Câu 1: \(\frac{17}{51}\)x \(\frac{45}{30}\)= \(\frac{1}{3}\)x \(\frac{3}{2}\)

                                   = \(\frac{1}{2}\).

Câu 2: \(\frac{24}{15}\)x \(\frac{56}{72}\)x \(\frac{10}{14}\)= \(\frac{8}{5}\)x \(\frac{7}{9}\)x \(\frac{5}{7}\)

                                                 = \(\frac{56}{45}\)x \(\frac{5}{7}\)

                                                 = \(\frac{8}{9}\)

Câu 3: \(\frac{32}{48}\times\frac{35}{21}\times\frac{63}{14}\times\frac{9}{30}=\frac{2}{3}\times\frac{5}{3}\times\frac{9}{2}\times\frac{3}{10}=\frac{3}{2}\)

k nha

a)17/51x45/40=1/3x3/2=3/6=1/2

b)24/15x56/72x10/14=8/5x7/9x5/7=8/9

c)32/48x35/21x63/14x9/30=2/3x5/3x9/2x3/10=3/2

x x 134 -x x24 -x x 10 = x x ( 134 - 24 - 10)

x = x x 100

x = 1300 : 100

x = 13

\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+...+\frac{89}{90}\)

\(=1-\frac{1}{2}+1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+...+1-\frac{1}{90}\)

\(=9-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)\)

\(=9-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)

\(=9-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{9}-\frac{1}{10}\right)\)

\(=9-\left(1-\frac{1}{10}\right)\)

\(=9-\frac{9}{10}=\frac{81}{10}\)

a 168 x 168 - 168 x 58/110

= 168 x (168 - 58/100)

= 168 x 8371/50

= 28126,56

b 1/20 + 1/30 + 1/42 + ... + 1/156

= 1/(4x5) + 1/(5x6) + 1/(6x7) + ... + 1/(12x13)

= 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + ... + 1/12 - 1/13

= 1/4 - 1/13

= 9/52

a) 

\(=\frac{7\cdot7\cdot8\cdot8\cdot9\cdot9\cdot10\cdot10\cdot11\cdot11}{6\cdot8\cdot7\cdot9\cdot8\cdot10\cdot9\cdot11\cdot10\cdot12}\)    

\(=\frac{7\cdot11}{6\cdot12}\)     

\(=\frac{77}{72}\)

b) 

\(=1+\frac{1}{6}+1+\frac{1}{12}+1+\frac{1}{20}+1+\frac{1}{30}+1+\frac{1}{42}+1+\frac{1}{56}\)  

\(=6+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}\)  

\(=6+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{7}-\frac{1}{8}\)  

\(=6+\frac{1}{2}-\frac{1}{8}\)  

\(=6+\frac{3}{8}\)

\(=\frac{51}{8}\)

Chia thành...a và b nhé.

Bg

a)Ta có: \(\frac{49}{48}.\frac{64}{63}.\frac{81}{80}.\frac{100}{99}.\frac{121}{120}\)

= \(\frac{49.64.81.100.121}{48.63.80.99.120}\)

= \(\frac{7.7.8.8.9.9.10.10.11.11}{6.8.7.9.8.10.9.11.10.12}\)

= \(\frac{7.11}{6.12}\)    (chịt tiêu trên dưới)

= \(\frac{77}{72}\)

b) Ta có: \(\frac{7}{6}+\frac{13}{12}+\frac{21}{20}+\frac{31}{30}+\frac{43}{42}+\frac{57}{56}\)

Có 6 số hạng  (đếm)

= \(1+\frac{1}{6}+1+\frac{1}{12}+1+\frac{1}{20}+1+\frac{1}{30}+1+\frac{1}{42}+1+\frac{1}{56}\)

= \(1+1+...+1+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}\)

= \(1.6+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)

= \(6+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}\)

= \(6+\frac{1}{2}-\frac{1}{8}\)

= \(\frac{13}{2}-\frac{1}{8}\)

= \(\frac{51}{8}\)

Hơi dài....

THANK YOU

\(x\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\right)=\frac{4034}{5}\)

\(x.\frac{2}{5}=\frac{4034}{5}\)

\(x=\frac{4034}{5}:\frac{2}{5}\)

\(x=\frac{4034}{5}.\frac{5}{2}\)

x = 2017

1-1/2+1/2-1/3+1/3+1/4-1/4+1/5-1/5+1/6-1/6+1/7-1/7+1/8-1/8+1/9-1/9+1/10-(1-1/3+1/3-3/5+3/5-4/7+5/9-5/9+6/11-6/11-7/13)=1+1/10-1+7/13=83/130

b: =8,12(6+8-4)=8,12x10=81,2

a: \(A=\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+...+\dfrac{1}{10\cdot11}\)

\(=\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{10}-\dfrac{1}{11}\)

=1/4-1/11=7/44

c: =>0,2a+0,4a=12

=>0,6a=12

hay a=20