\(\frac{2009\cdot2010-1000}{2011\cdot2009-1009}\)
Tính bằng cách thuận tiện:
\(\frac{2007\cdot2010-1007}{2008\cdot2009-1009}\)
\(=\frac{2007.2009+2007-1007}{2007.2009+2009-1009}\)
\(=\frac{2007.2009+1000}{2007.2009+1000}\)
=1
Tính nhanh:
\(\frac{2008\cdot2009+2000}{2009\cdot2010-2018}\)
\(\frac{2008.2009+2000}{2009.2010-2018}\)
\(=\frac{2008.\left(2010-1\right)+2010}{\left(2008+1\right).2010-2018}\)
\(=\frac{2008.2010-2008+2010}{2008.2010+2010-2018}\)
\(=\frac{2008.2010+2}{2008.2010-18}\)
Mình nghĩ bài này sai đề, nếu đề là 2018 -> 2008 thì bảo mình, mình làm lại cho
2018-10+2010 -10/2010-2018=10+10 =20
h tui nhé
Bài 1
a) Tìm x, biết
\(\frac{2\cdot x-4,36}{0,125}\)= 0,25 * 42,9 - 11,7 * 0,25 + 0,25 * 0,8
b) Tính nhanh
\(N=\frac{1}{1\cdot5}+\frac{1}{5\cdot10}+\frac{1}{10\cdot15}+\frac{1}{15\cdot20}+...+\frac{1}{2005\cdot2010}\)
Bài 2
a) Tìm x, biết (x + 5,2) : 3,2 = 4,7 (dư 0,5).
b) Tính nhanh:\(A=\frac{4047991-2010\cdot2009}{4050000-2011\cdot2009}\)
Bài 3
a) Tìm x, biết 104,5 x X - 14,1 × X + 9,6 x X = 25
b) Tính nhanh
\(T=\frac{2009\cdot2010+2000}{2011\cdot2010-2020}\)
\(\frac{2x-4,36}{0,125}=0,25.42,9-11,7.0,25+0,25.0,8\)
\(\Leftrightarrow\frac{2x-4,36}{0,125}=0,25.\left(42,9-11.7+0,8\right)\)
\(\Leftrightarrow\frac{2x-4,36}{0,125}=0,25.32\)
\(\Leftrightarrow\frac{2x-4,36}{0,125}=8\)
\(\Leftrightarrow2x-4,36=1\)
\(\Leftrightarrow2x=5,36\)
\(\Leftrightarrow x=2,68\)
b) \(N=\frac{1}{1.5}+\frac{1}{5.10}+\frac{1}{10.15}+\frac{1}{15.20}+...+\frac{1}{2005.2010}\)
\(\Leftrightarrow N=\frac{1}{5}\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+\frac{1}{15}-\frac{1}{20}+...+\frac{1}{2005}-\frac{1}{2010}\right)\)
\(\Leftrightarrow N=\frac{1}{5}\left(1-\frac{1}{2010}\right)\)
\(\Leftrightarrow N=\frac{1}{5}.\frac{2009}{2010}=\frac{2009}{10050}\)
Bài 1:
a)\(\frac{2\cdot x-4,36}{0,125}=0,25\cdot42,9-11,7\cdot0,25+0,25\cdot0,8\)
\(\frac{2\cdot x-4,36}{0,125}=0,25\cdot\left(42,9-11,7+0,8\right)\)
\(\frac{2\cdot x-4,36}{0,125}=0,25\cdot32\)
\(\frac{2\cdot x-4,36}{0,125}=8\)
\(2\cdot x-4,36=8\cdot0,125\)
\(2\cdot x-4,36=1\)
\(2\cdot x=1+4,36\)
\(2\cdot x=5,36\)
\(x=\frac{5,36}{2}=2,68\)
b) \(N=\frac{1}{1\cdot5}+\frac{1}{5\cdot10}+\frac{1}{10\cdot15}+\frac{1}{15\cdot20}+...+\frac{1}{2005\cdot2010}\)
\(4N=\frac{4}{1\cdot5}+\frac{4}{5\cdot10}+\frac{4}{10\cdot15}+\frac{4}{15\cdot20}+...+\frac{4}{2005\cdot2010}\)
\(4N=1-\frac{1}{5}+\frac{1}{5}-\frac{1}{10}+\frac{1}{10}-\frac{1}{15}+\frac{1}{15}-\frac{1}{20}+...+\frac{1}{2005}-\frac{1}{2010}\)
\(4N=1-\frac{1}{2010}=\frac{2009}{2010}\)
\(N=\frac{2009}{2010}\div4=\frac{2009}{8040}\)
Bài 2:
a) ( x + 5,2 ) : 3,2 = 4,7 ( dư 0,5 )
\(x+5,2=4,7\cdot3,2+0,5\)
\(x+5,2=15,54\)
\(x=15,54-5,2=10,34\)
b)\(A=\frac{4047991-2010\cdot2009}{4050000-2011\cdot2009}\)
\(A=\frac{4047991-2010\cdot2009}{4050000-2009-2010\cdot2009}\)
\(A=\frac{4047991-2010\cdot2009}{4047991-2010\cdot2009}=1\)
Bài 3:
a) \(104,5\cdot x-14,1\cdot x+9,6\cdot x=25\)
\(x\cdot\left(104,5-14,1+9,6\right)=25\)
\(x\cdot100=25\)
\(x=\frac{25}{100}=\frac{1}{4}=0,25\)
b) \(T=\frac{2009\cdot2010+2000}{2011\cdot2010-2020}\)
\(T=\frac{2009\cdot2010+2000}{2009\cdot2010+4020-2020}\)
\(T=\frac{2009\cdot2010+2000}{2009\cdot2010+2000}=1\)
So sánh A và B
a)\(A=\frac{2008\cdot2009-1}{2008\cdot2009}\) và \(B=\frac{2009\cdot2010-1}{2009\cdot2010}\)
b)\(A=\frac{5^{10}+1}{5^{11}+1}\) và \(B=\frac{5^{11}+1}{5^{12}+1}\)
a) \(A=1-\frac{1}{2008.2009}\) ; \(B=1-\frac{1}{2009.2010}\)
Vì \(\frac{1}{2008.2009}>\frac{1}{2009.2010}\) nên A < B
So sánh phân số
A/ \(\frac{2009}{2010}\)và\(\frac{2010}{2011}\)
B/ \(\frac{1}{3^{400}}\) và \(\frac{1}{4^{300}}\)
C/\(\frac{200}{201}+\frac{201}{202}và\frac{200+201}{201+202}\)
D/\(\frac{2008}{2008\cdot2009}và\frac{2009}{2009\cdot2010}\)
mik làm câu A thôi nha
ta có :
1 - 2009/2010 = 1/2010
1 - 2010/2011 = 1/2011
Phần bù nào bé thì phân số đó lớn .
Vì 1/2010 > 1/2011
Nên 2009/2010 > 2010/2011
Ta thấy hiệu giữa mẫu số và tử số của hai phân số bằng nhau ( = 1 )
Để so sánh hai phân số, ta so sánh các hiệu.
\(1-\frac{2009}{2010}\)và \(1-\frac{2010}{2011}\)
Ta có :
\(1-\frac{2009}{2010}=\frac{2010}{2010}-\frac{2009}{2010}=\frac{1}{2010}\)
\(1-\frac{2010}{2011}=\frac{2011}{2011}-\frac{2010}{2011}=\frac{1}{2011}\)
Ta thấy :
\(\frac{1}{2010}>\frac{1}{2011}\)
Hay :
\(1-\frac{2009}{2010}>1-\frac{2010}{2011}\)
Vậy \(\frac{2009}{2010}< \frac{2010}{2011}\)
Cho A =\(\frac{2008\cdot2010+477}{2009\cdot2009+476}\)
Hãy so sánh A với 1 .
A=\(\frac{2008.\left(2009+1\right)+447}{\left(2008+1\right).2009+476}\)=\(\frac{2008.2008+2008+447}{2008.2009+2009+446}\)=1
\(\frac{1\cdot2010+2\cdot2009+3\cdot2008+...+2010\cdot1}{\left(1+2+3+...+2010\right)+\left(1+2+3+...+2009\right)+...+\left(1+2\right)+1}\)
Chứng minh : A=\(\frac{\left(2009^2+6\cdot2009+8\right)\cdot\left(2011^2+4\cdot2009+11\right)}{\left(2009\cdot2016+10\right)\left(2010\cdot2008+7\cdot2009+13\right)}=1\)
tinh hop li\(\frac{2011\cdot2010-1}{2009\cdot2011\cdot2010}\)