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D= (1-1/7).(1-2/7).(1-3/7)...(1-10/7
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TD
8 tháng 2 2019
Gọi tích trên là A
Ta có : \(A=\left(1-\frac{1}{7}\right)\times\left(1-\frac{2}{7}\right)\times\left(1-\frac{3}{7}\right)\times.....\times\left(1-\frac{10}{7}\right)\)
\(A=\frac{6}{7}\times\frac{5}{7}\times\frac{4}{7}\times.....\times\frac{-3}{7}\)
\(A=\frac{6\times5\times4\times3\times2\times1\times0\times\left(-1\right)\times\left(-2\right)\times\left(-3\right)}{7}\)
Vì tử số của phân số A có chứa thừa số 0 nên phân số A có tử số là 0
\(\Rightarrow A=\frac{0}{7}\)
\(\Rightarrow A=0\)
DT
1
28 tháng 3 2018
\(D=\left(1-\frac{1}{7}\right).\left(1-\frac{2}{7}\right).\left(1-\frac{3}{7}\right)...\left(1-\frac{10}{7}\right)\)
\(D=\frac{6}{7}.\frac{5}{7}.\frac{4}{7}...\frac{-3}{7}\)
\(D=\frac{6.5.4.3.2.1.0.\left(-1\right).\left(-2\right).\left(-3\right)}{7}\)
\(D=\frac{0}{7}\)
\(D=0\)
10 tháng 1 2022
\(1.\) \(\dfrac{7}{36}-\dfrac{8}{-9}+\dfrac{-2}{3}=\dfrac{7}{36}+\dfrac{8}{9}-\dfrac{2}{3}=\dfrac{7+32-24}{36}=\dfrac{5}{12}.\)
\(2.\) \(\dfrac{-1}{2}+\dfrac{3}{7}-\dfrac{1}{9}+\dfrac{-7}{18}+\dfrac{4}{7}=\dfrac{-9-2-7}{18}+\dfrac{4+3}{7}=\dfrac{-18}{18}+\dfrac{7}{7}=-1+1=0.\)
\(3.\) \(-\dfrac{10}{3}+\dfrac{13}{10}-\dfrac{1}{6}+\dfrac{1}{10}=\dfrac{13+1}{10}+\dfrac{-20-1}{6}=\dfrac{14}{10}+\dfrac{-21}{6}=\dfrac{7}{5}-\dfrac{7}{2}=-\dfrac{21}{10}.\)
\(4.\) \(\dfrac{10}{17}-\dfrac{5}{13}-\left(-\dfrac{7}{17}\right)-\dfrac{8}{13}+\dfrac{11}{25}=\dfrac{10+7}{17}+\dfrac{-5-8}{13}+\dfrac{11}{25}=\dfrac{17}{17}-\dfrac{13}{13}+\dfrac{11}{25}=\dfrac{11}{25}.\)
10 tháng 1 2022
1: \(=\dfrac{7}{36}+\dfrac{32}{36}+\dfrac{-24}{36}=\dfrac{15}{36}=\dfrac{5}{12}\)
2: \(=\left(-\dfrac{1}{2}-\dfrac{1}{9}-\dfrac{7}{18}\right)+\dfrac{3}{7}+\dfrac{4}{7}\)
\(=\dfrac{-9-2-7}{18}+1=-1+1=0\)
3: \(=\left(-\dfrac{10}{3}-\dfrac{1}{6}\right)+\dfrac{14}{10}\)
\(=-\dfrac{21}{6}+\dfrac{14}{10}=\dfrac{-7}{2}+\dfrac{14}{10}=\dfrac{-35+14}{10}=-\dfrac{21}{10}\)
4: \(=\left(\dfrac{10}{17}+\dfrac{7}{17}\right)-\left(\dfrac{5}{13}+\dfrac{8}{13}\right)+\dfrac{11}{25}=\dfrac{11}{25}\)
H
10 tháng 1 2023
`a, 2/3 + 1/5 . 10/7`
`= 2/3 + 10/35`
`=2/3 +2/7`
`=14/21 + 6/21`
`=20/21`
`b, 2/7 + 5/7 . 14/25`
`= 2/7 +2/5`
`= 10/35+14/35`
`= 24/35`
`c, 7/12 - 27/7 . 1/18`
`= 7/12 - 3/14`
`= 31/84`
`d, 3/10 . (-5/6) - 1/8`
`= -1/4 -1/8`
`= -2/8 -1/8`
`= -3/8`
VN
10 tháng 1 2023
a)
\(\dfrac{2}{3}+\dfrac{1}{5}.\dfrac{10}{7}\)
\(=\dfrac{2}{3}+\dfrac{2}{7}\)
\(=\dfrac{14}{21}+\dfrac{6}{21}\)
\(=\dfrac{20}{21}\)
b)
\(\dfrac{2}{7}+\dfrac{5}{7}.\dfrac{14}{25}\)
\(=\dfrac{2}{7}+\dfrac{2}{5}\)
\(=\dfrac{10}{35}+\dfrac{14}{35}\)
\(=\dfrac{24}{35}\)
c)
\(\dfrac{7}{12}-\dfrac{27}{7}.\dfrac{1}{18}\)
\(=\dfrac{7}{12}-\dfrac{3}{14}\)
\(=\dfrac{98}{168}-\dfrac{36}{168}\)
\(=\dfrac{31}{84}\)
d)
\(\dfrac{3}{10}.\left(-\dfrac{5}{6}\right)-\dfrac{1}{8}\)
\(=-\dfrac{1}{4}-\dfrac{1}{8}\)
\(=-\dfrac{2}{8}-\dfrac{1}{8}\)
\(=\dfrac{-3}{8}\)
31 tháng 7 2018
A = ( 6 : 3/5 - 7/6 * 6/7 ) : ( 21/5 * 10/11 + 57/11 )
A = ( 10 - 1 ) : ( 42/11 + 57/11)
A = 9 : 9
A = 1
B = 59 /10 : 3/2 - ( 7/3 * 9/2 - 2 * 7/3 ) : 7/4
B = 59/15 - ( 21/2 - 14/3 ) : 7/4
B = 59/15 - 35/6 : 7/4
B = 59/15 - 10/3
B = 3/5
TT
2
VN
Võ Ngọc Phương
VIP
7 tháng 10 2023
\(\dfrac{4}{7}-\dfrac{1}{7}.\dfrac{10}{13}\)
\(=\dfrac{4}{7}-\dfrac{10}{91}\)
\(=\dfrac{52}{91}-\dfrac{10}{91}\)
\(=\dfrac{42}{91}=\dfrac{6}{13}\)
_______
\(\dfrac{1}{8}+\dfrac{1}{6}:\dfrac{2}{3}\)
\(=\dfrac{1}{8}+\dfrac{1}{6}.\dfrac{3}{2}\)
\(=\dfrac{1}{8}+\dfrac{1}{4}\)
\(=\dfrac{1}{8}+\dfrac{2}{8}\)
\(=\dfrac{3}{8}\)
___________
\(\left(\dfrac{7}{9}-\dfrac{2}{18}\right):\dfrac{4}{7}\)
\(=\left(\dfrac{14}{18}-\dfrac{2}{18}\right).\dfrac{7}{4}\)
\(=\dfrac{12}{18}.\dfrac{7}{4}\)
\(=\dfrac{7}{6}\)
\(#WendyDang\)
AH
Akai Haruma
Giáo viên
7 tháng 10 2023
Lời giải:
$\frac{4}{7}-\frac{1}{7}\times \frac{10}{13}=\frac{1}{7}\times 4-\frac{1}{7}\times \frac{10}{13}$
$=\frac{1}{7}\times (4-\frac{10}{13})=\frac{1}{7}\times \frac{42}{13}$
$=\frac{42}{7\times 13}=\frac{6\times 7}{7\times 13}=\frac{6}{13}$
-----------------
$\frac{1}{8}+\frac{1}{6}: \frac{2}{3}=\frac{1}{8}+\frac{1}{6}\times \frac{3}{2}=\frac{1}{8}+\frac{1}{4}=\frac{1}{8}+\frac{2}{8}=\frac{3}{8}$
------------------
$(\frac{7}{9}-\frac{2}{18}): \frac{4}{7}=(\frac{7}{9}-\frac{1}{9})\times \frac{7}{4}$
$=\frac{6}{9}\times \frac{7}{4}=\frac{2}{3}\times \frac{7}{4}=\frac{7}{6}$
D= (1-1/7).(1-2/7).(1-3/7)...(1-10/7)
= 6/7 . 5/7 . 4/7 ..... ( -3/7)
= \(\frac{6.5.4.3.2.1.0.\left(-1\right).\left(-2\right).\left(-3\right)}{7}\)
Vì só nào nhân với 0 cũng bằng 0
=> \(\frac{6.5.4.3.2.1.0.\left(-1\right).\left(-2\right).\left(-3\right)}{7}\)
= \(\frac{0}{7}=0\)
D=(1-1/7)(1-2/7)...(1-7/7)...(1-10/7)
D=(1-1/7)(1-2/7)...0...(1-10/7)
D=0