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1-\(\left(3\frac{3}{8}+x-2\frac{5}{24}\right)\)\(.\frac{12}{17}=0\)
\(\Rightarrow\left(3\frac{3}{8}+x-2\frac{5}{24}\right)\)\(.\frac{12}{17}\)\(=1\)
\(\frac{27}{8}+x-\frac{53}{24}\) \(=1:\frac{12}{17}\)
\(\frac{27}{8}+x=\frac{17}{12}+\frac{53}{24}\)
\(\frac{27}{8}+x=\frac{34+53}{24}\)
\(\frac{27}{8}+x=\frac{87}{24}\)
\(x=\frac{87}{24}-\frac{27}{8}\)
\(x=\frac{87-81}{24}\)
\(x=\frac{6}{24}=\frac{1}{4}\)
\(\frac{2}{3}.\frac{4}{5}+\frac{1}{3}.\frac{4}{5}=\frac{4}{5}\left(\frac{2}{3}+\frac{1}{3}\right)=\frac{4}{5}.\frac{3}{3}=\frac{4}{5}.1=\frac{4}{5}\)
\(\frac{1}{2}:\frac{3}{4}+\frac{1}{6}:\frac{3}{4}=\frac{3}{4}:\left(\frac{1}{2}+\frac{1}{6}\right)=\frac{3}{4}:\frac{2}{3}=\frac{9}{8}\)
\(\frac{2}{3}.\frac{4}{5}-\frac{1}{3}.\frac{4}{5}=\frac{4}{5}\left(\frac{2}{3}-\frac{1}{3}\right)=\frac{4}{5}.\frac{1}{3}=\frac{4}{15}\)
\(\frac{1}{2}:\frac{3}{4}-\frac{1}{6}:\frac{3}{4}=\frac{3}{4}:\left(\frac{1}{2}-\frac{1}{6}\right)=\frac{3}{4}:\frac{1}{3}=\frac{9}{4}\)
\(\frac{2}{3}.\frac{4}{5}+\frac{1}{3}.\frac{4}{5}=\left(\frac{2}{3}+\frac{1}{3}\right).\frac{4}{5}=1.\frac{4}{5}=\frac{4}{5}\)
\(\frac{1}{2}:\frac{3}{4}+\frac{1}{6}:\frac{3}{4}=\frac{1}{2}.\frac{4}{3}+\frac{1}{6}.\frac{4}{3}=\left(\frac{1}{2}+\frac{1}{6}\right).\frac{4}{3}=\frac{2}{3}.\frac{4}{3}=\frac{8}{9}\)
c,d tương tự
=2,(6) có chu kì vì phép tính có dư
nếu đổi ra phân số là:\(\frac{8}{3}\)
\(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot\frac{5}{6}=\frac{1\cdot2\cdot3\cdot4\cdot5}{2\cdot3\cdot4\cdot5\cdot6}=\frac{1}{6}\)
\(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}.\frac{5}{6}\)
= \(\frac{1.2.3.4.5}{2.3.4.5.6}\)
= \(\frac{1}{6}\)
Ta có:
\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{99}\right).\left(1-\frac{1}{100}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...\frac{98}{99}.\frac{99}{100}\) \(=\frac{1.2.3...98.99}{2.3.4...99.100}=\frac{1}{100}\)
nha
A=\(\frac{1}{2}\).\(\frac{2}{3}\)....\(\frac{2012}{2013}\)=\(\frac{1}{2013}\)
B=\(\frac{2012}{2012.2013}\)=\(\frac{1}{2013}\)
vậy A=B
\(\frac{\frac{1}{4}+\frac{1}{24}+\frac{1}{124}}{\frac{3}{4}+\frac{3}{24}+\frac{3}{124}}+\frac{\frac{2}{7}+\frac{2}{17}+\frac{2}{127}}{\frac{3}{7}+\frac{3}{17}+\frac{3}{127}}=\frac{\frac{1}{4}+\frac{1}{24}+\frac{1}{124}}{3\left(\frac{1}{4}+\frac{1}{24}+\frac{1}{124}\right)}+\frac{2\left(\frac{1}{7}+\frac{1}{17}+\frac{1}{127}\right)}{3\left(\frac{1}{7}+\frac{1}{17}+127\right)}=\frac{1}{3}+\frac{2}{3}=\) \(1\)
\(\frac{3}{4}\cdot\frac{15}{17}+\frac{3}{4}\cdot\frac{2}{17}+\frac{1}{17}\)
\(=\frac{3}{4}\cdot\left(\frac{15}{17}+\frac{2}{17}\right)+\frac{1}{17}\)
\(=\frac{3}{4}\cdot1+\frac{1}{17}\)
\(=\frac{5}{8}\)
\(\frac{3}{4}.\frac{15}{17}+\frac{3}{4}.\frac{2}{17}+\frac{1}{17}\)
=\(\frac{3}{4}.\left(\frac{15}{17}+\frac{2}{17}\right)+\frac{1}{17}\)
=\(\frac{3}{4}.1+\frac{1}{17}\)
=\(\frac{51}{68}+\frac{4}{68}=\frac{55}{68}\)