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a) \(\left(\frac{1}{3}+\frac{1}{5}\right)+\left(\frac{1}{6}-\frac{1}{5}\right)=\left(\frac{1}{3}+\frac{1}{6}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)=\frac{1}{2}\)
b) \(\frac{3}{16}\times\frac{7}{5}+\frac{3}{5}\times\frac{9}{16}=\frac{21}{80}+\frac{27}{80}=\frac{48}{80}=\frac{3}{5}\)
c) \(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{2020\times2021}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2020}-\frac{1}{2021}\)
\(=1-\frac{1}{2021}=\frac{2020}{2021}\)
d) \(\frac{1}{1\times3}+\frac{1}{3\times5}+...+\frac{1}{2021\times2023}=\frac{1}{2}\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+...+\frac{2}{2021\times2023}\right)\)
\(=\frac{1}{2}\times\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2021}-\frac{1}{2023}\right)\)
\(=\frac{1}{2}\times\left(1-\frac{1}{2023}\right)=\frac{1}{2}\times\frac{2022}{2023}=\frac{1011}{2023}\)
e) \(\frac{3}{2}\times\frac{1}{7}\times\frac{5}{4}+\frac{15}{2}\times\frac{6}{7}\times\frac{1}{4}==\frac{15}{56}+\frac{80}{56}=\frac{95}{56}\)
Cửa hàng đã bán:
420 x 25% = 105(kg)
Lượng gạo cửa hàng còn lại sau bán:
420 - 105= 315 (kg)
\(\left(\dfrac{5}{6}+\dfrac{7}{x}\right)-\dfrac{16}{12}=\dfrac{2}{3}\)
\(\Rightarrow\dfrac{5}{6}+\dfrac{7}{x}=\dfrac{2}{3}+\dfrac{16}{12}=\dfrac{8}{12}+\dfrac{16}{12}=\dfrac{24}{12}=2\)
\(\Rightarrow\dfrac{7}{x}=2-\dfrac{5}{6}=\dfrac{12}{6}-\dfrac{5}{6}=\dfrac{7}{6}\)
=> x = 6
(\(\dfrac{5}{6}\) + \(\dfrac{7}{x}\)) - \(\dfrac{16}{12}\) = \(\dfrac{2}{3}\)
\(\dfrac{5}{6}\) + \(\dfrac{7}{x}\) = \(\dfrac{2}{3}\) + \(\dfrac{16}{12}\)
\(\dfrac{5}{6}\) + \(\dfrac{7}{x}\) = 2
\(\dfrac{7}{x}\) = 2 - \(\dfrac{5}{6}\)
\(\dfrac{7}{x}\) = \(\dfrac{1}{6}\)
\(x\) = 6 x (7 : 1)
\(x\) = 6 x 7
\(x\) = 42
#Yu
b)0,5x+2/3x+2/3=7/2
1/2x+2/3x+2/3=7/2
x(1/2+2/3)+2/3=7/12
x.7/6+2/3 =7/12
x.7/6 =7/12-2/3
x.7/6 =-1/12
x =-1/12:7/6
x =-1/14
b)3/5-2/15:x=1/2
2/15:x =3/5-1/2
2/15:x =1/10
x =2/15:1/10
x = 4/3
\(\frac{2}{5}\times\frac{1}{2}-\frac{2}{5}\times\frac{1}{3}-\frac{2}{5}\times\)\(\frac{1}{6}\)
\(=\frac{2}{5}\times\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)
\(=\frac{2}{5}\times\frac{0}{6}\)
\(=\frac{2}{5}\times0\)
\(=0\)
\(\frac{2}{5}\times\frac{1}{2}-\frac{2}{5}\times\frac{1}{3}-\frac{2}{5}\times\frac{1}{6}\)
\(=\frac{2}{5}\times\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)
\(=\frac{2}{5}\times0\)
\(=0\)
Ta có:
\(A=10\times\left(1-\frac{1}{2}+1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+...+1-\frac{1}{90}\right)\)
\(=10\times\left[9-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)\right]\)
\(=10\times\left[9-\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{9\times10}\right)\right]\)
\(=10\times\left[9-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\right]\)
\(=10\times\left[9-\left(1-\frac{1}{10}\right)\right]\)
\(=10\times\left(9-\frac{9}{10}\right)\)
\(=10\times\frac{81}{10}\)
\(=81\)
Vậy; A = 81
=.= hk tốt!!
5/6 : x + 1/2 : 1/6 = 6 .
5/6 : x + 3 = 6 .
5/6 : x = 6 - 3 .
5/6 : x = 3 .
x = 5/6 : 3 .
x = 5/18 .
Vậy x = 5/18 .
`5/6 : x + 1/2 : 1/6=6`
`5/6 : x + 3=6`
`5/6 :x= 3`
`x=5/6 : 3`
`x=5/18`