a: \(5-\dfrac{7}{8}+\dfrac{15}{-20}\)

\(=5-\dfrac{7}{8}-\dfrac{3}{4}\)

\(=\dfrac{5\cdot8-7-3\cdot2}{8}\)

\(=\dfrac{40-7-6}{8}=\dfrac{27}{8}\)

b: \(\dfrac{10}{-13}:\dfrac{-4}{13}\cdot\dfrac{11}{-10}\)

\(=-\dfrac{10}{13}\cdot\dfrac{13}{4}\cdot\dfrac{11}{10}\)

\(=-\dfrac{11}{4}\)

c: \(\dfrac{-3}{2}\cdot\dfrac{5}{2}+\dfrac{3}{-8}\)

\(=\dfrac{-15}{4}+\dfrac{-3}{8}\)

\(=\dfrac{-15\cdot2+\left(-3\right)}{8}=\dfrac{-33}{8}\)

d: \(\dfrac{7}{-8}-\dfrac{-4}{5}:\dfrac{3}{10}\)

\(=-\dfrac{7}{8}+\dfrac{4}{5}\cdot\dfrac{10}{3}\)

\(=-\dfrac{7}{8}+\dfrac{8}{3}\)

\(=\dfrac{-7\cdot3+8\cdot8}{24}=\dfrac{43}{24}\)

e: \(\dfrac{-5}{8}\cdot\dfrac{25}{111}+\dfrac{25}{111}\cdot\dfrac{3}{10}\)

\(=\dfrac{25}{111}\left(-\dfrac{5}{8}+\dfrac{3}{10}\right)\)

\(=\dfrac{25}{111}\cdot\dfrac{-25+12}{40}\)

\(=\dfrac{25}{40}\cdot\dfrac{-13}{111}=\dfrac{-5}{8}\cdot\dfrac{13}{111}=\dfrac{-65}{888}\)

\(B=\dfrac{2n-3}{n-2}=\dfrac{2n-4+1}{n-2}=\dfrac{2\left(n-2\right)}{n-2}+\dfrac{1}{n-2}=2+\dfrac{1}{n-2}\)

Do \(2\in Z\Rightarrow B\in Z\) khi \(\dfrac{1}{n-2}\in Z\)

\(\Rightarrow n-2=Ư\left(1\right)\)

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

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

\(-5,2+3,5.\left(-2\right)-6,9:3+\left(-0,04\right)\\ =-5,2-7-2,3-0,04\\ =-5,2-3-0,04\\ =-8,24\)

TK:

=−5,2−7−2,3−0,04

=−5,2−3−0,04

=−8,24

\(\dfrac{1}{4^2}+\dfrac{1}{5^2}+\dfrac{1}{6^2}+...+\dfrac{1}{100^2}< \dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+...+\dfrac{1}{99.100}\)

\(\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+...+\dfrac{1}{99.100}=\)

\(=\dfrac{4-3}{3.4}+\dfrac{5-4}{4.5}+\dfrac{6-5}{5.6}+...++\dfrac{100-99}{99.100}=\)

\(=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{99}-\dfrac{1}{100}=\dfrac{1}{3}-\dfrac{1}{100}< \dfrac{1}{3}\)

\(\Rightarrow\dfrac{1}{4^2}+\dfrac{1}{5^2}+\dfrac{1}{6^2}+...+\dfrac{1}{100^2}< \dfrac{1}{3}\)

Đặt số chia là a và thương là b ta có

\(\dfrac{200-13}{a}=b\Rightarrow b=\dfrac{187}{a}\Rightarrow187⋮a\)

\(\Rightarrow a=\left\{1;11;17\right\}\Rightarrow b=\left\{187;17;11\right\}\)

A = \([20;31;42;53;64;75;86;97]\)

Hiệu vận tốc của 2 xe là:

     12-11=1 (km/giờ)

Hai xe gặp nhau sau thời gian là:

     7:1=7 (giờ)

Hai xe gặp nhau lúc:

     7 giờ + 7 giờ = 14 giờ

Chỗ gặp nhau cách A  là:

     12.7=84 (km)

          Đáp số: 2 xe gặp nhau lúc 14 giờ và chỗ gặp nhau cách A 84 km

\(\dfrac{5}{13}\cdot\dfrac{-3}{10}\cdot\dfrac{-3}{5}\)

\(=\dfrac{5}{5}\cdot\dfrac{-3}{13}\cdot\dfrac{-3}{10}\)

\(=\dfrac{3}{13}\cdot\dfrac{3}{10}=\dfrac{9}{130}\)

5/3 . (-3/10).(-3/5) 

=5/3 . 3/10 . 3/5

=45/150

=3/10

\(\dfrac{3}{4}\cdot\dfrac{1}{13}-\dfrac{3}{4}\cdot\dfrac{14}{13}\)

\(=\dfrac{3}{4}\left(\dfrac{1}{13}-\dfrac{14}{13}\right)\)

\(=\dfrac{3}{4}\cdot\dfrac{-13}{13}=-\dfrac{3}{4}\)

3/4×1/13-3/4×14/13

=3/4×(1/13-14/13)

=3/4×(-13/13)

=3/4×(-1)

=(-3/4)

\(\dfrac{10}{-13}:\dfrac{-4}{13}\cdot\dfrac{11}{-10}\)

\(=\dfrac{10}{13}\cdot\dfrac{13}{4}\cdot\dfrac{11}{-10}\)

\(=\dfrac{10}{4}\cdot\dfrac{11}{-10}=-\dfrac{11}{4}\)

\(\dfrac{10}{-13}:\dfrac{-4}{13}.\dfrac{11}{-10}\)

\(=\dfrac{10}{-13}.\dfrac{13}{4}.\dfrac{11}{-10}\)

\(=\dfrac{1430}{520}\)

\(=\dfrac{11}{4}\)