a)\(\frac{4}{3.7}+\frac{4}{7.11}+...+\frac{4}{23.27}=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{23}-\frac{1}{27}=\frac{1}{3}-\frac{1}{27}=\frac{8}{27}\)

b)\(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{6.7}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}=\frac{1}{2}-\frac{1}{7}=\frac{5}{14}\)

c)\(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{11.13}+\frac{2}{1.2}+\frac{2}{2.3}+...+\frac{2}{9.10}=\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\right)+2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right)\)

\(=\frac{1}{3}-\frac{1}{13}+2\left(1-\frac{1}{10}\right)=\frac{10}{39}+\frac{9}{5}=\frac{401}{195}\)

a) 3/7 - 4/11 - 3/7

= (3/7 - 3/7) - 4/11

= -4/11

b) -5/11 + 3/8 - 6/11

= (-5/11 -6/11) + 3/8

= -1 + 3/8

= -5/8

c) 3/4 - 1/3 - 11/4

= (3/4 - 11/4) - 1/3

= -2 - 1/3

= -7/3

ai mần tr mình cho tich

A) 3/7 - 4/11 - 3/7

= (3/7 - 3/7) - 4/11

= -4/11

B) -5/11 + 3/8 - 6/11

= (-5/11 -6/11) + 3/8

= -1 + 3/8

= -5/8

C) 3/4 - 1/3 - 11/4

= (3/4 - 11/4) - 1/3

= -2 - 1/3

= -7/3

a: \(\dfrac{7}{4}+\dfrac{-3}{5}=\dfrac{35-12}{20}=\dfrac{23}{20}\)

d: \(\left(-\dfrac{1}{4}\right)^2\cdot\dfrac{4}{11}+\dfrac{7}{11}\cdot\left(-\dfrac{1}{4}\right)^2=\dfrac{1}{16}\)

\(\dfrac{7}{4}+\dfrac{-3}{5}=\dfrac{35}{20}+\dfrac{-12}{20}=\dfrac{23}{20}\)

a) 3/4 + (-7/5) + 1/4 + (-3/5)

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

= 1 - 2

= -1

b) 4/9 . 7/11 - 4/11 . 2/9 + 6/11 . 4/9

= 4/9 . (7/11 - 2/11 + 6/11)

= 4/9 . 1

= 4/9

a) 

\(\dfrac{3}{4}+\dfrac{-7}{5}+\dfrac{1}{4}+\dfrac{-3}{5}\)

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

\(=1-2\)

\(=-1\)

b)

\(\dfrac{4}{9}.\dfrac{7}{11}-\dfrac{4}{11}.\dfrac{2}{9}+\dfrac{6}{11}.\dfrac{4}{9}\)

\(=\dfrac{28}{99}-\dfrac{8}{99}+\dfrac{24}{99}\)

\(=\dfrac{28-8+24}{99}\)

\(=\dfrac{44}{99}\)

\(=\dfrac{4}{9}\)

Hicc mình hông còn tgian mấy bạn giúp minh 2 câu thui cũng đc ạk

a)  5/9 + 4/9 . 3/7 + 4/9 . 4/7

  = 5/9 + 4/9 . (3/7 + 4/7)

  = 5/9 + 4/9 . 1

  = 5/9 + 4/9

  = 1 

mình lười nghĩ lắm sorry

\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}+\frac{1}{99.100}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)

\(A=1-\frac{1}{100}\)

\(A=\frac{99}{100}\)

\(B=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{107.111}\)

\(B=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{107}-\frac{1}{111}\)

\(B=\frac{1}{3}-\frac{1}{111}\)

\(B=\frac{12}{37}\)

\(C=\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)

\(C=7\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{69}-\frac{1}{70}\right)\)

\(C=7\left(\frac{1}{10}-\frac{1}{70}\right)\)

\(C=7.\frac{3}{35}\)

\(C=\frac{3}{5}\)

Ta có:

\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}+\frac{1}{99.100}\)

\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)

\(A=\frac{1}{1}-\frac{1}{100}=\frac{99}{100}\)

\(B=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{107.111}\)

\(B=4.\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{107}-\frac{1}{111}\right)\)

\(B=4.\left(\frac{1}{3}-\frac{1}{111}\right)=4.\frac{12}{37}=\frac{48}{37}\)

\(C=\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)

\(C=7.\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+...+\frac{1}{69.70}\right)\)

\(C=7.\left(\frac{1}{10}-\frac{1}{70}\right)=7.\frac{3}{35}=\frac{3}{5}\)

\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{98.99}+\frac{1}{99.100}\) 

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)

\(A=1-\frac{1}{100}=\frac{99}{100}\)

\(B=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{107.111}\)

\(B=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{107}-\frac{1}{111}\)

\(B=\frac{1}{3}-\frac{1}{111}=\frac{12}{37}\)

\(C=\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)

\(C=7.\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{69}-\frac{1}{70}\right)\)

\(C=7.\left(\frac{1}{10}-\frac{1}{70}\right)=7.\frac{3}{35}\)

\(\Rightarrow C=\frac{3}{5}\)

a) \(\dfrac{1}{5}+\dfrac{4}{11}+\dfrac{1}{5}+\dfrac{7}{11}=\dfrac{1}{5}+\left(\dfrac{4}{11}+\dfrac{7}{11}\right)=\dfrac{1}{5}+1=\dfrac{1}{5}+\dfrac{5}{5}=\dfrac{6}{5}\)

b) \(\dfrac{3}{5}\times\dfrac{4}{7}+\dfrac{2}{5}\times\dfrac{4}{7}=\left(\dfrac{3}{5}+\dfrac{2}{5}\right)\times\dfrac{4}{7}=1\times\dfrac{4}{7}=\dfrac{4}{7}\)

a: =-1/3+1/3=0

b: \(=\dfrac{4}{11}\left(-\dfrac{2}{7}-\dfrac{4}{7}-\dfrac{1}{7}\right)=\dfrac{4}{11}\cdot\left(-1\right)=-\dfrac{4}{11}\)

c: \(=10+\dfrac{5}{9}-3-\dfrac{5}{7}-4-\dfrac{5}{9}=3-\dfrac{5}{7}=\dfrac{16}{7}\)

d: \(=\dfrac{1}{3}+\dfrac{7}{4}-\dfrac{7}{4}+\dfrac{4}{5}=\dfrac{1}{3}+\dfrac{4}{5}=\dfrac{5+12}{15}=\dfrac{17}{15}\)

a: =-1/3+1/3=0

b: =10+59−3−57−4−59=3−57=167=10+59−3−57−4−59=3−57=167

d: 

12+3/7-11+3/7 tính bằng cách thuận tiện nhé

a)  \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)....\left(1-\frac{1}{20}\right)\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}...........\frac{19}{20}=\frac{1}{20}\)

b)  \(A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{2012}}\)

=>  \(2A=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2011}}\)

=> \(2A-A=\left(2+1+\frac{1}{2}+...+\frac{1}{2^{2011}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2012}}\right)\)

=>  \(A=2-\frac{1}{2^{2012}}\)

c) \(\frac{7}{4}.\left(\frac{3333}{1212}+\frac{3333}{2020}+\frac{3333}{3030}+\frac{3333}{4242}\right)\)

\(=\frac{7}{4}\left(\frac{33}{12}+\frac{33}{20}+\frac{33}{30}+\frac{33}{42}\right)\)

\(=\frac{7}{4}.33\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\)

\(=\frac{231}{4}.\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)

\(=\frac{231}{4}.\left(\frac{1}{3}-\frac{1}{7}\right)\)

\(=\frac{231}{4}.\frac{4}{21}=11\)

d.e)  ktra lại đề