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O
3 tháng 5 2022
a) \(\left(1-\dfrac{1}{3}\right)\times\left(1-\dfrac{2}{5}\right)\times\left(1-\dfrac{2}{7}\right)\times\left(1-\dfrac{2}{9}\right)\)
\(=\left(\dfrac{3}{3}-\dfrac{1}{3}\right)\times\left(\dfrac{5}{5}-\dfrac{2}{5}\right)\times\left(\dfrac{7}{7}-\dfrac{2}{7}\right)\times\left(\dfrac{9}{9}-\dfrac{2}{9}\right)\)
\(=\dfrac{2}{3}\times\dfrac{3}{5}\times\dfrac{5}{7}\times\dfrac{7}{9}\)
\(=\dfrac{2\times3\times5\times7}{3\times5\times7\times9}\)
\(=\dfrac{2}{9}\)
b) \(\dfrac{1}{1\times3}+\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+\dfrac{1}{7\times9}\)
\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}\)
\(=1-\dfrac{1}{9}\)
\(=\dfrac{9}{9}-\dfrac{1}{9}\)
\(=\dfrac{8}{9}\)
O
3 tháng 5 2022
Sửa câu b)
b) \(\dfrac{1}{1\times3}+\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+\dfrac{1}{7\times9}\)
Đặt \(A=\dfrac{1}{1\times3}+\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+\dfrac{1}{7\times9}\)
\(2A=\dfrac{2}{1\times3}+\dfrac{2}{3\times5}+\dfrac{2}{5\times7}+\dfrac{2}{7\times9}\)
\(2A=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}\)
\(2A=1-\dfrac{1}{9}\)
\(2A=\dfrac{9}{9}-\dfrac{1}{9}\)
\(2A=\dfrac{8}{9}\)
\(A=\dfrac{8}{9}:2\)
\(A=\dfrac{8}{18}\)
\(A=\dfrac{4}{9}\)
Vậy : \(\dfrac{1}{1\times3}+\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+\dfrac{1}{7\times9}=\dfrac{4}{9}\)
N
2
T
29 tháng 8 2018
\(x\times7\times9=\frac{10}{3}\)
\(x\times63=\frac{10}{3}\)
\(x=\frac{10}{3}:63\)
\(x=\frac{10}{189}\)
\(x\times\frac{2}{5}=\frac{1}{4}\times4\)
\(x\times\frac{2}{5}=1\)
\(x=1:\frac{2}{5}\)
\(x=\frac{5}{2}\)
\(x:\frac{1}{7}=\frac{1}{2}+\frac{3}{5}\)
\(x:\frac{1}{7}=\frac{11}{10}\)
\(x=\frac{11}{10}\times\frac{1}{7}\)
\(x=\frac{11}{70}\)
\(x:\frac{8}{9}=\frac{2}{9}+5\)
\(x:\frac{8}{9}=\frac{47}{9}\)
\(x=\frac{47}{9}\times\frac{8}{9}\)
\(x=\frac{376}{81}\)
29 tháng 8 2018
a)X x 7x9 = 10/3 b) X x 2/5 =1/4 x4 c)X : 1/7 = 1/2 + 3/5
X \(\times\)7=\(\frac{10}{3}\div9\) X\(\times\frac{2}{5}=1\) \(x\div\frac{1}{7}=\frac{11}{10}\)
X\(\times\)7=\(\frac{10}{27}\) X\(=1\div\frac{2}{5}\) \(x=\frac{11}{10}\times\frac{1}{7}\)
X=\(\frac{10}{27}\)\(\div7\) X\(=\frac{5}{2}\) \(x=\frac{11}{70}\)
X=\(\frac{10}{198}\)
d)X : 8/9 =2/9 +5
\(x\div\frac{8}{9}=\frac{47}{9}\)
\(x=\frac{47}{9}\times\frac{8}{9}\)
\(x=\frac{376}{81}\)
G
4
18 tháng 2 2019
\(B=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{99.101}\)
\(\Rightarrow B=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)
\(\Rightarrow B=1-\frac{1}{101}=\frac{101}{101}-\frac{1}{101}=\frac{100}{101}\)
_Học tốt_
3
TA
2
ND
16 tháng 4 2022
7/4 x 15/7 + 13/7 x 9/4 -7/4 x 2/7
=7/4 x ( 15/7- 2/7) + 13/7 x 9/4
=7/4 x 13/7 + 13/7 x 9/4
=13/7 x (7/4 x 9/4)
=13/7 x 16/4
=13/7 x 4
=52/7
ND
16 tháng 4 2022
7/4 x 15/7 + 13/7 x 9/4 -7/4 x 2/7
=7/4 x ( 15/7- 2/7) + 13/7 x 9/4
=7/4 x 13/7 + 13/7 x 9/4
=13/7 x (7/4 + 9/4)
=13/7 x 16/4
=13/7 x 4
=52/7
NT
2
15 tháng 4 2016
2/3x5 + 2/5x7 + 2/7x9 + ......+ 2/97x99 = 1/3 - 1/5 + 1/5 - 1/7 + 1/7 - 1/9 + ... + 1/97 - 1/99
= 1/3 - 1/99 = 96/3.99 = 32/99
15 tháng 4 2016
\(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{97\cdot99}\)
=\(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{97}-\frac{1}{99}\)
=\(\frac{1}{3}-\frac{1}{99}\)
=\(\frac{32}{99}\)
\(\dfrac{2}{7}\) \(\times\) \(\dfrac{9}{7}\) - \(\dfrac{18}{49}\) \(\times\) \(\dfrac{1}{2}\)
= \(\dfrac{18}{49}\) - \(\dfrac{18}{49}\) \(\times\) \(\dfrac{1}{2}\)
= \(\dfrac{18}{49}\) \(\times\) 1 - \(\dfrac{18}{49}\) \(\times\) \(\dfrac{1}{2}\)
= \(\dfrac{18}{49}\) \(\times\) ( 1 - \(\dfrac{1}{2}\) )
= \(\dfrac{18}{49}\) \(\times\) \(\dfrac{1}{2}\)
= \(\dfrac{18}{98}\)
= \(\dfrac{9}{49}\)