\(\dfrac{-13}{4}.\dfrac{3}{7}-\dfrac{13}{4}.\dfrac{10}{7}-\dfrac{13}{7}\)

\(=\dfrac{13}{4}.\dfrac{-3}{7}-\dfrac{13}{4}.\dfrac{10}{7}-\dfrac{13}{7}\)

\(=\dfrac{13}{4}.\left(\dfrac{-3}{7}-\dfrac{10}{7}\right)-\dfrac{13}{7}\)

\(=\dfrac{13}{4}.\dfrac{-13}{7}-\dfrac{13}{7}\)

\(=\dfrac{-13}{4}.\dfrac{13}{7}-\dfrac{13}{7}\)

\(=\dfrac{13}{7}.\left(\dfrac{-13}{4}-1\right)\)

\(=\dfrac{13}{7}.-\dfrac{17}{4}\)

\(=-\dfrac{221}{28}\)

* Cách làm nhanh: Với biểu thức như trên, hai phân số nhân với nhau có thể đổi dấu cho nhau.*

-13/4 . 3/7 - 13/4 . 10/7 - 13/7

= -13/4 . (3/7 + 10/7) - 13/7

= -13/4 . 13/7 - 13/7

= 13/7 . (-13/4 - 1)

= 13/7 . (-17/4)

= -221/28

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:

\(\frac{x}{1\cdot4}+\frac{x}{4\cdot7}+\frac{x}{7\cdot10}+\frac{x}{10\cdot13}+\frac{x}{13\cdot16}=\frac{5}{2}\)

\(\Rightarrow\frac{x}{3}\left[\frac{3}{1\cdot4}+\frac{3}{4\cdot7}+\frac{3}{7\cdot10}+\frac{3}{10\cdot13}+\frac{3}{13\cdot16}\right]=\frac{5}{2}\)

\(\Rightarrow\frac{x}{3}\left[1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{16}\right]=\frac{5}{2}\)

\(\Rightarrow\frac{x}{3}\left[1-\frac{1}{16}\right]=\frac{5}{2}\)

\(\Rightarrow\frac{x}{3}\cdot\frac{15}{16}=\frac{5}{2}\)

\(\Rightarrow\frac{x}{3}=\frac{5}{2}:\frac{15}{16}\)

\(\Rightarrow\frac{x}{3}=\frac{5}{2}\cdot\frac{16}{15}\)

\(\Rightarrow\frac{x}{3}=\frac{1}{1}\cdot\frac{8}{3}\)

\(\Rightarrow\frac{x}{3}=\frac{8}{3}\Leftrightarrow x=8\)

a) Thiếu đề

b) ` 4/7 xx 8/13 + 8/13 xx 3/7`

= ` 8/13 xx ( 4/7 + 3/7)`

` = 8/13 xx 7/7`

` = 8/13 xx 1`

` = 8/13`

a) thiếu đề

b) \(=\left(\dfrac{4}{7}+\dfrac{3}{7}\right)\times\dfrac{8}{13}\\ =1\times\dfrac{8}{13}=\dfrac{8}{13}\)

1) = \(\frac{3}{5}\)

2) =\(\frac{6}{7}\)

3)\(\frac{9}{13}\)

4)\(\frac{4}{13}\)

\(\dfrac{-4}{3}-\dfrac{5}{7}+\dfrac{4}{3}=\left(\dfrac{4}{3}+\dfrac{-4}{3}\right)-\dfrac{5}{7}=0-\dfrac{5}{7}=-\dfrac{5}{7}\)

\(\dfrac{3}{13}\cdot\dfrac{6}{11}+\dfrac{3}{13}\cdot\dfrac{9}{11}-\dfrac{3}{13}\cdot\dfrac{4}{11}=\dfrac{3}{13}\cdot\left(\dfrac{6}{11}+\dfrac{9}{11}-\dfrac{4}{11}\right)=\dfrac{3}{13}\cdot1=\dfrac{3}{13}\)

9/13 x 7/12 + 9/13 x 5/12 - 9/13

= 9/13 x (7/12 + 5/12 - 1)

= 9/13 x 0

= 0

4/13 x 5/12 + 4/13 x 7/12 - 4/3

= 4/13 x (5/12 + 7/12) - 4/3

= 4/13 x 1 - 4/3

= 4/13 - 4/3

= -40/39

a) 9/13 x 7/12 + 9/13 x 5/12 - 9/13

= 9/13 x ( 5/12 + 7/12 - 1 )

= 9/13 x 0

= 0

b) 4/13 x 5/12 + 4/13 x 7/ 12 - 4/3

= 4/13 x ( 5/12 + 7/12 - 13/3 )

= 4/13 x ( - 10/3 )

= -40/39 

a) \(\frac{9}{13}\cdot\frac{7}{12}+\frac{9}{13}\cdot\frac{5}{12}-\frac{9}{13}\)

\(=\frac{9}{13}.\left(\frac{7}{12}+\frac{5}{12}-1\right)=\frac{9}{13}.\left(1-1\right)=\frac{9}{13}.0=0\)

b) \(\frac{4}{13}\cdot\frac{5}{12}+\frac{4}{13}\cdot\frac{7}{12}-\frac{4}{3}\)

\(=\frac{4}{13}.\left(\frac{5}{12}+\frac{7}{12}\right)-\frac{4}{3}=\frac{4}{13}.1-\frac{4}{3}=\frac{4}{13}-\frac{4}{3}\)

trình bày đày đủ giúp em ạ

\(a,\dfrac{5}{3}\times\dfrac{4}{5}=\dfrac{4}{3}\) (phần rút gọn : bỏ 5)

\(b,\dfrac{2}{3}\times\dfrac{3}{7}=\dfrac{2}{7}\) (phần rút gọn : bỏ 3)

\(c,\dfrac{7}{13}\times\dfrac{13}{7}=1\) (phần rút gọn : bỏ 7 và 13)

a)\(\dfrac{5}{3}\)x\(\dfrac{4}{5}\)=\(\dfrac{5x4}{3x5}\)=\(\dfrac{20}{15}\)=\(\dfrac{4}{3}\)(rút gọn \(\dfrac{20}{15}\)=\(\dfrac{4}{3}\))

b)\(\dfrac{2}{3}\)x\(\dfrac{3}{7}\)=\(\dfrac{2x3}{3x7}\)=\(\dfrac{6}{21}\)=\(\dfrac{2}{7}\)(rút gọn\(\dfrac{6}{21}\)=\(\dfrac{2}{7}\))

c)\(\dfrac{7}{13}\)x\(\dfrac{13}{7}\)=\(\dfrac{7x13}{13x7}\)=\(\dfrac{91}{91}\)=1(rút gọn\(\dfrac{91}{91}\)=1)

\(\frac{315}{316}\cdot\frac{316}{314}\cdot\frac{316}{315}\cdot\frac{317}{313}=\frac{315.316.316.317}{316.314.315.313}=\frac{1.1.316.317}{1.314.1.313}=\frac{100172}{98282}\)

Ta có : \(\frac{3}{2}\times\frac{4}{5}\times\frac{2}{3}\)

\(=\frac{3}{2}\times\frac{2}{3}\times\frac{4}{5}=1\times\frac{4}{5}\)

\(=\frac{4}{5}\)

\(\frac{4}{5}\) nhé bn

a) \(\frac{18}{45}-\frac{4}{12}-\frac{6}{9}-\frac{21}{35}=\frac{2}{5}-\frac{1}{3}-\frac{2}{3}-\frac{3}{5}\)

\(=\left(\frac{2}{5}-\frac{3}{5}\right)-\left(\frac{1}{3}+\frac{2}{3}\right)\)

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

\(=\frac{-4}{3}\)

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

\(=4+1=5\)

c) \(\frac{1}{3}.\frac{4}{5}.\frac{1}{3}.\frac{6}{5}=\frac{8}{75}\)

d) \(\frac{6}{7}.\frac{8}{13}+\frac{6}{7}.\frac{9}{13}-\frac{3}{13}.\frac{6}{7}\)

\(=\frac{6}{7}.\left(\frac{8}{13}+\frac{9}{13}-\frac{3}{13}\right)\)

\(=\frac{6}{7}.\frac{14}{13}\)

\(=\frac{12}{13}\)