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a, Ta có : 5 < 7 nên \(\frac{1}{5}>\frac{1}{7}\)
b, Ta có : \(\frac{-3}{4}=\frac{\left(-3\right).5}{4.5}=\frac{-15}{20};\frac{2}{5}=\frac{2.4}{5.4}=\frac{8}{20}\)
Vì ( -15 ) < 8 nên \(\frac{-15}{20}< \frac{8}{20}\)hay \(\frac{-3}{4}< \frac{2}{5}\)
c, Ta có : \(\frac{-5}{7}=\frac{\left(-5\right).2}{7.2}=\frac{-10}{14};\frac{-3}{14}=\frac{-3}{14}\)
Vì ( -10 ) < ( -3 ) nên \(\frac{-10}{14}< \frac{-3}{14}\)hay \(\frac{-5}{7}< \frac{-3}{14}\)
cách này mình tự nghĩ
\(\hept{\begin{cases}A=\frac{4}{7}+5+\frac{3}{7^2}+\frac{5}{7^3}+\frac{6}{7^4}\\B=\frac{5}{7^4}+5+\frac{6}{7^2}+\frac{4}{7}+\frac{5}{7^3}\end{cases}}\)
\(\Rightarrow A-B=\left(\frac{4}{7}-\frac{4}{7}\right)+\left(\frac{5}{7^3}-\frac{5}{7^3}\right)+\left(5-5\right)+\left(\frac{3}{7^2}-\frac{6}{7^2}\right)+\left(\frac{6}{7^4}-\frac{5}{7^4}\right)\)
\(\Rightarrow A-B=-\frac{3}{7^2}+\frac{1}{7^4}\)
\(\Rightarrow A-B=\frac{-3\times7^2}{7^4}+\frac{1}{7^4}\)
mà \(-3\times7^2< 1\Rightarrow\frac{1}{7^4}>\frac{-3\times7^2}{7^4}\Rightarrow B>A\)
a: \(\dfrac{6}{7}:\left(\dfrac{2}{5}\cdot\dfrac{6}{7}\right)\)
\(=\dfrac{6}{7}:\dfrac{12}{35}\)
\(=\dfrac{6}{7}\cdot\dfrac{35}{12}=\dfrac{6}{12}\cdot\dfrac{35}{7}=\dfrac{5}{2}\)
b: \(\dfrac{6}{7}+\dfrac{5}{7}:5-\dfrac{8}{9}\)
\(=\dfrac{6}{7}+\dfrac{1}{7}-\dfrac{8}{9}\)
\(=1-\dfrac{8}{9}=\dfrac{1}{9}\)
c: \(\dfrac{6}{7}+\dfrac{5}{8}\cdot\dfrac{1}{5}-\dfrac{3}{16}\cdot4\)
\(=\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{3}{4}\)
\(=\dfrac{48+7-42}{56}=\dfrac{13}{56}\)
d: \(\dfrac{-1}{6}+\dfrac{2}{3}\cdot\dfrac{-3}{4}+\dfrac{4}{5}\)
\(=-\dfrac{1}{6}-\dfrac{1}{2}+\dfrac{4}{5}\)
\(=\dfrac{-5-15+24}{30}=\dfrac{4}{30}=\dfrac{2}{15}\)
