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\(\dfrac{18}{17}:9=\dfrac{18}{17}\times\dfrac{1}{9}=\dfrac{18}{153}=\dfrac{2}{17}\)
\(\dfrac{8}{5}-\dfrac{18}{27}=\dfrac{216}{135}-\dfrac{90}{135}=\dfrac{126}{135}=\dfrac{14}{15}\)
\(\dfrac{2}{7}+\dfrac{5}{9}=\dfrac{18}{63}+\dfrac{35}{63}=\dfrac{53}{63}\)
2/3 x 4/5 + 4/5 x 8/3 = 4/5 x (2/3 + 8/3) = 4/5 x 10/3 = 8/3
27/32 x 16/9 -27/32 x7/9 + 27/32
= 27/32 x (16/9 - 7/9 + 1 )
=27/32 x 2
=27/16
\(\frac{2}{3}\) x \(\frac{4}{5}\) + \(\frac{4}{5}\) x \(\frac{8}{3}\)
=\(\frac{4}{5}\) x ( \(\frac{2}{3}\) + \(\frac{8}{3}\) )
= \(\frac{4}{5}\) x \(\frac{10}{3}\)
= \(\frac{40}{15}\) = \(\frac{8}{5}\)
C = 1 + 2 + 4 + 8 + ... + 1024
2 x C = 2 + 4 + 8 + ... + 1024 + 2048
2 x C - C = C = (2 + 4 + 8 + ... + 1024 + 2048) - (1 + 2 + 4 + 8 + ... + 1024) = 2048 - 1 = 2047
D = 1 + 3 + 9 + 27 + ... + 2187
3 x D = 3 + 9 + 27 + ... + 2187 + 6561
3 x D - D = 2 x D = (3 + 9 + 27 + ... + 2187 + 6561) - (1 + 3 + 9 + 27 + ... + 2187) = 6561 - 1 = 6560
D = 6560 : 2 = 3280
a: A=2^0+2^1+...+2^9
2A=2+2^2+...+2^10
=>A=2^10-1
b: B=1+3+3^2+...+3^6
=>3B=3+3^2+...+3^7
=>2B=3^7-1
=>\(B=\dfrac{3^7-1}{2}\)
\(\frac{9}{35}\cdot\frac{25}{36}=\frac{9\cdot25}{35\cdot36}=\frac{9\cdot5\cdot5}{5\cdot7\cdot4\cdot9}=\frac{5}{28}\)
a ) 37 x 27 + 63 x 27
= ( 37 + 63 ) x 27
= 100 x 27
= 2700
b ) 1 + 2 + 3 + 4 + ... + 97 + 98 + 99
= ( 99 - 1 ) : 1 + 1
= 99 x ( 99 + 1 ) : 2
= 4950
c ) 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10
= ( 1 + 9 ) + ( 2 + 8 ) + ( 3 + 7 ) + ( 4 + 6 ) + ( 5 + 10 )
= 10 + 10 + 10 + 10 + 15
= 55
a. =(1+10)×10 :2
=11×10:2
=110:2
=55
b. Số các số hạng là =(90-9):9+1= 10
Tổng = (9+90)×10:2=495
2/9 + 6/27 + 8/36 + 12/54 + 16/72 + 18/81=\(\frac{2}{9}+\frac{2}{9}+\frac{2}{9}+\frac{2}{9}+\frac{2}{9}+\frac{2}{9}\) = \(\frac{2}{9}\). 6 = \(\frac{12}{9}\)= \(\frac{4}{3}\)
\(\frac{2}{9}+\frac{6}{27}+\frac{8}{36}+\frac{12}{54}+\frac{16}{72}+\frac{18}{81}\)
\(=\frac{2}{9}+\frac{2}{9}+\frac{2}{9}+\frac{2}{9}+\frac{2}{9}+\frac{2}{9}\)
\(=\frac{2}{9}×6=\frac{4}{3}\)
