\(\frac{1}{2.3}+\frac{1}{6.5}+\frac{1}{10.7}+\frac{1}{14.9}+...+\frac{1}{198.101}\)

= \(2.\left(\frac{1}{2.6}+\frac{1}{6.10}+\frac{1}{10.14}+\frac{1}{14.18}+...+\frac{1}{198.202}\right)\)

= \(2.\frac{1}{4}.\left(\frac{1}{2}-\frac{1}{6}+\frac{1}{6}-\frac{1}{10}+\frac{1}{10}-\frac{1}{14}+\frac{1}{14}-\frac{1}{18}+...+\frac{1}{198}-\frac{1}{202}\right)\)

= \(\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{202}\right)\)

= \(\frac{1}{2}.\frac{50}{101}\)

= \(\frac{25}{101}\)

A=25/101

ta có 

\(\frac{2.6.10+6.10.14+..+194.198.202}{1.3.5+3.5.7+..+97.99.101}=\frac{8.1.3.5+8.3.5.7+..+8.97.99.101}{1.3.5+3.5.7+..+97.99.101}\)

\(=\frac{8.\left(1.3.5+3.5.7+..+97.99.101\right)}{1.3.5+3.5.7+..+97.99.101}=8\)

A=\(\frac{2.6.10+6.10.14+...+194+198+202}{1.3.5+3.5.7+...+97.99.101}\)\(=\frac{2.2.2\left(1.3.5\right)+2.2.2\left(3.5.7\right)+...+2.2.2\left(97.99.101\right)}{1.3.5+3.5.7+...+97.99.101}\)

\(=\frac{2.2.2\left(1.3.5+3.5.7+...+97.99.101\right)}{1.3.5+3.5.7+...+97.99.101}\)\(=\frac{2.2.2}{1}=8\)

A=(1-3)+(5-7)+(9-11)+...+(97-99)+101

Từ 1 đến 99 có 50 số số hạng

=> A=(-2) x 50 +101

<=> A=-100 x 101

<=> A=-10100

a) 1/2x(3/4+2/5)                               

1/2x23/20                                         

23/40                                               

b) 3/4:(8/9+16/3)

3/4:56/9

27/224

c) 1/5:1/10-1/3

2-1/3

5/3

d) 3/4x(20/9-8/15)

3/4x76/45

19/15

e) 1/7:5/14-3/2

=2/5-3/2

-11/10 ( Chị nghĩ lớp 4 chưa học đến số âm nên em xem lại đề nhé)

g) 3/2x(11/6-5/12)

3/2x17/12

17/8

a)\(\frac{1}{2}x\left(\frac{3}{4}+\frac{2}{5}\right)\)

\(=\frac{1}{2}x\left(\frac{15}{20}+\frac{8}{20}\right)\)

\(=\frac{1}{2}x\frac{23}{20}\)

\(=\frac{23}{40}\)

b)\(\frac{3}{4}:\left(\frac{8}{9}+\frac{16}{3}\right)\)

\(=\frac{3}{4}:\left(\frac{8}{9}+\frac{48}{9}\right)\)

\(=\frac{3}{4}:\frac{56}{9}\)

\(=\frac{3}{4}x\frac{9}{56}\)

\(=\frac{27}{224}\)

c) \(\frac{1}{5}:\frac{1}{10}-\frac{1}{3}\)

\(=\frac{1}{5}x10-\frac{1}{3}\)

\(=2-\frac{1}{3}\)

\(=\frac{6}{3}-\frac{1}{3}=\frac{5}{3}\)

d) \(\frac{3}{4}x\left(\frac{20}{9}-\frac{8}{15}\right)\)

\(=\frac{3}{4}x\left(\frac{100}{45}-\frac{24}{45}\right)\)

\(=\frac{3}{4}x\frac{76}{45}\)

\(=\frac{19}{5}\)

e) \(\frac{1}{7}:\frac{5}{14}-\frac{3}{2}\)

\(=\frac{1}{7}x\frac{14}{5}-\frac{3}{2}\)

\(=\frac{2}{5}-\frac{3}{2}\)

\(=\frac{4}{10}-\frac{15}{10}\)

\(=\frac{-11}{10}\)

g) \(\frac{3}{2}x\left(\frac{11}{6}-\frac{5}{12}\right)\)

\(=\frac{3}{2}x\left(\frac{22}{12}-\frac{5}{12}\right)\)

\(=\frac{3}{2}x\frac{17}{12}\)

=\(=\frac{17}{8}\)