`5/6:3/4`

`=5/6xx4/3`

`=20/18=10/9`

5/6 : 3/4 = 5/6 x 4/3 = 20/18 = 10/9

`5/6-3/4`

`=20/24-18/24`

`=2/24=1/12`

     \(\dfrac{5}{6}\) - \(\dfrac{3}{4}\)

=   \(\dfrac{10}{12}\) - \(\dfrac{9}{12}\)

= \(\dfrac{1}{12}\)

theo đề bài ta có

\(\dfrac{3}{5}< \dfrac{x}{5}< \dfrac{4}{5}\\ =>\dfrac{15}{25}< \dfrac{x}{25}< \dfrac{20}{25}\)

=> 4 phân số đó là \(\dfrac{16}{25};\dfrac{17}{25};\dfrac{18}{25};\dfrac{19}{25}\)

\(\dfrac{3}{5}\) = \(\dfrac{3\times5}{5\times5}\) = \(\dfrac{15}{25}\);

\(\dfrac{4}{5}\) = \(\dfrac{4\times5}{5\times5}\) = \(\dfrac{20}{25}\)

Vậy bốn phân số nằm giữa \(\dfrac{3}{5}\)và \(\dfrac{4}{5}\) là bốn phân số nằm giữa \(\dfrac{15}{25}\) và\(\dfrac{20}{25}\), đó lần lượt là các phân số sau:

\(\dfrac{16}{25}\); \(\dfrac{17}{25}\); \(\dfrac{18}{25}\); \(\dfrac{19}{25}\)

\(\dfrac{23}{5}\) + \(\dfrac{11}{3}\) 

= \(\dfrac{69}{15}\) + \(\dfrac{55}{15}\)

= \(\dfrac{124}{15}\)

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

=  \(\dfrac{10}{15}\) + \(\dfrac{12}{15}\)

= \(\dfrac{22}{15}\)

`7/2-x=4/5`

`=>x=7/2-4/5`

`=>x=35/10-8/10`

`=>x=27/10`

7/2 - x = 4/5

x = 7/2 - 4/5 = 23/10

x : 8/16 = 4/5

x = 4/5 x 8/16 = 2/5

`6/5xx x =8/9`

`=>x=8/9:6/5`

`=>x=8/9xx5/6`

`=>x=20/27`

\(\dfrac{6}{5}.X=\dfrac{8}{9}\)

\(\Leftrightarrow X=\dfrac{8}{9}:\dfrac{6}{5}=\dfrac{8}{9}.\dfrac{5}{6}=\dfrac{20}{27}\)

=1/6 : 1/4

=2/3

    \(\dfrac{1}{2}\) x \(\dfrac{1}{3}\) : \(\dfrac{1}{4}\)

=  \(\dfrac{1}{6}\) : \(\dfrac{1}{4}\)

=  \(\dfrac{1}{6}\) x \(\dfrac{4}{1}\)

= \(\dfrac{4}{6}\)

= \(\dfrac{2}{3}\)

\(\dfrac{5}{2}+\dfrac{1}{4}.\dfrac{1}{8}\)

\(=\dfrac{5}{2}+\dfrac{1}{32}=\dfrac{5.16+1}{32}=\dfrac{80+1}{32}=\dfrac{81}{32}\)

    \(\dfrac{5}{2}\)  + \(\dfrac{1}{4}\) x \(\dfrac{1}{8}\)

=  \(\dfrac{5}{2}\) + \(\dfrac{1}{32}\)

= \(\dfrac{80}{32}\) +  \(\dfrac{1}{32}\)

= \(\dfrac{81}{32}\)