\left(\dfrac{1}{72}+\dfrac{1}{56}+\dfrac{1}{42}+\dfrac{1}{30}+\dfrac{1}{20}+\dfrac{1}{12}+\dfrac{1}{6}+\dfrac{1}{2}\right)\
=\dfrac{8}{9}-\left(\dfrac{1}{8\cdot9}+\dfrac{1}{7\cdot8}+\dfrac{1}{6\cdot7}+\dfrac{1}{6\cdot5}+\dfrac{1}{4\cdot5}+\dfrac{1}{3\cdot4}+\dfrac{1}{2\cdot3}+\dfrac{1}{1\cdot2}\right)\
=\dfrac{8}{9}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}\right)\
=\dfrac{8}{9}-\left(1-\dfrac{1}{9}\right)\
=\dfrac{8}{9}-\dfrac{8}{9}\
=0$ Câu trả lời: a) $\dfrac{8}{9}-\dfrac{1}{72}-\dfrac{1}{56}-\dfrac{1}{42}-\dfrac{1}{30}-\dfrac{1}{20}-\dfrac{1}{12}-\dfrac{1}{6}-\dfrac{1}{2}\
=\dfrac{8}{9}-\left(\dfrac{1}{72}+\dfrac{1}{56}+\dfrac{1}{42}+\dfrac{1}{30}+\dfrac{1}{20}+\dfrac{1}{12}+\dfrac{1}{6}+\dfrac{1}{2}\right)\
=\dfrac{8}{9}-\left(\dfrac{1}{8\cdot9}+\dfrac{1}{7\cdot8}+\dfrac{1}{6\cdot7}+\dfrac{1}{6\cdot5}+\dfrac{1}{4\cdot5}+\dfrac{1}{3\cdot4}+\dfrac{1}{2\cdot3}+\dfrac{1}{1\cdot2}\right)\
=\dfrac{8}{9}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}\right)\
=\dfrac{8}{9}-\left(1-\dfrac{1}{9}\right)\
=\dfrac{8}{9}-\dfrac{8}{9}\
=0$

HT.Phong (9A5) · Answer

b) $\left(-\dfrac{1}{2}\right)-\left(\dfrac{-3}{5}\right)+\left(-\dfrac{1}{9}\right)+\dfrac{1}{127}-\dfrac{7}{18}+\dfrac{4}{35}-\left(\dfrac{-2}{7}\right)\
=\left(-\dfrac{1}{2}-\dfrac{1}{9}-\dfrac{7}{18}\right)+\left(\dfrac{3}{5}+\dfrac{2}{7}+\dfrac{4}{35}\right)+\dfrac{1}{127}\
=\dfrac{-9-2-7}{18}+\dfrac{21+10+4}{35}+\dfrac{1}{127}\
=-1+1+\dfrac{1}{127}\
=\dfrac{1}{127}$c) (*sửa*)$\dfrac{3}{5}+\dfrac{3}{11}-\dfrac{-3}{7}+\dfrac{2}{97}-\dfrac{1}{35}-\dfrac{3}{4}-\dfrac{23}{44}\
=\dfrac{3}{5}+\dfrac{3}{11}+\dfrac{3}{7}+\dfrac{2}{97}-\dfrac{1}{35}-\dfrac{3}{4}+\dfrac{23}{44}\
=\left(\dfrac{3}{5}+\dfrac{3}{7}-\dfrac{1}{35}\right)+\left(\dfrac{3}{11}-\dfrac{3}{4}-\dfrac{23}{44}\right)+\dfrac{2}{97}\
=\dfrac{21+15-1}{35}+\dfrac{12-33-23}{44}+\dfrac{2}{97}\
=1+\left(-1\right)+\dfrac{2}{97}\
=\dfrac{2}{97}$Câu trả lời: b) $\left(-\dfrac{1}{2}\right)-\left(\dfrac{-3}{5}\right)+\left(-\dfrac{1}{9}\right)+\dfrac{1}{127}-\dfrac{7}{18}+\dfrac{4}{35}-\left(\dfrac{-2}{7}\right)\
=\left(-\dfrac{1}{2}-\dfrac{1}{9}-\dfrac{7}{18}\right)+\left(\dfrac{3}{5}+\dfrac{2}{7}+\dfrac{4}{35}\right)+\dfrac{1}{127}\
=\dfrac{-9-2-7}{18}+\dfrac{21+10+4}{35}+\dfrac{1}{127}\
=-1+1+\dfrac{1}{127}\
=\dfrac{1}{127}$c) (*sửa*)$\dfrac{3}{5}+\dfrac{3}{11}-\dfrac{-3}{7}+\dfrac{2}{97}-\dfrac{1}{35}-\dfrac{3}{4}-\dfrac{23}{44}\
=\dfrac{3}{5}+\dfrac{3}{11}+\dfrac{3}{7}+\dfrac{2}{97}-\dfrac{1}{35}-\dfrac{3}{4}+\dfrac{23}{44}\
=\left(\dfrac{3}{5}+\dfrac{3}{7}-\dfrac{1}{35}\right)+\left(\dfrac{3}{11}-\dfrac{3}{4}-\dfrac{23}{44}\right)+\dfrac{2}{97}\
=\dfrac{21+15-1}{35}+\dfrac{12-33-23}{44}+\dfrac{2}{97}\
=1+\left(-1\right)+\dfrac{2}{97}\
=\dfrac{2}{97}$

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