Lời giải:
a.

$x=\frac{-5}{6}-\frac{2}{3}=\frac{-3}{2}$

b.

$\frac{2}{3}x=\frac{1}{10}-\frac{1}{2}=\frac{-2}{5}$

$x=\frac{-2}{5}: \frac{2}{3}=\frac{-3}{5}$

c.

$\frac{7}{8}x=\frac{2}{9}-\frac{1}{3}=\frac{-1}{9}$
$x=\frac{-1}{9}: \frac{7}{8}=\frac{-8}{63}$

d.

$\frac{5}{7}: x=\frac{1}{6}-\frac{4}{5}=\frac{-19}{30}$

$x=\frac{5}{7}: \frac{-19}{30}=\frac{-150}{133}$

e.

$(\frac{2}{5}-1\frac{2}{3}):x=\frac{2}{5}+\frac{3}{5}=1$

$\frac{-19}{15}: x=1$

$x=\frac{-19}{15}:1 =\frac{-19}{15}$

f.

$(-\frac{3}{4}+x).2\frac{2}{3}=1$

$\frac{-3}{4}+x=1: 2\frac{2}{3}=\frac{3}{8}$

$x=\frac{3}{8}+\frac{3}{4}=\frac{9}{8}$

5/7x : 1/8 = 5/4

x            =  5/4 : 5/7

x             = 24

\(3\dfrac{2}{7}x:\dfrac{1}{8}=2\dfrac{3}{4}\\ \dfrac{23}{7}x:\dfrac{1}{8}=\dfrac{11}{4}\\ \dfrac{23}{7}x=\dfrac{11}{4}\times\dfrac{1}{8}\\ \dfrac{23}{7}x=\dfrac{11}{32}\\ x=\dfrac{11}{32}:\dfrac{23}{7}\\ x=\dfrac{77}{736}\)

`2/5 - 3/8 + 7/6 : 7/5`

`= 2/5 - 3/8 + 7/6 xx 5/7`

`= 2/5 - 3/8 +5/6`

`= 1/40+5/6`

`=103/120`

MSC : `24`

`-5/6=-5.4/6.4=-20/24`

`7/8=7.3/8.3=21/24`

`7/24=7/24`

`-3/4=-3.6/4.6=-18/24`

`2/3=2.8/3.8=16/24`

`1=24/24`

Sắp xếp các phân số sau theo thứ tự tăng dần : 

`-20/24;-18/24;7/24;16/24;21/24;24/24`

\(-\dfrac{5}{7}\times\dfrac{2}{13}+\dfrac{-5}{7}\times\dfrac{3}{13}-\dfrac{5}{7}\times\dfrac{8}{13}\)

\(=-\dfrac{5}{7}\left(\dfrac{2}{13}+\dfrac{3}{13}+\dfrac{8}{13}\right)\)

\(=-\dfrac{5}{7}\times\dfrac{13}{13}\)

\(=-\dfrac{5}{7}\times1=-\dfrac{5}{7}\)

\(-\dfrac{5}{7}.\dfrac{2}{13}+\dfrac{-5}{7}.\dfrac{3}{13}-\dfrac{5}{7}.\dfrac{8}{13}\)

\(=-\dfrac{10}{91}-\dfrac{15}{91}-\dfrac{40}{91}\)

\(=\dfrac{-10-15-40}{91}\)

\(=-\dfrac{65}{91}=-\dfrac{5}{7}\)

\(\dfrac{-5}{7}.\dfrac{2}{13}+\left(\dfrac{-5}{7}\right).\dfrac{3}{13}-\dfrac{5}{7}.\dfrac{8}{13}\)

\(=\dfrac{5}{7}.\left(\dfrac{-2}{13}+\dfrac{-3}{13}-\dfrac{8}{13}\right)\)

\(=\dfrac{5}{7}.\left(-1\right)\)

\(=-\dfrac{5}{7}\)

\(#PaooNqoccc\)

`6/7 . 8/13 +6/7 . 9/13+3/13 . 6/7`

`=6/7 . (8/13+9/13+3/13)`

`=6/7 . 20/13`

`=120/91`

\(\dfrac{6}{7}.\dfrac{8}{13}+\dfrac{6}{7}.\dfrac{9}{13}+\dfrac{3}{13}.\dfrac{6}{7}\)

\(=\dfrac{6}{7}.\left(\dfrac{8}{13}+\dfrac{9}{13}+\dfrac{3}{13}\right)\)

\(=\dfrac{6}{7}.\left(\dfrac{8+9+3}{13}\right)\)

\(=\dfrac{6}{7}.\dfrac{20}{13}\)

\(=\dfrac{6.20}{7.13}\)

\(=\dfrac{120}{91}\)

`6/7 . 8/13 + 6/7 . 9/13 + 3/13 . 6/7`

`= 6/7 . ( 8/13 + 9/13 + 3/13)`

`=6/7 . 20/13`

`= 120/91`

\(\dfrac{1}{3}+\dfrac{1}{7}+\dfrac{1}{5}+\dfrac{32}{40}+\dfrac{48}{56}+\dfrac{14}{21}\\ =\dfrac{1}{3}+\dfrac{1}{7}+\dfrac{1}{5}+\dfrac{4}{5}+\dfrac{6}{7}+\dfrac{2}{3}\\ =\left(\dfrac{1}{3}+\dfrac{2}{3}\right)+\left(\dfrac{1}{7}+\dfrac{6}{7}\right)+\left(\dfrac{1}{5}+\dfrac{4}{5}\right)\\ =1+1+1=3\)

Lời giải:

$\frac{1}{3}+\frac{1}{7}+\frac{1}{5}+\frac{32}{40}+\frac{48}{56}+\frac{14}{21}$

$=\frac{1}{3}+\frac{1}{7}+\frac{1}{5}+\frac{4}{5}+\frac{6}{7}+\frac{2}{3}$

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

$=\frac{3}{3}+\frac{7}{7}+\frac{5}{5}=1+1+1=3$

=(7/21 +14/21)+(8/56+48)+(8/40+32/40)

=1+1+1

=3

\(=\dfrac{2}{2}+\dfrac{2}{6}+\dfrac{2}{12}+...+\dfrac{2}{56}\)

\(=2\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{7}-\dfrac{1}{8}\right)\)

=2*7/8=7/4

Ta có: \(\dfrac{-5}{13}\cdot\dfrac{3}{7}-\dfrac{2}{17}\cdot\dfrac{8}{13}+\dfrac{5}{13}\cdot\dfrac{1}{7}\)

\(=\dfrac{5}{13}\left(-\dfrac{3}{7}+\dfrac{1}{7}\right)-\dfrac{2}{17}\cdot\dfrac{8}{13}\)

\(=\dfrac{5}{13}\cdot\dfrac{-2}{7}-\dfrac{2}{17}\cdot\dfrac{8}{13}\)

\(=\dfrac{-10}{91}-\dfrac{16}{221}\)

\(=\dfrac{-282}{1547}\)

\(\dfrac{-5}{13}.\dfrac{3}{7}-\dfrac{2}{17}.\dfrac{8}{13}+\dfrac{5}{13}.\dfrac{1}{7}\) 

\(=\dfrac{5}{13}.\dfrac{-3}{7}-\dfrac{2}{17}.\dfrac{8}{13}+\dfrac{5}{13}.\dfrac{1}{7}\)

\(=\dfrac{5}{13}.\left(\dfrac{-3}{7}+\dfrac{1}{7}\right)+\dfrac{-2}{17}.\dfrac{8}{13}\) 

\(=\dfrac{5}{13}.\dfrac{-2}{7}+\dfrac{-2}{13}.\dfrac{8}{17}\)

\(=\dfrac{-2}{13}.\dfrac{5}{7}+\dfrac{-2}{13}.\dfrac{8}{17}\) 

\(=\dfrac{-2}{13}.\left(\dfrac{5}{7}+\dfrac{8}{17}\right)\) 

\(=\dfrac{-2}{13}.\dfrac{141}{119}\) 

\(=\dfrac{-282}{1547}\)