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3 tháng 6 2022
\(=\dfrac{1}{2}-\left(\dfrac{1}{3\cdot7}+\dfrac{1}{7\cdot11}+...+\dfrac{1}{23\cdot27}\right)\)
\(=\dfrac{1}{2}-\dfrac{1}{4}\left(\dfrac{4}{3\cdot7}+\dfrac{4}{7\cdot11}+...+\dfrac{4}{23\cdot27}\right)\)
\(=\dfrac{1}{2}-\dfrac{1}{4}\left(\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+...+\dfrac{1}{23}-\dfrac{1}{27}\right)\)
\(=\dfrac{1}{2}-\dfrac{1}{4}\cdot\dfrac{9-1}{27}\)
\(=\dfrac{1}{2}-\dfrac{1}{4}\cdot\dfrac{8}{27}=\dfrac{1}{2}-\dfrac{2}{27}=\dfrac{27-4}{54}=\dfrac{23}{54}\)
Y
6 tháng 6 2023
\(\dfrac{\dfrac{1}{3}+\dfrac{1}{7}-\dfrac{1}{23}}{\dfrac{2}{3}+\dfrac{2}{7}-\dfrac{2}{23}}\times\dfrac{\dfrac{1}{3}-0,25-0,2}{1\dfrac{1}{6}-0,875-0,7}\)
\(=\dfrac{\dfrac{1}{3}+\dfrac{1}{7}-\dfrac{1}{23}}{\dfrac{1}{3}+\dfrac{1}{3}+\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{23}-\dfrac{1}{23}}\times\dfrac{\dfrac{1}{3}-\dfrac{1}{4}-\dfrac{1}{5}}{\dfrac{7}{6}-\dfrac{7}{8}-\dfrac{7}{10}}\)
\(=\dfrac{\dfrac{1}{3} +\dfrac{1}{7}-\dfrac{1}{23}}{\dfrac{1}{3}\times2+\dfrac{1}{7}\times2-\dfrac{1}{23}\times2}\times\dfrac{\dfrac{2}{6}-\dfrac{2}{8}-\dfrac{2}{10}}{7\times\left(\dfrac{1}{6}-\dfrac{1}{8}-\dfrac{1}{10}\right)}\)
\(=\dfrac{\dfrac{1}{3}+\dfrac{1}{7}-\dfrac{1}{23}}{2\times\left(\dfrac{1}{3}+\dfrac{1}{7}-\dfrac{1}{23}\right)}\times\dfrac{2\times\left(\dfrac{1}{6}-\dfrac{1}{8}-\dfrac{1}{10}\right)}{7\times\left(\dfrac{1}{6}-\dfrac{1}{8}-\dfrac{1}{10}\right)}\)
\(=\dfrac{1}{2}\times\dfrac{2}{7}\)
\(=\dfrac{1}{7}\)
DL
2
FC
14 tháng 10 2018
Bài 1:
a, Ta có: \(\dfrac{27}{23}+\dfrac{5}{21}-\dfrac{4}{23}+\dfrac{16}{21}+\dfrac{1}{2}\)
= \(\left(\dfrac{27}{23}-\dfrac{4}{23}\right)+\left(\dfrac{5}{21}+\dfrac{16}{21}\right)+\dfrac{1}{2}\)
=\(\dfrac{23}{23}+\dfrac{21}{21}+\dfrac{1}{2}\) = \(1+1+\dfrac{1}{2}\)
= \(2\dfrac{1}{2}\)
NT
9
9 tháng 10 2019
Tùy bạn sao cũng được nhuwng giải theo cách lớp 7 cho mình với
26 tháng 3 2020
a) Ta có: \(\frac{7}{8}+\frac{15}{23}+\frac{1}{8}+\left(-\frac{15}{23}\right)+\frac{1}{3}\)
\(=\left(\frac{7}{8}+\frac{1}{8}\right)+\left(\frac{15}{23}-\frac{15}{23}\right)+\frac{1}{3}\)
\(=1+\frac{1}{3}=\frac{4}{3}\)
b) Ta có: \(\frac{3-\frac{2}{3}}{\frac{1}{3}-3}\)
\(=\left(3-\frac{2}{3}\right)\cdot\frac{1}{\frac{1}{3}-3}=\left(3-\frac{2}{3}\right)\cdot\frac{1}{-\frac{8}{3}}\)
\(=\left(3-\frac{2}{3}\right)\cdot\frac{-3}{8}\)
\(=-\frac{9}{8}+\frac{1}{4}=\frac{-9}{8}+\frac{2}{8}=-\frac{7}{8}\)
c) Ta có: \(8\cdot\left(-\frac{1}{2}\right)^3+3\cdot\left(-\frac{1}{2}\right)^2-0,75\)
\(=8\cdot\frac{-1}{8}+3\cdot\frac{1}{4}-\frac{3}{4}\)
\(=-1\)
XO
1 tháng 1 2020
A = \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{23.24.25}\)
= \(\frac{1}{2}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{23.24.25}\right)\)
= \(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{23.24}-\frac{1}{24.25}\right)\)
= \(\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{24.25}\right)=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{600}\right)=\frac{1}{2}.\frac{299}{600}=\frac{299}{1200}\)
LT
1
6 tháng 12 2018
1, \(\frac{5}{21}+0,5-\frac{19}{23}+\frac{16}{21}-\frac{4}{23}\)
\(=\frac{5+16}{21}-\frac{19+4}{23}+0,5\)
\(=1-1+0,5\)
\(=0,5\)
2,\(\frac{27}{23}+\frac{5}{21}-\frac{4}{23}+\frac{6}{21}+\frac{1}{2}\)
\(=\frac{27-4}{23}+\frac{5+6}{21}+\frac{1}{2}\)
\(=1+\frac{11}{21}+\frac{1}{2}\)
\(=\frac{42+22+21}{42}\)
\(=\frac{85}{42}\)
1- { 1 : [8 + 1 - 1/4]}
= 1 - {1 : 35/4}
= 1 - 4/35
= 31/35
1-{1:[23+1-(-1/2)2]}
=1-{1:[8+1-1/4]}
=1-{1:[9-1/4]}
=1-{1:35/4}
=1-4/35
=31/35