tính bằng cách thuận tiện nhất
\(\left(\dfrac{4}{5}+\dfrac{5}{4}\right)\)x\(\dfrac{3}{4}\)
Tính bằng cách thuận tiện nhất:
\(\left(1-\dfrac{1}{2}\right)\text{× }\left(1-\dfrac{1}{3}\right)\text{ × }\left(1-\dfrac{1}{4}\right)\text{ × }\left(1-\dfrac{1}{5}\right)\text{}\text{}\text{× }\left(1-\dfrac{1}{6}\right)\)
Lời giải:
Gọi tích trên là $A$. Ta có:
$A=\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}\times \frac{4}{5}\times \frac{5}{6}$
$=\frac{1\times 2\times 3\times 4\times 5}{2\times 3\times 4\times 5\times 6}=\frac{1}{6}$
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 6 : Tính bằng cách thuận tiện nhất
a) \(\dfrac{7}{6}x\)\(\dfrac{3}{4}+\dfrac{3}{4}x\)\(\dfrac{5}{6}-\dfrac{3}{4}\)
b) \(\dfrac{6x7x15x8}{4x21x10x3}\)
\(\dfrac{7}{6}\times\dfrac{3}{4}+\dfrac{3}{4}\times\dfrac{5}{6}-\dfrac{3}{4}\\ =\left(\dfrac{7}{6}+\dfrac{5}{6}-1\right)\times\dfrac{3}{4}\\ =1\times\dfrac{3}{4}=\dfrac{3}{4}\\ \dfrac{6\times7\times15\times8}{4\times21\times10\times3}\\ =\dfrac{2\times3\times7\times5\times3\times4\times2}{4\times7\times3\times5\times2\times3}\\ =2\)
Tính bằng cách thuận tiện nhất:
\(\dfrac{2}{5}\) *\(\dfrac{4}{7}\)+\(\dfrac{3}{5}\)*\(\dfrac{4}{7}\)
\(\dfrac{4}{7}x\left(\dfrac{2}{5}+\dfrac{3}{5}\right)=\dfrac{4}{7}x1=\dfrac{4}{7}\)
2/5 x 4/7 + 3/5 x 4/7
= (2/5 + 3/5 ) x 4/7
= 1 x 4/7
= 4/7
2/5 *4/7+3/5*4/7
=( 2/5 + 3/5 ) *4/7
= 1 * 4/7
= 4/7
Tính bằng cách thuận tiện nhất:
a) \(\left(689+875\right)+125\); \(581+\left(878+419\right)\).
b) \(\left(\dfrac{2}{7}+\dfrac{4}{9}\right)+\dfrac{5}{7}\); \(\dfrac{17}{11}+\left(\dfrac{7}{15}+\dfrac{5}{11}\right)\).
c) \(5,87+28,69+4,13\); \(83,75+46,98+6,25\).
a) (689 + 875) + 125
= 689 + (875 + 125)
= 689 + 1000 = 1689.
581 + (878 + 419)
= (581 + 419) = 878
= 1000 + 878 = 1878.
b)
c) 5,87 + 28,69 + 4,13
= (5,87 + 4,13) + 28,69
= 10 + 28,69
= 38,69.
83,75 + 46,98 + 6,25
= (83,75 + 6,25) + 46,98
= 90 + 46,98
= 136,98.
a)(689+875)+125=689+(875+125)=689+1000=1689
581 + (878+419)=581+419+878=1000+878=1878
b)(2/7+4/9)+5/7=2/7+5/7+4/9=7/7+4/9=1+4/9=9/9+4/9=13/9
17/11+(7/15+5/11)=17/11+5/11+7/15=2+7/15=30/15+7/15=3/15
c)5,87+28,69+4,13=5,87+4,13+28,69=10+28,69=38,69
83,75+46,98+6,25=83,75+6,25+46,98=90+46,98=136,98
1. Tính bằng cách thuận tiện nhất:
\(\dfrac{2}{5}x\dfrac{12}{3}+\dfrac{2}{5}x\dfrac{15}{3}+\dfrac{2}{5}\)
2. Tìm số tự nhiên a, biết: \(\dfrac{3}{4}< a< \dfrac{11}{4}\)
1.
=2/5 x 12/3 + 2/5 x 15/3 + 2/5 x 1
= 2/5 x (12/3 + 15/3 + 1)
=2/5 x 1
=2/5
2.a=1;2
Tính bằng cách thuận tiện nhất
\(\dfrac{2}{3}\times\dfrac{3}{4}\times\dfrac{4}{5}\)
\(\dfrac{2}{3}\times\dfrac{3}{4}\times\dfrac{4}{5}\) \(=\dfrac{2\times3\times4}{3\times4\times5}\) \(=\) \(\dfrac{2}{5}\)
\(\dfrac{2}{3}x\dfrac{3}{4}x\dfrac{4}{5}=\dfrac{2}{5}\)
\(\dfrac{2}{3}\)x\(\dfrac{3}{5}\)=\(\dfrac{2}{5}\)
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\(\dfrac{3}{5}\)=
\(a,\dfrac{5}{13}\times\dfrac{4}{15}\times13=\dfrac{5\times4\times13}{13\times5\times3}=\dfrac{4}{3}\\ b,\left(\dfrac{3}{7}+\dfrac{5}{2}\right)\times\dfrac{7}{5}=\dfrac{3}{7}\times\dfrac{7}{5}+\dfrac{5}{2}\times\dfrac{7}{5}=\dfrac{3}{5}+\dfrac{7}{2}=\dfrac{6}{10}+\dfrac{35}{10}=\dfrac{41}{10}\\ c,\dfrac{1}{5}\times\dfrac{11}{18}+\dfrac{11}{18}\times\dfrac{3}{5}=\dfrac{11}{18}\times\left(\dfrac{1}{5}+\dfrac{3}{5}\right)=\dfrac{11}{18}\times\dfrac{4}{5}=\dfrac{22}{45}\)