`a, 1/5 +5/9 + 4/5 +1/9 +3/9`

`=(1/5 +4/5)+(5/9 + 1/9+3/9)`

`= 5/5 + 9/9`

`=1+1`

`=2`

`b, 1/3 +1/6 +4/3 +2/6 + 2/3 + 5/6`

`=(1/3 + 4/3+2/3)+(1/6 +2/6+5/6)`

`= 7/3 + 8/6`

`=7/3 + 4/3`

`= 11/3`

`@ yL`

A = \(\dfrac{1}{2}\)+ \(\dfrac{1}{3}\)+ \(\dfrac{1}{4}\)+ \(\dfrac{1}{2}\)+ \(\dfrac{2}{3}\)+ \(\dfrac{3}{4}\)

A = ( \(\dfrac{1}{2}\)+ \(\dfrac{1}{2}\)) + ( \(\dfrac{1}{4}\)+\(\dfrac{3}{4}\)) +( \(\dfrac{1}{3}\)+ \(\dfrac{2}{3}\))

A = 1 + 1 + 1

A = 3

B = ( \(\dfrac{3}{4}\) + \(\dfrac{5}{7}\)+ \(\dfrac{16}{64}\)+ \(\dfrac{2}{7}\)) - 2

B = ( \(\dfrac{3}{4}\)+ \(\dfrac{1}{4}\)) + ( \(\dfrac{5}{7}\)+ \(\dfrac{2}{7}\)) - 2

B = 1 + 1 - 2

B = 2 - 2

B = 0

1/2 x 1/3 + 1/3 x 1/4 + 1/4 x 1/5 + 1/5 x 1/6

= 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6

= 1/2 - 1/6

= 1/3

1) Ta có: \(\left(\dfrac{3}{4}\cdot\dfrac{5}{97}+\dfrac{1}{9}\cdot\dfrac{13}{47}\right)\cdot\left(\dfrac{1}{5}-\dfrac{7}{25}\cdot\dfrac{5}{7}\right)\)

\(=\left(\dfrac{3}{4}\cdot\dfrac{5}{97}+\dfrac{1}{9}\cdot\dfrac{13}{47}\right)\cdot\left(\dfrac{1}{5}-\dfrac{1}{5}\right)\)

=0

2) Ta có: \(\dfrac{8}{17}\cdot\dfrac{4}{15}+\dfrac{8}{17}\cdot\dfrac{22}{15}-\dfrac{8}{15}\cdot\dfrac{9}{17}\)

\(=\dfrac{8}{17}\left(\dfrac{4}{15}+\dfrac{22}{15}-\dfrac{9}{15}\right)\)

\(=\dfrac{8}{17}\cdot\dfrac{15}{15}=\dfrac{8}{17}\)

3) Ta có: \(\dfrac{2021}{2}\cdot\dfrac{1}{3}+\dfrac{4042}{4}\cdot\dfrac{1}{5}+\dfrac{6063}{3}\cdot\dfrac{22}{15}\)

\(=\dfrac{2021}{2}\left(\dfrac{1}{3}+\dfrac{1}{5}\right)+2021\cdot\dfrac{22}{15}\)

\(=\dfrac{2021}{2}\cdot\dfrac{8}{15}+\dfrac{2021}{2}\cdot\dfrac{44}{15}\)

\(=\dfrac{2021}{2}\cdot\dfrac{52}{15}\)

\(=\dfrac{52546}{15}\)

4) Ta có: \(\dfrac{4}{7}\cdot\dfrac{2}{13}+\dfrac{8}{13}:\dfrac{7}{4}+\dfrac{4}{7}:\dfrac{13}{2}+\dfrac{4}{7}\cdot\dfrac{1}{13}\)

\(=\dfrac{4}{7}\left(\dfrac{2}{13}+\dfrac{8}{13}+\dfrac{2}{13}+\dfrac{1}{13}\right)\)

\(=\dfrac{4}{7}\)

1) Tính biểu thức:

= 3/2 + 2/3 + 2/4 + 2/5

= (6/4 + 2/4) + (2/3 + 2/5)

= 8/4 + 16/ 15 

= 46/15

=46/15

\(\frac{1}{7}+\frac{2}{7}+\frac{3}{7}+\frac{4}{7}+\frac{5}{7}+\frac{6}{7}\)

\(=\left(\frac{1}{7}+\frac{6}{7}\right)+\left(\frac{2}{7}+\frac{5}{7}\right)+\left(\frac{3}{7}+\frac{4}{7}\right)\)

\(=1+1+1=3\)

\(5\dfrac{3}{4}:3+2\dfrac{1}{4}\times\dfrac{1}{3}-\dfrac{1}{8}=\left(5\dfrac{3}{4}+2\dfrac{1}{4}\right)\times\dfrac{1}{3}-\dfrac{1}{8}\\ =8\times\dfrac{1}{3}-\dfrac{1}{8}=\dfrac{8}{3}-\dfrac{1}{8}=\dfrac{61}{24}\\ ----\\ \dfrac{3}{5}:\dfrac{5}{6}:\dfrac{6}{7}:\dfrac{7}{8}+\dfrac{2}{5}+\dfrac{23}{35}\\ =\dfrac{3}{5}\times\dfrac{6}{5}\times\dfrac{7}{6}\times\dfrac{8}{7}+\dfrac{2}{5}+\dfrac{23}{35}=\dfrac{18}{25}\times\dfrac{4}{3}+\dfrac{2}{5}+\dfrac{23}{35}=\dfrac{353}{175}\)

\(\dfrac{2}{3}:\dfrac{4}{3}:\dfrac{5}{4}:\dfrac{1}{5}\)

=\(\dfrac{2}{3}\cdot\dfrac{3}{4}:\dfrac{5}{4}\cdot\dfrac{5}{1}\)

=\(\dfrac{1}{2}\cdot\dfrac{25}{4}\)

=\(\dfrac{25}{8}\)