\(\dfrac{-2}{7}\cdot\dfrac{7}{4}+\dfrac{-2}{7}\cdot\dfrac{-3}{4}-2\dfrac{1}{7}\)

\(=\dfrac{-2}{7}\left(\dfrac{7}{4}-\dfrac{3}{4}\right)-\dfrac{15}{7}\)

\(=\dfrac{-2}{7}-\dfrac{15}{7}=\dfrac{-17}{7}\)

Lời giải:

Gọi chiều dài và chiều rộng ban đầu là $a$ và $b$ (m) 

Theo bài ra ta có:

$(a+36)b.0,84=ab.1,05$

$\Rightarrow b[(a+36).0,84-1,05a]=0$

$\Rightarrow (a+36).0,84-1,05a=0$

$\Rightarrow 30,24=0,21a$

$\Rightarrow a=144$ (m) 

Vậy chiều dài mới là: $a+36=144+36=180$ (m)

Bài 2:

a: \(\dfrac{7}{8}+x=\dfrac{3}{5}\)

=>\(x=\dfrac{3}{5}-\dfrac{7}{8}=\dfrac{24-35}{40}=\dfrac{-11}{40}\)

b: \(\dfrac{17}{2}:x=5\)

=>\(x=\dfrac{17}{2}:5\)

=>\(x=\dfrac{17}{2\cdot5}=\dfrac{17}{10}\)

c: \(x-\dfrac{3}{8}=2+\dfrac{1}{4}\)

=>\(x-\dfrac{3}{8}=\dfrac{9}{4}\)

=>\(x=\dfrac{9}{4}+\dfrac{3}{8}=\dfrac{18}{8}+\dfrac{3}{8}=\dfrac{21}{8}\)

d: \(\dfrac{1}{2}+\dfrac{3}{5}\left(x-2\right)=\dfrac{1}{5}\)

=>\(\dfrac{3}{5}\left(x-2\right)=\dfrac{1}{5}-\dfrac{1}{2}=\dfrac{-3}{10}\)

=>\(x-2=-\dfrac{1}{2}\)

=>\(x=2-\dfrac{1}{2}=\dfrac{3}{2}\)

Bài 1:

a: \(\dfrac{-3}{4}+\dfrac{1}{5}=\dfrac{-15}{20}+\dfrac{4}{20}=\dfrac{-15+4}{20}=\dfrac{-11}{20}\)

b: \(\dfrac{-2}{5}-\dfrac{1}{3}=\dfrac{-6}{15}-\dfrac{5}{15}=\dfrac{-6-5}{15}=\dfrac{-11}{15}\)

c: \(\dfrac{3}{7}\cdot\dfrac{2}{5}-\dfrac{2}{5}=\dfrac{2}{5}\left(\dfrac{3}{7}-1\right)=\dfrac{2}{5}\cdot\dfrac{-4}{7}=\dfrac{-8}{35}\)

d: \(\dfrac{1}{4}+\dfrac{3}{4}\left(\dfrac{2}{3}-\dfrac{1}{2}\right)\)

\(=\dfrac{1}{4}+\dfrac{3}{4}\cdot\dfrac{4-3}{6}\)

\(=\dfrac{1}{4}+\dfrac{3}{4}\cdot\dfrac{1}{6}=\dfrac{1}{4}+\dfrac{1}{8}=\dfrac{3}{8}\)

e: \(\dfrac{7}{2}\cdot\dfrac{8}{13}+\dfrac{8}{13}\cdot\dfrac{-5}{12}+\dfrac{8}{13}\)

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

\(=\dfrac{8}{13}\cdot2=\dfrac{16}{13}\)

f: \(1+\dfrac{1}{8}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{80}+\dfrac{1}{120}\)

\(=1+\dfrac{1}{2\cdot4}+\dfrac{1}{4\cdot6}+\dfrac{1}{6\cdot8}+\dfrac{1}{8\cdot10}+\dfrac{1}{10\cdot12}\)

\(=1+\dfrac{1}{2}\left(\dfrac{2}{2\cdot4}+\dfrac{2}{4\cdot6}+...+\dfrac{2}{10\cdot12}\right)\)

\(=1+\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{10}-\dfrac{1}{12}\right)\)

\(=1+\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{12}\right)\)

\(=1+\dfrac{1}{2}\cdot\dfrac{5}{12}=1+\dfrac{5}{24}=\dfrac{29}{24}\)

-1/4 + 2/5 . x = 4/15

2/5 . x = 4/15 + 1/4

2/5 . x = 31/60

x = 31/60 : 2/5

x = 31/24

-1/4+2/5.x=4/15

        2/5.x=4/15-1/4

        2/5.x=1/60

              X=1/60:2/5

              X=1/60.5/2

             X= 1/24

-1/4+2/5.x=4/15

\(\dfrac{8}{9}.-\dfrac{7}{13}-\dfrac{8}{9}.\dfrac{6}{13}+2\dfrac{8}{9}\\ =\dfrac{8}{9}.\left(-\dfrac{7}{13}-\dfrac{6}{13}\right)+\dfrac{26}{9}\\ =\dfrac{8}{9}.-1+\dfrac{26}{9}\\ =-\dfrac{8}{9}+\dfrac{26}{9}\\ =2.\)

1.27626194866²⁹⁴ nha (câu này phải sử dụng phần mềm lập trình để tính ra)

máy tính cầm tay không tính nổi ;)

a.

Đặt \(A=\dfrac{n}{n+1}+\dfrac{3}{n+1}=\dfrac{n+3}{n+1}=\dfrac{n+1+2}{n+1}=1+\dfrac{2}{n+1}\)

A nguyên khi \(\dfrac{2}{n+1}\) nguyên

\(\Rightarrow n+1=Ư\left(2\right)\)

\(\Rightarrow n+1=\left\{-2;-1;1;2\right\}\)

\(\Rightarrow n=\left\{-3;-2;0;1\right\}\)

b.

\(S=\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{2021.2023}\)

\(2S=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{2021.2023}\)

\(2S=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{2021}-\dfrac{1}{2023}\)

\(2S=1-\dfrac{1}{2023}\)

\(2S=\dfrac{2022}{2023}\)

\(S=\dfrac{1011}{2023}\)

a: \(\dfrac{8}{x}=\dfrac{-4}{5}\)

=>\(x=\dfrac{8\cdot5}{-4}\)

=>\(x=\dfrac{40}{-4}=-10\)

b: \(\dfrac{5}{8}-3x=\dfrac{7}{16}\)

=>\(3x=\dfrac{5}{8}-\dfrac{7}{16}=\dfrac{3}{16}\)

=>\(x=\dfrac{1}{16}\)

b/5/8-3x=7/16

         3x=5/8-7/16

         3x=3/16

           x=3/16:3

           x=1/16

a: \(\dfrac{5}{18}+\dfrac{1}{6}=\dfrac{5}{18}+\dfrac{3}{18}=\dfrac{5+3}{18}=\dfrac{8}{18}=\dfrac{4}{9}\)

b: \(\dfrac{5}{7}\cdot\dfrac{-1}{5}:\dfrac{3}{14}\)

\(=\dfrac{-1}{7}\cdot\dfrac{14}{3}=\dfrac{-2}{3}\)

c: Sửa đề: \(\dfrac{4}{11}+\dfrac{-2}{5}+\dfrac{-8}{23}+\dfrac{7}{11}+\dfrac{-15}{23}\)

\(=\left(\dfrac{4}{11}+\dfrac{7}{11}\right)+\left(-\dfrac{8}{23}-\dfrac{15}{23}\right)+\dfrac{-2}{5}\)

\(=1-1-\dfrac{2}{5}=-\dfrac{2}{5}\)

❤\(\dfrac{5}{18}\) +\(\dfrac{1}{6}\)=\(\dfrac{5}{18}\)+\(\dfrac{3}{18}\)=\(\dfrac{4}{9}\)