\(A=\frac{1}{2}×\frac{3}{4}+\frac{1}{4}×\frac{1}{2}\)

\(A=\frac{1}{2}×\left(\frac{3}{4}+\frac{1}{4}\right)\)

\(A=\frac{1}{2}×\left(\frac{3+1}{4}\right)\)

\(A=\frac{1}{2}×1\)

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

\(B=\frac{1212}{2121}×\frac{151515}{161616}\)

\(B=\frac{1212:101}{2121:101}×\frac{151515:10101}{161616:10101}\)

\(B=\frac{12}{21}×\frac{15}{16}\)

\(B=\frac{12×15}{21×16}\)

\(B=\frac{3×4×3×5}{3×7×4×4}\)

\(B=\frac{15}{28}\)

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

1) 3/9 + 5/9 = 8/9

2) 1/2 x 2/3 x 3/4 x 4/5

= 1/5

(1-1/2)×(1-1/3)×(1-1/4)×(1-1/5)×1-1/6=1/2×2/3×3/4×4/5×5/6=1/6

Những cái như 1 3/5 là hỗn số nha 

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

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

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

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

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

51541 

theo mình nghĩ là 

( 112 x 115 ) x ( 113 x 114 ) x 116 

sai thì cho xin lỗi nha bn