Tính bằng cách thuận tiện nhất :
( 1 - \(\dfrac{1}{2}\) ) x ( 1 - \(\dfrac{1}{3}\) ) x ( 1 - \(\dfrac{1}{4}\) ) x ( 1 - \(\dfrac{1}{5}\) ) x ( 1 - \(\dfrac{1}{6}\) )
Tính bằng cách thuận tiện nhất
(1+\(\dfrac{1}{2}\)) x (1+\(\dfrac{1}{3}\)) x (1+\(\dfrac{1}{4}\)) x (1+\(\dfrac{1}{5}\)) =
( 1 + 1/2 ) . ( 1+ 1/3) . ( 1+ 1/4 ) . ( 1+ 1/5 )
=3/2 . 4/3.5/4.6/5
= 3.4.5.6/2.3.4.5
=6/2 = 3
= 1 x ( \(\dfrac{1}{2}\) + \(\dfrac{1}{3}\) + \(\dfrac{1}{4}\) + \(\dfrac{1}{5}\) )
= 1 x \(\dfrac{77}{60}\)
= \(\dfrac{77}{60}\)
Tính bằng cách thuận tiện nhất
B=\(\dfrac{1+\dfrac{1}{7}+\dfrac{1}{7^2}-\dfrac{1}{7^3}}{4+\dfrac{4}{7}+\dfrac{4}{7^2}-\dfrac{4}{7^3}}x\dfrac{858585}{313131}x\left(-1\dfrac{14}{17}\right)\)
\(B=\dfrac{1+\dfrac{1}{7}+\dfrac{1}{7^2}-\dfrac{1}{7^3}}{4+\dfrac{4}{7}+\dfrac{4}{7^2}-\dfrac{4}{7^3}}\cdot\dfrac{858585}{313131}\cdot\left(-1\dfrac{14}{17}\right)\)
\(=\dfrac{1}{4}\cdot\dfrac{85}{31}\cdot\dfrac{-31}{17}\)
\(=\dfrac{-5}{4}\)
Ta có: \(B=\dfrac{1+\dfrac{1}{7}+\dfrac{1}{7^2}-\dfrac{1}{7^3}}{4+\dfrac{4}{7}+\dfrac{4}{7^2}-\dfrac{4}{7^3}}.\dfrac{858585}{313131}.\left(-1\dfrac{14}{17}\right)\)
\(=\dfrac{1+\dfrac{1}{7}+\dfrac{1}{7^2}-\dfrac{1}{7^3}}{4\left(1+\dfrac{1}{7}+\dfrac{1}{7^2}-\dfrac{1}{7^3}\right)}.\dfrac{85.10101}{32.10101}.\dfrac{-31}{17}=\dfrac{1}{4}.\dfrac{85}{31}.\dfrac{-31}{17}=-\dfrac{5}{4}\)
Bài 1: Tính
a) \(\dfrac{9}{5}+\dfrac{2}{5}\) x \(\dfrac{4}{6}\) b) \(\dfrac{3}{8}\) x 2 - \(\dfrac{6}{7}\) x \(\dfrac{1}{3}\)
Bài 2: Tính bằng cách thuận tiện nhất:
a) \(\dfrac{11}{23}+\dfrac{2}{23}+\dfrac{9}{23}+\dfrac{18}{23}\) b)\(\dfrac{25}{12}+\dfrac{17}{6}-\dfrac{15}{36}-\dfrac{15}{6}\)
Bài 3: Một hình chữ nhật có chiều rộng là \(\dfrac{3}{5}\) m và bằng một nửa chiều dài. Tính diện tích hình chữ nhật đó.
a) \(\dfrac{3}{7}\)+\(\dfrac{4}{9}\)+\(\dfrac{8}{14}\)+\(\dfrac{10}{18}\)
b) \(\dfrac{1}{2}\)x\(\dfrac{2}{3}\):\(\dfrac{5}{6}\)x\(\dfrac{5}{6}\)
bài này là bài tính bằng cách thuận tiện nhất nha !
a) tính nhanh
( 1 + \(\dfrac{1}{2}\) ) x ( 1 + \(\dfrac{1}{3}\) ) x ..... x ( 1 + \(\dfrac{1}{2005}\) )
b) tính bằng cách thuận tiện
\(\dfrac{2}{3}\) x \(\dfrac{1}{2}\) + \(\dfrac{1}{3}\) x \(\dfrac{1}{2}\)
a)\(=\left(\dfrac{2}{2}+\dfrac{1}{2}\right)\times\left(\dfrac{3}{3}+\dfrac{1}{3}\right)\times...\times\left(\dfrac{2005}{2005}+\dfrac{1}{2005}\right)\)
\(=\dfrac{3}{2}\times\dfrac{4}{3}\times...\times\dfrac{2006}{2005}=\dfrac{2006}{2}=1003\)
b)\(=\left(\dfrac{2}{3}+\dfrac{1}{3}\right)\times\dfrac{1}{2}=\dfrac{3}{3}\times\dfrac{1}{2}=\dfrac{1}{2}\)
b)
\(\dfrac{1}{2}x\left(\dfrac{2}{3}+\dfrac{1}{3}\right)=\dfrac{1}{2}x1=\dfrac{1}{2}\)
Tính bằng cách thuận tiện:
(1-\(\dfrac{3}{4}\)) x (1 - \(\dfrac{3}{7}\)) x (1 - \(\dfrac{3}{10}\)) x (1 - \(\dfrac{3}{13}\)) x ....... x (1 - \(\dfrac{3}{97}\)) x (1 - \(\dfrac{3}{100}\))
Giải:
\(\left(1-\dfrac{3}{4}\right).\left(1-\dfrac{3}{7}\right).\left(1-\dfrac{3}{10}\right).\left(1-\dfrac{3}{13}\right).....\left(1-\dfrac{3}{97}\right).\left(1-\dfrac{3}{100}\right)\)
\(=\dfrac{1}{4}.\dfrac{4}{7}.\dfrac{7}{10}.\dfrac{10}{13}.....\dfrac{94}{97}.\dfrac{97}{100}\)
\(=\dfrac{1.4.7.10.....94.97}{4.7.10.13.....97.100}\)
\(=\dfrac{1}{100}\)
Tính bằng cách thuận tiện nhất:
a) 60 x (\(\dfrac{7}{12}\) + \(\dfrac{4}{15}\))
b) \(\dfrac{1}{2}\) x \(\dfrac{2}{3}\) x \(\dfrac{3}{4}\) x \(\dfrac{4}{5}\) x \(\dfrac{5}{6}\) x \(\dfrac{6}{7}\) x \(\dfrac{7}{8}\) x \(\dfrac{8}{9}\)
60x [7/12+4/15]
60x153/180
=9180/180
b 1/2x2/3x3/4x4/5x5/6x6/7x7/8x8/9=40320/4032
Tìm x:
\(\dfrac{3}{4}-x=\dfrac{1}{8}\)
Tính bằng cách thuận tiện:
\(\dfrac{2}{5}\)x\(\dfrac{9}{4}-\dfrac{5}{4}\)x\(\dfrac{2}{5}\)
x=3/4-1/8
x=6/8-1/8
x=6/8
=2/5.(9/4-5/4)
=2/5.1
=2/5
\(x=\dfrac{3}{4}-\dfrac{1}{8}\)\(\)
\(x=\dfrac{6}{8}-\dfrac{1}{8}\)
\(x=\dfrac{5}{8}\)
\(=\dfrac{2}{5}x\left(\dfrac{9}{4}-\dfrac{5}{4}\right)\)
\(=\dfrac{2}{5}x1\)
\(=\dfrac{2}{5}\)
`x=3/4-1/8`
`x=5/8`
------------------------
`=2/5xx(9/4+5/4)`
`=2/5xx7/2=5/7`
tính bằng cách thuận tiện nhất a, \(\dfrac{5}{13}\)x\(\dfrac{4}{15}\)x13= b, (\(\dfrac{3}{7}\)+\(\dfrac{5}{2}\))x\(\dfrac{7}{5}\)= c, \(\dfrac{1}{5}\)x\(\dfrac{11}{18}\)+\(\dfrac{11}{18}\)x\(\dfrac{3}{5}\)=
\(a,\dfrac{5}{13}\times\dfrac{4}{15}\times13=\dfrac{5\times4\times13}{13\times5\times3}=\dfrac{4}{3}\\ b,\left(\dfrac{3}{7}+\dfrac{5}{2}\right)\times\dfrac{7}{5}=\dfrac{3}{7}\times\dfrac{7}{5}+\dfrac{5}{2}\times\dfrac{7}{5}=\dfrac{3}{5}+\dfrac{7}{2}=\dfrac{6}{10}+\dfrac{35}{10}=\dfrac{41}{10}\\ c,\dfrac{1}{5}\times\dfrac{11}{18}+\dfrac{11}{18}\times\dfrac{3}{5}=\dfrac{11}{18}\times\left(\dfrac{1}{5}+\dfrac{3}{5}\right)=\dfrac{11}{18}\times\dfrac{4}{5}=\dfrac{22}{45}\)