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

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

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

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

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

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

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

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

`1/5 . 4/7 + 3/7 . 1/5 -1/5`

`=1/5 . 4/7 + 3/7 . 1/5 -1/5 . 1`

`=1/5 . ( 4/7+3/7-1)`

`=1/5 . ( 7/7-1)`

`= 1/5 . 0`

`=0`

\(\dfrac{1}{5}\times\dfrac{4}{7}+\dfrac{3}{7}\times\dfrac{1}{5}-\dfrac{1}{5}=\dfrac{1}{5}\times\left(\dfrac{4}{7}+\dfrac{3}{7}-1\right)=\dfrac{1}{5}\times0=0\)

`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`

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

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

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

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

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

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

`5/9+4/9:x=1/3`

`=>4/9:x=1/3-5/9`

`=>4/9:x=3/9-5/9`

`=>4/9:x=-2/9`

`=>x=4/9:(-2/9)`

`=>x=4/9.(-9/2)`

`=>x=-4/2`

`=>x=-2`

`5/9 + 4/9 : x= 1/3`

`=> 4/9 : x= 1/3-5/9`

`=> 4/9 : x= 3/9-5/9`

`=> 4/9 : x= -2/9`

`=> x= 4/9 :(-2/9)`

`=>x= 4/9 xx (-9/2)`

`=>x= -36/18`

`=>x=-2`

`S_1 = 5/(1.4) + 5/(4.7) +...+ 5/(97.100)`

`S_1 = 5 (1/(1.4) + 1/(4.7) +...+ 1/(97.100))`

`S_1 = 5/3 (3/(1.4) + 3/(4.7) +...+ 3/(97.100))`

`S_1 = 5/3 (1 - 1/4 + 1/4 - 1/7 + ...+ 1/97 - 1/100)`

`S_1 = 5/3 (1 - 1/100)`

`S_1 = 5/3 . 99/100`

`S_1 = 33/20`

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`

\(-\dfrac{3}{7}\times\dfrac{15}{13}-\dfrac{3}{7}\times\dfrac{11}{13}-\dfrac{3}{7}\)

\(=-\dfrac{3}{7}\left(\dfrac{15}{13}+\dfrac{11}{13}+1\right)\)

\(=-\dfrac{3}{7}\left(\dfrac{15}{13}+\dfrac{11}{13}+\dfrac{13}{13}\right)\)

\(=-\dfrac{3}{7}\times\dfrac{39}{13}=-\dfrac{3}{7}\times3=-\dfrac{9}{7}\)

\(=5\left(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}\right)\)

\(=5\left(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{7}-\dfrac{1}{8}\right)\)

\(=5\cdot\dfrac{5}{24}=\dfrac{25}{24}\)

`5/12 + 5/20 + 5/30 + 5/42 + 5/56`

`= 5/(3.4) + 5/(4.5) + 5/(5.6) + 5/(6.7) + 5/(7.8)`

`= 5 . (1/(3.4) + 1/(4.5) + ... + 5/(7.8))`

`= 5 . (1/3 - 1/4 + 1/4 - 1/5 + ...+ 1/7 - 1/8)`

`= 5 . (1/3 - 1/8) `

`= 5 . 5/24 = 25/24`

a: \(=\dfrac{-39+19+10}{12}=\dfrac{-10}{12}=\dfrac{-5}{6}\)

b: \(=\dfrac{2^{30}\cdot3^{16}\cdot7-2^{34}\cdot3^{15}}{2^{28}\cdot3^{21}-2^{28}\cdot3^{17}}\)

\(=\dfrac{2^{30}\cdot3^{15}\left(3\cdot7-2^4\right)}{2^{28}\cdot3^{17}\left(3^4-1\right)}=\dfrac{2^2}{3^2}\cdot\dfrac{21-16}{80}=\dfrac{4}{9}\cdot\dfrac{5}{80}\)

\(=\dfrac{20}{720}=\dfrac{1}{36}\)