7 / 15 < 14 / ... < 7 / 14
K
Khách
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19 tháng 5 2020
Ta có: \(\frac{15}{14}\left(\frac{14}{9}-\frac{3}{7}\right)-\frac{15}{14}\left(\frac{14}{6}-\frac{3}{7}\right)\)
\(=\frac{15}{14}\left[\left(\frac{14}{9}-\frac{3}{7}\right)-\left(\frac{14}{6}-\frac{3}{7}\right)\right]\)
\(=\frac{15}{14}\left(\frac{14}{9}-\frac{3}{7}-\frac{14}{6}+\frac{3}{7}\right)\)
\(=\frac{15}{14}\left(\frac{14}{9}-\frac{14}{6}\right)\)
\(=\frac{15}{14}\cdot\left(\frac{28}{18}-\frac{42}{18}\right)\)
\(=\frac{15}{14}\cdot\frac{-14}{18}\)
\(=\frac{-15}{18}=-\frac{5}{6}\)
30 tháng 9 2017
\(\frac{5\cdot\left(3\cdot7^{15}-19\cdot7^{14}\right)}{7^{16}+3\cdot7^{14}}=\frac{5\cdot\left(3\cdot7-19\right)\cdot7^{14}}{\left(7^2+3\right)\cdot7^{14}}=\frac{5\cdot2\cdot7^{14}}{52\cdot7^{14}}=\frac{5\cdot2}{52}=\frac{5\cdot2}{26\cdot2}=\frac{5}{26}\)
NK
8
NN
1
9 tháng 7 2021
\(\dfrac{\dfrac{7}{13}+\dfrac{7}{14}-\dfrac{7}{15}}{\dfrac{8}{13}+\dfrac{8}{14}-\dfrac{8}{15}}-\dfrac{\dfrac{5}{11}-\dfrac{5}{13}+\dfrac{5}{15}}{\dfrac{8}{11}-\dfrac{8}{13}+\dfrac{8}{15}}\)
\(=\dfrac{7\left(\dfrac{1}{13}+\dfrac{1}{14}-\dfrac{1}{15}\right)}{8\left(\dfrac{1}{13}+\dfrac{1}{14}-\dfrac{1}{15}\right)}-\dfrac{5\left(\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{15}\right)}{8\left(\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{15}\right)}\)
\(=\dfrac{7}{8}-\dfrac{5}{8}\)
\(=\dfrac{2}{8}=\dfrac{1}{4}\)
MD
4
8 tháng 7 2017
\(A=\dfrac{14}{8.11}+\dfrac{14}{11.14}+\dfrac{14}{14.17}+.....+\dfrac{14}{197.200}\)
\(A=\dfrac{14}{3}\left(\dfrac{1}{8}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{14}+\dfrac{1}{14}-\dfrac{1}{17}+...+\dfrac{1}{197}-\dfrac{1}{200}\right)\)
\(A=\dfrac{14}{3}.\left(\dfrac{1}{8}-\dfrac{1}{200}\right)\)
\(A=\dfrac{14}{3}.\dfrac{24}{200}=\dfrac{28}{25}\)
\(B=\dfrac{7}{15}+\dfrac{7}{35}+\dfrac{7}{63}+...+\dfrac{7}{399}\)
\(B=\dfrac{7}{3.5}+\dfrac{7}{5.7}+\dfrac{7}{7.9}+.....\dfrac{7}{19.21}\)
\(B=\dfrac{7}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+....+\dfrac{1}{19}-\dfrac{1}{21}\right)\)
\(B=\dfrac{7}{2}.\left(\dfrac{1}{3}-\dfrac{1}{21}\right)\)
\(B=\dfrac{7}{2}.\dfrac{6}{21}=1\)
KS
8 tháng 4 2022
9/14 .<.. 11/14 4/25 .<.. 4/23 5/6 ..<. 7/8 1 ..>. 14/15
8/9 ..=. 24/27 20/19 ..>. 20/27 8/7 .>.. 9/8 1 .<..15/14
\(\dfrac{7}{15}< \dfrac{14}{a}< \dfrac{7}{14}\Rightarrow\dfrac{14}{30}< \dfrac{14}{a}< \dfrac{14}{28}\\ \Rightarrow a=29\)
Vậy số đó là \(\dfrac{14}{29}\)
Vậy số đó là 1429