tính 1+ \(\dfrac{6}{1+\dfrac{6}{1+\dfrac{6}{1+\dfrac{6}{1+..}}}}\)
K
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GL
24 tháng 8 2023
a) \(1+\dfrac{4}{9}=\dfrac{9}{9}+\dfrac{4}{9}=\dfrac{9+4}{9}=\dfrac{13}{9}\)
b) \(5+\dfrac{1}{2}=\dfrac{10}{2}+\dfrac{1}{2}=\dfrac{10+1}{2}=\dfrac{11}{2}\)
c) \(3-\dfrac{5}{6}=\dfrac{18}{6}-\dfrac{5}{6}=\dfrac{18-5}{6}=\dfrac{13}{6}\)
d) \(\dfrac{31}{7}-2=\dfrac{31}{7}-\dfrac{14}{7}=\dfrac{31-14}{7}=\dfrac{17}{7}\)
4 tháng 1 2023
\(M=\dfrac{6}{10.13}+\dfrac{6}{13.16}+\dfrac{6}{16.19}+\dfrac{6}{19.21}\)
\(\dfrac{1}{2}M=\dfrac{3}{10.13}+\dfrac{3}{13.16}+\dfrac{3}{16.19}+\dfrac{3}{19.21}\)
\(\dfrac{1}{6}M=\dfrac{1}{10}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{21}\)
\(\dfrac{1}{6}M=\dfrac{1}{10}-\dfrac{1}{21}\)
\(M=\dfrac{11}{210}:\dfrac{1}{6}=\dfrac{11}{35}\)
\(N=\dfrac{1}{20}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{26}+\dfrac{1}{26}-\dfrac{1}{29}+\dfrac{1}{29}-\dfrac{1}{30}\)
\(=\dfrac{1}{20}-\dfrac{1}{30}\)
\(=\dfrac{1}{60}\)
\(\dfrac{M}{N}=\dfrac{11}{35}:\dfrac{1}{60}=\dfrac{132}{7}\)= \(\dfrac{132}{25}\)
AH
Akai Haruma
Giáo viên
17 tháng 9 2023
Lời giải:
1.
$3\frac{1}{4}-2\frac{1}{3}=3+\frac{1}{4}-(2+\frac{1}{3})$
$=3-2+\frac{1}{4}-\frac{1}{3}$
$=1+\frac{1}{4}-\frac{1}{3}=\frac{5}{4}-\frac{1}{3}=\frac{11}{12}$
2.
$6\frac{5}{9}+2\frac{5}{6}=6+\frac{5}{9}+2+\frac{5}{6}=8+\frac{5}{6}+\frac{5}{9}=8+\frac{25}{18}=8+1+\frac{7}{18}=9+\frac{7}{18}=9\frac{7}{18}$
3.
$6\frac{5}{9}-2\frac{5}{6}=6+\frac{5}{9}-(2+\frac{5}{6})$
$=6+\frac{5}{9}-2-\frac{5}{6}$
$=(6-2)+\frac{5}{9}-\frac{5}{6}$
$=4+\frac{5}{9}-\frac{5}{6}=\frac{41}{9}-\frac{5}{6}=\frac{67}{8}$
MH
8 tháng 5 2022
\(\dfrac{13}{7}+\dfrac{5}{6}+\dfrac{2}{7}+\dfrac{7}{6}=\dfrac{15}{7}+\dfrac{12}{6}=\dfrac{29}{7}\)
\(\dfrac{1}{2}\times\dfrac{5}{6}+\dfrac{1}{2}\times\dfrac{11}{6}=\dfrac{1}{2}\times\left(\dfrac{5}{6}+\dfrac{11}{6}\right)=\dfrac{1}{2}\times\dfrac{16}{6}=\dfrac{4}{3}\)
3 tháng 8 2023
` a/`
` 2 - 1 5/6 + 2 2/3 = 2 - 11/6 - 8/3 = 1/6+ 8/3 = 1/6 + 16/6 = 17/6 `
`b/`
`5/9 xx ( 2 5/6 - 1 2/3 ) = 5/9 xx ( 17/6 - 5/3 ) = 5/9 xx 7/6 = 35/54 `
`c/`
` 1 1/3 : ( 2 + 1 1/6 : 2 5/6 ) `
`= 4/3 : ( 2 + 7/6 : 17/6 ) `
`= 4/3 : ( 2 + 7/6 xx 6/17 )`
`= 4/3 : ( 2 + 7/17 ) `
`= 4/3 : ( 34/17 + 7/17 ) `
`= 4/3 : 41/17 `
`= 4/3 xx 17/41 `
`= 68/123`
` d/`
` 2 3/5 : 3/4 xx 1 4/5 = 13/5 xx 4/3 xx 9/5 =52/15 xx 9/5 = 156/25`
24 tháng 2 2022
a, \(=\dfrac{1+4}{5}+\dfrac{5+1+3}{9}=1+1=2\)
b, \(=\dfrac{1+4+2}{3}+\dfrac{1+2+5}{6}=\dfrac{6}{3}+\dfrac{8}{6}=2+\dfrac{4}{3}=\dfrac{6+4}{3}=\dfrac{10}{3}\)
CC
3 tháng 10 2018
\(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{8}-\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{7}\)
\(\left(\dfrac{1}{2}-\dfrac{1}{2}\right)+\left(-\dfrac{1}{3}+\dfrac{1}{3}\right)+\left(\dfrac{1}{4}-\dfrac{1}{4}\right)+\left(-\dfrac{1}{5}+\dfrac{1}{5}\right)+\left(\dfrac{1}{6}-\dfrac{1}{6}\right)+\left(\dfrac{-1}{7}+\dfrac{1}{7}\right)+\dfrac{1}{8}\)
=0+0+0+0+0+0+\(\dfrac{1}{8}\)
=\(\dfrac{1}{8}\)