Tính nhanh bằng cách thuận tiện nhất
a) 10,11+11,12+11,13+...+98,99+99,10
b) \(\frac{1}{1\cdot6}\cdot\frac{1}{6\cdot11}\cdot\frac{1}{11\cdot16}\cdot...\cdot\frac{1}{491\cdot496}\cdot\frac{1}{496\cdot501}\)
Những câu hỏi liên quan
\(\sqrt[2]{4\cdot9\frac{8}{8}+\frac{48\cdot11+5}{1\cdot\frac{814}{5+\frac{6145}{1\cdot\frac{821}{614}}}}}2548-\frac{8452}{14\cdot\frac{58}{96\cdot\frac{41}{\frac{24}{1\cdot\frac{975545}{1421+\frac{84874}{\frac{1+2+3+4+5+6+7+8+9\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9}{2\cdot\frac{2}{1}}}}}}}}\)
TÍNH BẰNG CÁCH THUẬN TIỆN NHẤT
A)\(\frac{2}{3}\cdot\frac{4}{5}+\frac{1}{3}\cdot\frac{4}{5}=\)
B)\(\frac{1}{2}:\frac{3}{4}+\frac{1}{6}:\frac{3}{4}=\)
C)\(\frac{2}{3}\cdot\frac{4}{5}-\frac{1}{3}\cdot\frac{4}{5}=\)
D)\(\frac{1}{2}:\frac{3}{4}-\frac{1}{6}:\frac{3}{4}=\)
\(\frac{2}{3}.\frac{4}{5}+\frac{1}{3}.\frac{4}{5}=\frac{4}{5}\left(\frac{2}{3}+\frac{1}{3}\right)=\frac{4}{5}.\frac{3}{3}=\frac{4}{5}.1=\frac{4}{5}\)
\(\frac{1}{2}:\frac{3}{4}+\frac{1}{6}:\frac{3}{4}=\frac{3}{4}:\left(\frac{1}{2}+\frac{1}{6}\right)=\frac{3}{4}:\frac{2}{3}=\frac{9}{8}\)
\(\frac{2}{3}.\frac{4}{5}-\frac{1}{3}.\frac{4}{5}=\frac{4}{5}\left(\frac{2}{3}-\frac{1}{3}\right)=\frac{4}{5}.\frac{1}{3}=\frac{4}{15}\)
\(\frac{1}{2}:\frac{3}{4}-\frac{1}{6}:\frac{3}{4}=\frac{3}{4}:\left(\frac{1}{2}-\frac{1}{6}\right)=\frac{3}{4}:\frac{1}{3}=\frac{9}{4}\)
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\(\frac{2}{3}.\frac{4}{5}+\frac{1}{3}.\frac{4}{5}=\left(\frac{2}{3}+\frac{1}{3}\right).\frac{4}{5}=1.\frac{4}{5}=\frac{4}{5}\)
\(\frac{1}{2}:\frac{3}{4}+\frac{1}{6}:\frac{3}{4}=\frac{1}{2}.\frac{4}{3}+\frac{1}{6}.\frac{4}{3}=\left(\frac{1}{2}+\frac{1}{6}\right).\frac{4}{3}=\frac{2}{3}.\frac{4}{3}=\frac{8}{9}\)
c,d tương tự
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A) \(\frac{2}{3}\). \(\frac{4}{5}\)+ \(\frac{1}{3}\). \(\frac{4}{5}\) B) \(\frac{1}{2}\). \(\frac{4}{5}\)+ \(\frac{1}{6}\): \(\frac{3}{4}\) C) \(\frac{2}{3}\). \(\frac{4}{5}\)- \(\frac{1}{3}\). \(\frac{4}{5}\)
= \(\left(\frac{2+1}{3}\right)\). \(\frac{4}{5}\) = \(\frac{2}{5}\)+ \(\frac{2}{9}\) = \(\frac{2}{3}\)- \(\frac{1}{3}\). \(\left(\frac{4-4}{5}\right)\)
= 1 . \(\frac{4}{5}\) = \(\frac{28}{45}\) = \(\frac{1}{3}\). 0
= \(\frac{4}{5}\) = 0
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Giải phương trình
\(\left(\frac{1}{1\cdot51}+\frac{1}{2\cdot52}+\frac{1}{3\cdot53}+\cdot\cdot\cdot+\frac{1}{10\cdot60}\right)\cdot x=\frac{1}{1\cdot11}+\frac{1}{2\cdot12}+\cdot\cdot\cdot+\frac{1}{50\cdot60}\)
tính bằng cách thuận tiện nhất
a,\(\frac{6}{7}\cdot\frac{16}{15}\cdot\frac{7}{6}\cdot\frac{21}{32}\)b, \(\frac{21}{17}\cdot\frac{13}{14}\cdot56\cdot\frac{3}{42}\) c,\(\frac{7}{4}\cdot\frac{11}{21}+\frac{11}{21}\cdot\frac{5}{4}\) d,\(\frac{23}{14}\cdot\frac{6}{14}-\frac{9}{14}\cdot\frac{6}{13}\)
a, \(\frac{6}{7}.\frac{16}{15}.\frac{7}{6}.\frac{21}{32}=\frac{6}{7}.\frac{7}{6}.\frac{16}{15}.\frac{21}{32}\)=\(1.\frac{16}{15}.\frac{21}{32}=\frac{7}{5.2}=\frac{7}{10}\)
Phần b T2
c,\(\frac{7}{4}.\frac{11}{21}+\frac{11}{21}.\frac{5}{4}=\frac{11}{21}.\left(\frac{7}{4}+\frac{5}{4}\right)\)=\(\frac{11}{21}.3=\frac{11}{7}\)
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Giải phương trình
\(\left(\frac{1}{1\cdot51}+\frac{1}{2\cdot52}+\frac{1}{3\cdot53}+\cdot\cdot\cdot+\frac{1}{10\cdot60}\right)x=\frac{1}{1\cdot11}+\frac{1}{2\cdot12}+\cdot\cdot\cdot+\frac{1}{50\cdot60}\)
Tính nhanh
\(\frac{4\cdot5\cdot6\cdot7}{14\cdot15\cdot16}\)
\(\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot\frac{5}{6}\)
giúp mình với
\(\frac{4.5.6}{14.15.16}\)=\(\frac{1.1.3}{7.3.4}\)=\(\frac{1.1.1}{7.1.4}\)=\(\frac{1}{28}\)
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\(\frac{4.5.6.7}{14.15.16.17}=\frac{2.2.5.2.3.7}{2.7.3.5.2.2.2.17}=\frac{1}{2.17}=\frac{1}{34}\) ( Gạch bỏ thừa số giống nhau)
\(\frac{2}{3}.\frac{3}{4}.\frac{4}{5}.\frac{5}{6}=\frac{2.3.4.5}{3.4.5.6}=\frac{1}{3}\)( Gạch bỏ thừa số giống nhau)
Tíc mình nha!
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\(\frac{1^2}{1\cdot2}\cdot\frac{2^2}{2\cdot3}\cdot\frac{3^2}{3\cdot4}\cdot\cdot\cdot\cdot\frac{10^2}{10\cdot11}\)
Tính
\(M=1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+\cdot\cdot\cdot\cdot+\frac{1}{16}\left(1+2+3+\cdot\cdot\cdot16\right)\)
giúp mình với
Tinh bằng cách thuật tiện nhất
\(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot\frac{5}{6}\)
\(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot\frac{5}{6}=\frac{1\cdot2\cdot3\cdot4\cdot5}{2\cdot3\cdot4\cdot5\cdot6}=\frac{1}{6}\)
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\(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}.\frac{5}{6}\)
= \(\frac{1.2.3.4.5}{2.3.4.5.6}\)
= \(\frac{1}{6}\)
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\(\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{5}{6}=\frac{1.2.3.4.5}{2.3.4.5.6}=\frac{1}{6}\)
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