Tính bằng cách thuận tiện.
a) \(\dfrac{599}{1000}+\dfrac{377}{1000}+\dfrac{1}{1000}\) b) \(\dfrac{15}{4}+\dfrac{15}{16}+\dfrac{5}{16}\)
Tính bằng cách thuận tiện nhất.
a) \(\dfrac{16}{15}+\dfrac{7}{15}+\dfrac{4}{15}\) b) \(\dfrac{5}{17}+\dfrac{7}{17}+\dfrac{13}{17}\)
a) \(\dfrac{16}{15}+\dfrac{7}{15}+\dfrac{4}{15}=\left(\dfrac{16}{15}+\dfrac{4}{15}\right)+\dfrac{7}{15}=\dfrac{20}{15}+\dfrac{7}{15}=\dfrac{27}{15}\)
b) \(\dfrac{5}{17}+\dfrac{7}{17}+\dfrac{13}{17}=\dfrac{5}{17}+\left(\dfrac{7}{17}+\dfrac{13}{17}\right)=\dfrac{5}{17}+\dfrac{20}{17}=\dfrac{25}{17}\)
So sánh A và B biết:
a) A= \(\dfrac{15^{16}+1}{15^{17}+1}\) và B= \(\dfrac{15^{15}+1}{15^{16}+1}\)
b) A= \(\dfrac{2006^{2007}+1}{2006^{2006}+1}\) và B= \(\dfrac{2006^{2006}+1}{2006^{2005}+1}\)
c) A= \(\dfrac{1000^9+2}{1000^9-1}\) và B= \(\dfrac{1000^9+1}{1000^9-2}\)
a) Vì A=\(\dfrac{15^{16}+1}{15^{17}+1}\) < 1
\(\Rightarrow\dfrac{15^{16}+1}{15^{17}+1}< \dfrac{15^{16}+1+14}{15^{17}+1+14}=\dfrac{15^{16}+15}{15^{17}+15}\) \(=\dfrac{15\left(15^{15}+1\right)}{15\left(15^{16}+1\right)}\) \(=\dfrac{15^{15}+1}{15^{16}+1}\)
Vậy A<B
b) A=\(\dfrac{2006^{2007}+1}{2006^{2006}+1}>1\)
\(\Rightarrow\dfrac{2006^{2007}+1+2005}{2006^{2006}+1+2005}\)
= \(\dfrac{2006^{2007}+2006}{2006^{2006}+2006}\)
= \(\dfrac{2006\left(2006^{2006}+1\right)}{2006\left(2006^{2005}+1\right)}\)
= \(\dfrac{2006^{2006+1}}{2006^{2005}+1}\)
Vậy A>B
a, \(A=\dfrac{15^{16}+1}{15^{17}+1}\) và \(B=\dfrac{15^{15}+1}{15^{16}+1}\)
A = \(\dfrac{15^{16}+1}{15^{17}+1}< 1\)
Vì A = \(\dfrac{15^{16}+1}{15^{17}+1}< \dfrac{15^{16}+1+14}{15^{17}+1+14}=\dfrac{15^{16}+15}{15^{17}+15}=\) \(\dfrac{15.\left(15^{15}+1\right)}{15.\left(15^{16}+1\right)}=\dfrac{15^{15}+1}{15^{16}+1}=B\)
1/ Tìm x,y biết:
a/ \(\dfrac{x}{2}\) = \(\dfrac{y}{5}\) và x+y=-21
b/ 7x = 3y và x-y=16
c/ \(\dfrac{x}{y}\) = \(\dfrac{5}{9}\) và 3x+2x=66
d/ \(\dfrac{x}{15}\) = \(\dfrac{y}{7}\) và x-2y=16
e/ \(\dfrac{x}{5}\) = \(\dfrac{y}{2}\) và x × y = 1000
2/ Tìm x,y,z biết
\(\dfrac{x}{13}\) = \(\dfrac{y}{7}\) = \(\dfrac{z}{5}\) và x-y-z=6
a. Áp dụng tính chất dãy tỉ số bằng nhau:
$\frac{x}{2}=\frac{y}{5}=\frac{x+y}{2+5}=\frac{-21}{7}=-3$
$\Rightarrow x=2(-3)=-6; y=5(-3)=-15$
b. Áp dụng tính chất dãy tỉ số bằng nhau:
$7x=3y=\frac{x}{\frac{1}{7}}=\frac{y}{\frac{1}{3}}=\frac{x-y}{\frac{1}{7}-\frac{1}{3}}=\frac{16}{\frac{-4}{21}}=-84$
$\Rightarrow x=(-84):7=-12; y=-84:3=-28$
c. $\frac{x}{y}=\frac{5}{9}\Rightarrow \frac{x}{5}=\frac{y}{9}$
Áp dụng tính chất dãy tỉ số bằng nhau:
$\frac{x}{5}=\frac{y}{9}=\frac{3x}{15}=\frac{2y}{18}=\frac{3x+2y}{15+18}=\frac{66}{33}=2$
$\Rightarrow x=2.5=10; y=9.2=18$
d. Áp dụng tính chất dãy tỉ số bằng nhau:
$\frac{x}{15}=\frac{y}{7}=\frac{2y}{14}=\frac{x-2y}{15-14}=\frac{16}{1}=16$
$\Rightarrow x=16.15=240; y=7.16=112$
e.
Đặt $\frac{x}{5}=\frac{y}{2}=k\Rightarrow x=5k ; y=2k$
Khi đó: $xy=5k.2k=10k^2=1000\Rightarrow k^2=100\Rightarrow k=\pm 10$
Với $k=10$ thì $x=5k=50; y=2k=20$
Với $k=-10$ thì $x=5k=-50; y=2k=-20$
Bài 2:
Áp dụng tính chất dãy tỉ số bằng nhau:
$\frac{x}{13}-\frac{y}{7}-\frac{z}{5}=\frac{x-y-z}{13-7-5}=\frac{6}{1}=6$
$\Rightarrow x=13.6=78; y=7.6=42; z=5.6=30$
(5+10+15+...+1000)\(\left[\dfrac{2}{5}:0.5+2\left(-0.4\right)\right]:\left(\dfrac{1}{5}+\dfrac{1}{10}+\dfrac{1}{15}+...\dfrac{1}{1000}\right)\)
viết sang số thập phân
\(\dfrac{815}{10000}\)= ?
81\(\dfrac{5}{10}\) =?
\(\dfrac{815}{1000}\)=?
8\(\dfrac{15}{1000}\) =?
Tính bằng cách thuận tiện.
a) \(\dfrac{2}{13}\times\dfrac{22}{5}\times\dfrac{13}{2}\) b) \(\dfrac{3}{5}\times\dfrac{6}{7}+\dfrac{6}{7}\times\dfrac{3}{5}\)
\(a,\dfrac{2}{13}\times\dfrac{22}{5}\times\dfrac{13}{2}\\ =\left(\dfrac{2}{13}\times\dfrac{13}{2}\right)\times\dfrac{22}{5}\\ =1\times\dfrac{22}{5}=\dfrac{22}{5}\\ b,\dfrac{3}{5}\times\dfrac{6}{7}+\dfrac{6}{7}\times\dfrac{3}{5}\\ =\dfrac{3}{5}\times\left(\dfrac{6}{7}+\dfrac{6}{7}\right)\\ =\dfrac{3}{5}\times\dfrac{12}{7}=\dfrac{36}{35}\)
\(a,=\left(\dfrac{2}{13}\times\dfrac{13}{2}\right)\times\dfrac{22}{5}=\dfrac{22}{5}\\ b,=\dfrac{3}{5}\times\left(\dfrac{6}{7}+\dfrac{6}{7}\right)\\ =\dfrac{3}{5}\times\dfrac{12}{7}\\ =\dfrac{36}{35}\)
bài 2: viết các phân số thập phân sau dưới dạng số thập phân
\(\dfrac{15}{10}=..;\dfrac{35}{100}=...;\dfrac{107}{100}=....\)
\(\dfrac{22109}{1000}=...;\dfrac{14}{5}=...;\dfrac{920}{1000}=...\)
\(\dfrac{138}{100}=...;\dfrac{2007}{10}=...;\dfrac{1}{1000}=...\)
\(\dfrac{15}{10}=1,5;\dfrac{35}{100}=0,35;\dfrac{107}{100}=1,07\)
\(\dfrac{22109}{1000}=22,109;\dfrac{14}{5}=\dfrac{28}{10}=2,8;\dfrac{920}{1000}=0,92\)
\(\dfrac{138}{100}=1,38;\dfrac{2007}{10}=200,7;\dfrac{1}{1000}=0,001\)
1,5
0,35
1,007
22,109
2,8
0,92
1,38
200,7
0,001
Tính bằng cách thuận tiện.
a) \(\dfrac{3}{5}\times\dfrac{7}{11}\times\dfrac{5}{3}\times11\)
b) \(\dfrac{3}{8}\times\dfrac{2}{7}+\dfrac{5}{7}\times\dfrac{3}{8}\)
a)
\(\dfrac{3}{5}\times\dfrac{7}{11}\times\dfrac{5}{3}\times11\\ =\left(\dfrac{3}{5}\times\dfrac{5}{3}\right)\times\left(\dfrac{7}{11}\times11\right)\\ =\dfrac{3\times5}{5\times3}\times\dfrac{7\times11}{11}\\ =1\times7\\ =7\)
b)
\(\dfrac{3}{8}\times\dfrac{2}{7}+\dfrac{5}{7}\times\dfrac{3}{8}\\ =\dfrac{3}{8}\times\left(\dfrac{2}{7}+\dfrac{5}{7}\right)\\ =\dfrac{3}{8}\times\dfrac{7}{7}\\ =\dfrac{3}{8}\times1=\dfrac{3}{8}\)
Tính bằng cách thuận tiện.
a) \(\dfrac{3}{5}\times\dfrac{17}{21}+\dfrac{2}{5}\times\dfrac{17}{21}\) b) \(\dfrac{11}{19}\times\dfrac{2}{7}+\dfrac{5}{7}\times\dfrac{11}{19}\)
a) \(\dfrac{3}{5}\times\dfrac{17}{21}+\dfrac{2}{5}\times\dfrac{17}{21}\)
\(=\dfrac{17}{21}\times\left(\dfrac{3}{5}+\dfrac{2}{5}\right)\)
\(=\dfrac{17}{21}\times1\)
\(=\dfrac{17}{21}\)
b) \(\dfrac{11}{19}\times\dfrac{2}{7}+\dfrac{5}{7}\times\dfrac{11}{19}\)
\(=\dfrac{11}{19}\times\left(\dfrac{2}{7}+\dfrac{5}{7}\right)\)
\(=\dfrac{11}{19}\times1\)
\(=\dfrac{11}{19}\)
a: =17/21(3/5+2/5)
=17/21*5/5
=17/21
b: =11/19(2/7+5/7)
=11/19*1
=11/19