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

`1/4+2/5+3/4+3/5`

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

`=4/4+5/5`

`=1+1`

`=2`

184 trang nha bạn

184

\(\dfrac{15}{5}-\dfrac{3}{7}-\dfrac{1}{7}\)
\(=\dfrac{15}{5}-\left(\dfrac{3}{7}+\dfrac{1}{7}\right)\)
\(=3-\dfrac{4}{7}\)
\(=\dfrac{21}{7}-\dfrac{4}{7}\)
\(=\dfrac{17}{7}\)

Ai bít ko 

\(\dfrac{21}{17}\times\dfrac{13}{14}\times56\times\dfrac{3}{42}\)
\(=\dfrac{21}{17}\times\dfrac{13}{14}\times56\times\dfrac{1}{14}\)
\(=\dfrac{21\times13\times56}{17\times14\times14}\)
\(=\dfrac{3\times7\times13\times14\times2\times2}{17\times2\times7\times14}\)
\(=\dfrac{3\times13\times2}{17}\)
\(=\dfrac{78}{17}\)

A = 1/1 - 1/2 + 1/3 - 1/3 + 1/4

A = 1/1 - 1/4

A = 3/4

vậy A = 3/4

\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}\)

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

\(=1-\dfrac{1}{4}=\dfrac{4-1}{4}=\dfrac{3}{4}\)

\(\dfrac{1}{42}+\dfrac{1}{30}+\dfrac{1}{12}+\dfrac{1}{6}+\dfrac{1}{2}\)
\(=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{30}+\dfrac{1}{42}\)
\(=\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{5\times6}+\dfrac{1}{6\times7}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}\)
\(=1-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{7}\)
\(=\dfrac{140}{140}-\dfrac{35}{140}+\dfrac{28}{140}-\dfrac{20}{140}\)
\(=\dfrac{113}{140}\)

\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{30}+\dfrac{1}{42}\)

\(=\dfrac{1}{2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{5.6}+\dfrac{1}{6.7}\)

\(=\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}\)

\(=1-\dfrac{1}{4}+\dfrac{1}{5}-\dfrac{1}{7}=\dfrac{140-35+28-20}{140}=\dfrac{113}{140}\)

Mình nghĩ đề bài cần thêm 1/20 mới tính nhanh được

\(\dfrac{5}{3}< x< \dfrac{7}{3}\)
\(\dfrac{5}{3}< \dfrac{x}{3}< \dfrac{7}{3}\)
\(x=\dfrac{6}{3}\)
\(x=2\)

vì 5/3 < x > 7/3 

=> x = 6/3 * hoặc x = 2 *

\(\dfrac{1}{3}=44:\dfrac{x}{66}\)
\(\dfrac{x}{66}=44:\dfrac{1}{3}\)
\(\dfrac{x}{66}=44\times3\)
\(\dfrac{x}{66}=132\)
\(x=132\times66\)
\(x=8712\)

Cách 1:
\(\dfrac{7}{5}-\dfrac{1}{3}-\dfrac{1}{5}\)
\(=\dfrac{21}{15}-\dfrac{5}{15}-\dfrac{3}{15}\)
\(=\dfrac{13}{15}\)
Cách 2:
\(\dfrac{7}{5}-\dfrac{1}{3}-\dfrac{1}{5}\)
\(=\left(\dfrac{7}{5}-\dfrac{1}{5}\right)-\dfrac{1}{3}\)
\(=\dfrac{6}{5}-\dfrac{1}{3}\)
\(=\dfrac{18}{15}-\dfrac{5}{15}\)
\(=\dfrac{13}{15}\)

\(A=\dfrac{1+2+3+...+9}{21+22+...+29}\)
\(=\dfrac{\left(1+9\right)+\left(2+8\right)+\left(3+7\right)+...+\left(5+5\right)}{\left(21+29\right)+\left(22+28\right)+\left(23+27\right)+...+\left(25+25\right)}\)
\(=\dfrac{10+10+10+...+10}{50+50+50+...+50}\)
\(=\dfrac{10\times5}{50\times5}\)
\(=\dfrac{10}{50}\)
\(=\dfrac{1}{5}\)