Answer:

\(\dfrac{4}{-5}.2,7-0,8.6,3-80\%\)

\(=\dfrac{-4}{5}.\dfrac{27}{10}-\dfrac{4}{5}.\dfrac{63}{10}-\dfrac{4}{5}\)

\(=\dfrac{4}{5}.\dfrac{-27}{10}-\dfrac{4}{5}.\dfrac{63}{10}-\dfrac{4}{5}.1\)

\(=\dfrac{4}{5}.\left(\dfrac{-27}{10}-\dfrac{63}{10}-\dfrac{10}{10}\right)\)

\(=\dfrac{4}{5}.\dfrac{-27-63-10}{10}\)

\(=\dfrac{4}{5}.\dfrac{-100}{10}\)

\(=\dfrac{4}{5}.\left(-10\right)\)

\(=\dfrac{4}{1}.\dfrac{-2}{1}\)

\(=-8\)

Gọi ƯCLN( 12n+1 , 30n+2 ) = d ( d E  Z ) => \(\left\{{}\begin{matrix}12n+1⋮d\\30n+2⋮d\end{matrix}\right.\) => \(\left\{{}\begin{matrix}60n+5⋮d\\60n+4⋮d\end{matrix}\right.\) => ( 60n + 5 ) - ( 60n + 4 ) \(⋮\) d =>                 1 \(⋮\) d =>  d E { 1 ; -1 } Vậy PS \(\dfrac{12n+1}{30n+2}\) là phân số tối giản 

a) \(2\left(\dfrac{2}{3.5}+\dfrac{4}{5.9}+...+\dfrac{16}{n\left(n+16\right)}\right)=\dfrac{16}{25}\)

\(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+...+\dfrac{1}{n}-\dfrac{1}{n+16}=\dfrac{8}{25}\)

\(\dfrac{1}{3}-\dfrac{1}{n+16}=\dfrac{8}{25}\)

\(\dfrac{n+13}{3\left(n+16\right)}=\dfrac{8}{25}\)

\(24n+384=25n+325\)

\(25n-24n=384-325\)

\(n=59\)

b) Sai đề nha

\(\left\{{}\begin{matrix}\dfrac{2018}{2019}< 1\\\dfrac{2019}{2020}< 1\\\dfrac{2020}{2021}< 1\\\dfrac{2021}{2022}< 1\end{matrix}\right.\)

\(\Rightarrow\dfrac{2018}{2019}+\dfrac{2019}{2020}+\dfrac{2020}{2021}+\dfrac{2021}{2022}< 4\)

Ta lấy 25kg * 120% = 30kg

TL:

120 x 25 : 120 = 30

Vậy 120% của của 25 là 30

HT