\(5\dfrac{3}{4}:3+2\dfrac{1}{4}\times\dfrac{1}{3}-\dfrac{1}{8}=\left(5\dfrac{3}{4}+2\dfrac{1}{4}\right)\times\dfrac{1}{3}-\dfrac{1}{8}\\ =8\times\dfrac{1}{3}-\dfrac{1}{8}=\dfrac{8}{3}-\dfrac{1}{8}=\dfrac{61}{24}\\ ----\\ \dfrac{3}{5}:\dfrac{5}{6}:\dfrac{6}{7}:\dfrac{7}{8}+\dfrac{2}{5}+\dfrac{23}{35}\\ =\dfrac{3}{5}\times\dfrac{6}{5}\times\dfrac{7}{6}\times\dfrac{8}{7}+\dfrac{2}{5}+\dfrac{23}{35}=\dfrac{18}{25}\times\dfrac{4}{3}+\dfrac{2}{5}+\dfrac{23}{35}=\dfrac{353}{175}\)

đáp án 1/6

Đặt A  = 1 - 1/2 + 1 - 1/6 + 1 - 1/12 + 1 - 1/20 + 1 - 1/30 + 1 - 1/42 + 1 - 1/56 + 1 - 1/72 + 1 - 1/89
=  (1 + 1 + 1 + .... 1 + 1) + (1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90)
= 9 - (1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7 + 1/7x8 + 1/8x9 + 1/9x10)
Mỗi phân số thành phần trong biểu thức () ta tách được như sau:
   1/1 x 2 = 1- 1/2
   1/2 x 3 = 1/2 - 1/3

 1/3 x 4 = 1/3 - 1/4
   ........
   1/9 x 10 = 1/9 - 1/10
Như vậy:
A  = 9 - (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)

  = 9 - (1 - 1/10)
    = 9 - 9/10
    = 81/10
                                               Đáp số: 81/10

\(\left(1-\frac{1}{2}\right)x\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{5}\right)x\)\(\left(1-\frac{1}{6}\right)\)

=\(\frac{1}{2}x\frac{2}{3}x\frac{3}{4}x\frac{4}{5}x\frac{5}{6}\)

=\(\frac{1x2x3x4x5}{2x3x4x5x6}\)

=\(\frac{1}{6}\)

(1-1/2)x(1-1/3)x(1-1/4)x(1-1/5)x(1-1/6)

=1/2x2/3x3/4x4/5x5/6

=1/6

\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)\times\left(1-\frac{1}{6}\right)\)

\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times\frac{5}{6}\)

\(=\frac{1\times2\times3\times4\times5}{2\times3\times4\times5\times6}=\frac{1}{6}\)

=\(\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times\frac{5}{6}\)

=1\(\times\frac{1}{6}\)

=\(\frac{1}{6}\)

= 3/2 + 2/3 + 2/4 + 2/5

= (6/4 + 2/4) + (2/3 + 2/5)

= 8/4 + 16/ 15 

= 46/15

=46/15

theo mình nghĩ là 

( 112 x 115 ) x ( 113 x 114 ) x 116 

sai thì cho xin lỗi nha bn

1/6

\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot\dfrac{4}{5}\cdot\dfrac{5}{6}=\dfrac{1.2.3.4.5}{2.3.4.5.6}=\dfrac{1}{6}\)

\(\dfrac{1}{6}\)

kết quả là 299/180 đó bạn

mk tính mãi nếu rút gọn được thì pn tự rút gọn nhé

\(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{4}{3}+\dfrac{2}{6}+\dfrac{2}{3}+\dfrac{5}{6}\)

\(=\left(\dfrac{1}{3}+\dfrac{4}{3}+\dfrac{2}{3}\right)+\left(\dfrac{1}{6}+\dfrac{2}{6}+\dfrac{5}{6}\right)\)

\(=\dfrac{7}{3}+\dfrac{8}{6}\)\(=\dfrac{7}{3}+\dfrac{4}{3}\)

\(=\dfrac{11}{3}\)

\(\frac{1}{2}-\frac{2}{5}+\frac{1}{3}-\frac{3}{5}+\frac{1}{6}\)

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

\(=\left(\frac{3}{6}+\frac{2}{6}+\frac{1}{6}\right)+\left(\frac{2}{5}+\frac{3}{5}\right)\)

\(=1+1\)

\(=2\)

@muối

1/2 - 2/5 + 1/3 - 3/5 + 1/6

= 1/2 + 1/3 + 1/6 - 2/5 - 3/5

= (1/2 + 1/3 + 1/6) - (2/5 + 3/5)

= 1 - 1 

= 0

Chúc bạn học tốt.

😁😁😁

1/2 - 2/5 + 1/3 - 3/5 + 1/6 = 0