rút gọn các phân số sau
a/ \(\frac{7.25-49}{7.24+21}\)
b/\(\frac{2.\left(-13\right).9.10}{\left(-3\right).4.\left(-5\right).26}\)
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Bài 2:
Ta thấy: 52 > 4.5
62 > 5.6
72 > 6.7
....
20172 > 2016.2017
\(\Rightarrow\)\(\frac{1}{5^2}< \frac{1}{4.5}\)
\(\frac{1}{6^2}< \frac{1}{5.6}\)
\(\frac{1}{7^2}< \frac{1}{6.7}\)
....
\(\frac{1}{2017^2}< \frac{1}{2016.2017}\)
Cộng vế với nhau, ta có:
\(\frac{1}{5^2}+\frac{1}{6^2}+\frac{1}{7^2}+...+\frac{1}{2017^2}\) < \(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{2016.2017}\)
\(\Rightarrow\)A < \(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{2016}-\frac{1}{2017}\)
\(\Rightarrow\)A < \(\frac{1}{4}-\frac{1}{2017}\)
\(\Rightarrow\)A < \(\frac{1}{4}\)( vì \(\frac{1}{2017}>0\))
k giúp mik ✅
a,\(\frac{1}{3}x=-2-\frac{2}{3}=\frac{-8}{3}\)
\(x=\frac{-8}{3}:\frac{1}{3}=\frac{-8}{3}.\frac{3}{1}=-8\)
\(b,\left[x+\frac{1}{1}\right]^2+\frac{5}{6}=\frac{7}{8}\)
\(\Rightarrow\left[x+1\right]^2=\frac{7}{8}-\frac{5}{6}\)
\(\Rightarrow\left[x+1\right]^2=\frac{7\cdot3}{24}-\frac{5\cdot4}{24}\)
\(\Rightarrow\left[x+1\right]^2=\frac{21}{24}-\frac{20}{24}\)
\(\Rightarrow\left[x+1\right]^2=\frac{1}{24}\)
\(\Rightarrow x\in\left\{\varnothing\right\}\)
a, \(\frac{3}{4}\times\frac{4}{7}+\frac{5}{14}\)
\(=\frac{3}{7}+\frac{5}{14}=\frac{6}{14}+\frac{5}{14}=\frac{11}{14}\)
b, \(\frac{5}{14}+\frac{9}{7}\div\frac{3}{4}\)
\(=\frac{5}{14}+\frac{9}{7}\times\frac{4}{3}=\frac{5}{14}+\frac{12}{7}=\frac{5}{14}+\frac{24}{14}=\frac{29}{14}\)
c, \(\frac{12}{17}\div x=\frac{3}{5}\)
\(x=\frac{12}{17}\div\frac{3}{5}=\frac{12}{17}\times\frac{5}{3}=\frac{20}{17}\)
\(\frac{3}{4}X\frac{4}{7}+\frac{5}{14}\)
\(=\frac{3}{7}+\frac{5}{14}\)
\(=\frac{6}{14}+\frac{5}{14}\)
\(=\frac{11}{14}\)
a, \(\frac{7.25-49}{7.24+21}\)
\(=\frac{7.25-7.7}{7.24+7.3}=\frac{7\left(25-7\right)}{7\left(24+3\right)}=\frac{18}{27}=\frac{2}{3}\)
b, \(\frac{2.\left(-13\right).9.10}{\left(-3\right).4.\left(-5\right).26}=\frac{2.\left(-13\right).\left(-3\right).\left(-3\right).\left(-5\right).\left(-2\right)}{\left(-3\right).2.2.\left(-5\right).\left(-13\right).\left(-2\right)}\)
\(=\frac{-3}{2}\)
DỄ LẮM !
a) \(\frac{7\cdot25-49}{7\cdot24+21}=\frac{7\cdot25-7\cdot7}{7\cdot24+7\cdot3}=\frac{7\left(25-7\right)}{7\left(24+3\right)}\)
=\(\frac{18}{27}=\frac{2}{3}\)
b) \(\frac{2\cdot\left(-13\right)\cdot9\cdot10}{\left(-3\right)\cdot4\cdot\left(-5\right)\cdot26}=\frac{-1\cdot2\cdot13\cdot3\cdot3\cdot5\cdot2}{1\cdot3\cdot2\cdot2\cdot5\cdot13\cdot2}=-\frac{3}{2}\)
Chúc bn học tốt !