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a) \(\dfrac{2}{3}+\dfrac{3}{5}=\dfrac{10}{15}+\dfrac{9}{15}=\dfrac{19}{15}\)
a) \(\dfrac{7}{12}-\dfrac{2}{7}+\dfrac{1}{12}=\dfrac{2}{3}-\dfrac{2}{7}=\dfrac{14}{21}-\dfrac{6}{21}=\dfrac{8}{21}\)
=13/12x14/13x15/14x16/15x...x2006/2005x2007/2006x2008/2007
=2008/12
=502/3
A = 1\(\dfrac{1}{12}\) \(\times\) 1\(\dfrac{1}{13}\) \(\times\) 1\(\dfrac{1}{14}\) \(\times\) 1\(\dfrac{1}{15}\) \(\times\) ... \(\times\) 1\(\dfrac{1}{2005}\) \(\times\) 1\(\dfrac{1}{2006}\) \(\times\) 1\(\dfrac{1}{2007}\)
A = ( 1 + \(\dfrac{1}{12}\)) \(\times\) ( 1 + \(\dfrac{1}{13}\)) \(\times\) ( 1 + \(\dfrac{1}{14}\)) \(\times\)...\(\times\) ( 1 + \(\dfrac{1}{2006}\))\(\times\)(1+\(\dfrac{1}{2007}\))
A = \(\dfrac{13}{12}\) \(\times\) \(\dfrac{14}{13}\) \(\times\) \(\dfrac{15}{14}\) \(\times\) ...\(\times\) \(\dfrac{2007}{2006}\) \(\times\) \(\dfrac{2008}{2007}\)
A = \(\dfrac{13\times14\times15\times...\times2007}{13\times14\times15\times...\times2007}\) \(\times\) \(\dfrac{2008}{12}\)
A = 1 \(\times\) \(\dfrac{502}{3}\)
A = \(\dfrac{502}{3}\)
a; (5142 - 17 x 8 + 242 : 11) x (27 - 3 x 9)
= (5142 - 17 x 8 + 242 : 11) x (27 - 27)
= (5142 - 17 x 8 + 242 : 11) x 0
= 0
b;
(1 + \(\dfrac{1}{2}\)) \(\times\) (1 + \(\dfrac{1}{3}\)) \(\times\) ( 1 + \(\dfrac{1}{4}\)) \(\times\) ... \(\times\) (1 + \(\dfrac{1}{2010}\)) \(\times\)(1 + \(\dfrac{1}{2011}\))
= \(\dfrac{2+1}{2}\) \(\times\) \(\dfrac{3+1}{3}\) \(\times\) \(\dfrac{4+1}{4}\)\(\times\) ... \(\times\) \(\dfrac{2010+1}{2010}\)\(\times\) \(\dfrac{2011+1}{2011}\)
= \(\dfrac{3}{2}\)\(\times\)\(\dfrac{4}{3}\)\(\times\)\(\dfrac{5}{4}\)\(\times\)...\(\times\)\(\dfrac{2011}{2010}\)\(\times\)\(\dfrac{2012}{2011}\)
= \(\dfrac{2012}{2}\)
= 1006
Ta có công thức tổng quát:
\(\dfrac{k}{n\cdot\left(n+k\right)}=\dfrac{1}{n}-\dfrac{1}{n+k}\)
\(a,A=\dfrac{1}{5\cdot8}+\dfrac{1}{8\cdot11}+...+\dfrac{1}{x\left(x+3\right)}\\ =\dfrac{1}{3}\left(\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+...+\dfrac{3}{x\left(x+3\right)}\right)\\ =\dfrac{1}{3}\left(\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{x}-\dfrac{1}{x+3}\right)\\ =\dfrac{1}{3}\cdot\left(\dfrac{1}{5}-\dfrac{1}{x+3}\right)\\ =\dfrac{1}{3}\cdot\dfrac{x-2}{5\left(x+3\right)}\\ =\dfrac{x-2}{15\left(x+3\right)}\)
Theo đề bài ta có:
\(A=\dfrac{101}{1540}\\ \Rightarrow\dfrac{x-2}{15\left(x+3\right)}=\dfrac{101}{1540}\\ \Rightarrow\dfrac{x-2}{x+3}=\dfrac{303}{308}\\ \Rightarrow\dfrac{x-2}{x+3}=\dfrac{305-2}{305+3}\\ \Rightarrow x=305\)
\(\dfrac{2}{5}+\dfrac{4}{9}=\dfrac{18}{45}+\dfrac{20}{45}=\dfrac{18+20}{45}=\dfrac{38}{45}\)
\(\dfrac{13+x}{20}\) = \(\dfrac{3}{4}\)
13 + \(x\) = 20 \(\times\) \(\dfrac{3}{4}\)
13 + \(x\) = 15
\(x\) = 15 - 13
\(x\) = 2
Cách khác :
\(\dfrac{13+x}{20}=\dfrac{3}{4}\)
\(\dfrac{13+x}{20}=\dfrac{15}{20}\)
\(13+x=15\)
\(x=15-13\)
\(x=2\)
Bài 1 :
a, 11/12 - 5/9 : 4/3
= 11/12 - 5/12
= 1/2
b, 8/5 x 2/3 - 14/15
= 16/15 - 14/15
= 2/15
c, 9/7 : 3/4 + 5/14
= 12/7 + 5/14
= 29/14
Bài 2:
a, x : 4/3 = 7/8 - 1/4
= x : 4/3 = 5/8
= x = 5/8 x 4/3
= x = 5/6
b, 5/7 + x/35 = 4/5
= x/35 = 4/5 - 5/7
= x/35 = 3/35
= x * 35 = 35 * 3
= x * 35 = 105
= x = 105 : 35
= x = 3
Bài 3 :
80 000kg = 80 tấn 8 tấn 7 tạ = 87 tạ 4000dm2 = 40 m2
96 giờ = 4 ngày 915 năm = 9 thế kỉ 15 năm 6km 24m = 6024 m
Bài 4 :
Đường chéo nhỏ là:
24 x 5/8 = 15 ( m )
Diện tích mảnh vườn hình thoi là:
15 x 24 : 2 = 180 ( m2 )
Đáp số:.....................
Bài 1 :
a) \(\dfrac{11}{12}-\dfrac{5}{9}:\dfrac{4}{3}=\dfrac{11}{12}-\dfrac{5}{9}\times\dfrac{3}{4}=\dfrac{11}{12}-\dfrac{5}{12}=\dfrac{1}{2}\)
b) \(\dfrac{8}{5}\times\dfrac{2}{3}-\dfrac{14}{15}=\dfrac{16}{15}-\dfrac{14}{15}=\dfrac{2}{15}\)
c) \(\dfrac{9}{7}:\dfrac{3}{4}+\dfrac{5}{14}=\dfrac{9}{7}\times\dfrac{4}{3}+\dfrac{5}{14}=\dfrac{12}{21}+\dfrac{5}{14}=\dfrac{13}{14}\)
Bài 2 :
a) \(x:\dfrac{4}{3}=\dfrac{7}{8}-\dfrac{1}{4}\)
\(x\times\dfrac{3}{4}=\dfrac{5}{8}\)
\(x=\dfrac{5}{8}:\dfrac{3}{4}=\dfrac{5}{6}\)
b) \(\dfrac{5}{7}+\dfrac{x}{35}=\dfrac{4}{5}\)
\(\dfrac{25}{35}+\dfrac{x}{35}=\dfrac{28}{35}\)
\(\dfrac{x}{35}=\dfrac{3}{35}\)
x = 3
Bài 3 :
80 000 kg = 80 tấn
8 tấn 7 tạ = 87 tạ
4000dm2 = 40 cm2
96 giờ = 4 ngày
915 năm = 9 thế kỉ 15 năm
6km 24m = 6024m
Bài 4 :
Đường chéo nhỏ dài :
24 x 5 : 8 = 15 ( m )
Diện tích mảnh vườn đó là :
\(24\times15\times\dfrac{1}{2}=180\left(m^2\right)\)