Tính hợp lí:
1+(-4)+7+(-10)+13+(-16)
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\(\left(\frac{3}{4}+\frac{2}{11}-\frac{8}{13}\right)+\left(\frac{1}{4}-\frac{5}{13}\right)\)
\(=\frac{3}{4}+\frac{2}{11}-\frac{8}{13}+\frac{1}{4}-\frac{5}{13}\)
\(=\left(\frac{3}{4}+\frac{1}{4}\right)+\frac{2}{11}-\left(\frac{8}{13}+\frac{5}{13}\right)\)
\(=1+\frac{2}{11}-1\)
\(=\frac{2}{11}\)
\(\left(\frac{9}{53}+\frac{21}{31}\right)+\left(\frac{44}{53}-\frac{16}{7}\right)+\frac{10}{31}\)
\(=\frac{9}{53}+\frac{21}{31}+\frac{44}{53}-\frac{16}{7}+\frac{10}{31}\)
\(=\left(\frac{9}{53}+\frac{44}{53}\right)+\left(\frac{21}{31}+\frac{10}{31}\right)-\frac{16}{7}\)
\(=1+1-\frac{16}{7}\)
\(=2-\frac{16}{7}\)
\(=\frac{14}{7}-\frac{16}{7}\)
\(=\frac{-2}{7}\)
\(\text{Phần a nên sửa đề thế này :}\) \(\frac{1}{7}.\frac{-3}{8}+\frac{1}{7}.\frac{-13}{8}\)
\(\text{Giải :}\)
\(\frac{1}{7}.\frac{-3}{8}+\frac{1}{7}.\frac{-13}{8}\)
\(=\frac{1}{7}\left(\frac{-3}{8}+\frac{-13}{8}\right)\)
\(=\frac{1}{7}.\left(-2\right)\)
\(=\frac{-2}{7}\)
\(\frac{3}{5}.\frac{13}{46}-\frac{1}{10}.\frac{16}{23}\)
\(=\frac{3}{5}.\left(\frac{1}{46}.13\right)-\frac{1}{10}.\frac{32}{46}\)
\(=\left(\frac{3}{5}.13\right).\frac{1}{46}-\left(\frac{1}{10}.32\right).\frac{1}{46}\)
\(=\frac{39}{5}.\frac{1}{46}-\frac{32}{10}.\frac{1}{46}\)
\(=\frac{78}{10}.\frac{1}{46}-\frac{32}{10}.\frac{1}{46}\)
\(=\left(\frac{78}{10}-\frac{32}{10}\right).\frac{1}{46}\)
\(=\frac{46}{10}.\frac{1}{46}\)
\(=\frac{1}{10}\)
b,1×2×3×...×9-1×2×3×...×8-1×2×3×...×7×8^2
=(1×2×3×...×8)×(9-1-8)
=(1×2×3×...×8)×0
=0
\(\frac{4^{10}.9^6+3^{12}.8^5}{6^{13}.4-2^{16}.3^{12}}\)
\(=\frac{\left(2^2\right)^{10}.\left(3^2\right)^6+3^{12}.\left(2^3\right)^5}{\left(2.3\right)^{13}.2^2-2^{16}.3^{12}}\)
\(=\frac{2^{20}.3^{12}+3^{12}.2^{15}}{2^{13}.3^{13}.2^2-2^{16}.3^{12}}\)
\(=\frac{2^{20}.3^{12}+3^{12}.2^{15}}{2^{15}.3^{12}.3-3^{12}.2^{16}}\)
\(=\frac{2^4}{3}\)
\(a,=\dfrac{14}{13}-\dfrac{1}{13}-\dfrac{19}{20}\\ =1-\dfrac{19}{20}=\dfrac{20}{20}-\dfrac{19}{20}\\ =\dfrac{1}{20}\\ b,=\dfrac{-24}{17}+\dfrac{7}{17}+\dfrac{1}{16}\\ =-1+\dfrac{1}{16}\\ =\dfrac{-16}{16}+\dfrac{1}{16}=\dfrac{-15}{16}\)
\(1.\dfrac{-7}{18}+\dfrac{-5}{12}-\dfrac{-13}{18}\text{=}\left(\dfrac{-7}{18}-\dfrac{-13}{18}\right)+\dfrac{-5}{12}\text{=}\dfrac{1}{3}+\dfrac{-5}{12}\text{=}\dfrac{-1}{12}\)
\(2.\dfrac{-13}{17}+\dfrac{-13}{21}+\dfrac{-4}{17}\text{=}\left(\dfrac{-13}{17}+\dfrac{-4}{17}\right)+\dfrac{-13}{21}\text{=}-1+\dfrac{-13}{21}\text{=}\dfrac{-34}{21}\)
\(3.\dfrac{-13}{10}-\dfrac{-4}{13}+\dfrac{-11}{10}\text{=}\dfrac{-12}{5}-\dfrac{-4}{13}\text{=}\dfrac{-136}{65}\)
\(4.\dfrac{13}{17}\times\left(\dfrac{-4}{5}+\dfrac{-3}{4}\right)\text{=}\dfrac{13}{17}\times\dfrac{-31}{20}\text{=}\dfrac{-403}{340}\)
\(5.\left(\dfrac{-5}{12}\times\dfrac{-9}{20}\right)\times\dfrac{-7}{17}\text{=}\dfrac{3}{16}\times\dfrac{-7}{17}\text{=}\dfrac{-21}{272}\)
\(6.\dfrac{11}{23}\times\left(\dfrac{5}{9}+\dfrac{17}{9}-\dfrac{13}{9}\right)\text{=}\dfrac{11}{23}\times1\text{=}\dfrac{11}{23}\)
\(=\left(-17\right)\cdot3=-51\)