M= \(\frac{1}{2}\times\frac{1}{-3}+\frac{1}{-3}+\frac{1}{4}+\frac{1}{4}\times\frac{1}{-5}+\frac{1}{-5}\times\frac{1}{6}\)
NHỚ CÓ LỜI GIẢI CHI TIẾT NHÉ, AI NHANH MK TICK CHO
Tính hợp lí:
A =\((\frac{2}{7}\times\frac{1}{4}-\frac{1}{3}\times\frac{2}{7})\div(\frac{2}{7}\times\frac{3}{9}-\frac{2}{7}\times\frac{2}{5})\)
B = \(\frac{(\frac{1}{5}-\frac{2}{7})\times\frac{3}{4}-\frac{3}{4}\times(\frac{1}{3}-\frac{2}{7})}{\frac{1}{5}\times\frac{2}{7}-\frac{1}{3}\times(\frac{2}{7}+\frac{3}{9})+\frac{3}{9}\times\frac{1}{5}}\)
CÓ LỜI GIẢI THÍCH CHI TIETS NHÉ AI NHANH MK TICK
A=\([\)\(\frac{2}{7}\)\(\times\)(\(\frac{1}{4}-\frac{1}{3}\))\(]\)\(\div\)\([\)(\(\frac{2}{7}\times\)(\(\frac{3}{9}-\frac{2}{5}\))\(]\)
=(\(\frac{2}{7}\times\)\(\frac{-1}{12}\))\(\div(\)\(\frac{2}{7}\times\)\(\frac{-1}{15}\))
=\(\frac{-1}{42}\)\(\div\)\(\frac{-2}{35}\)
=\(\frac{-1}{42}\)\(\times\)\(\frac{35}{-2}\)
=\(\frac{5}{12}\)
Tính nhanh:\(\frac{1}{2}\times\frac{1}{2}+\frac{1}{2}\times\frac{1}{3}+\frac{1}{3}\times\frac{1}{4}+\frac{1}{4}\times\frac{1}{5}+\frac{1}{5}\times\frac{1}{6}\)
\(\frac{1}{2}\times\frac{1}{2}+\frac{1}{2}\times\frac{1}{3}+...+\frac{1}{5}\times\frac{1}{6}\)
\(=\frac{1}{4}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\)
\(=\frac{1}{4}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(=\frac{1}{4}+\frac{1}{2}-\frac{1}{6}\)
\(=\frac{3+6-2}{12}=\frac{7}{12}\)
\(\frac{1}{2}\)* \(\frac{1}{2}\)+ \(\frac{1}{2}\)*\(\frac{1}{3}\)+ \(\frac{1}{3}\)* \(\frac{1}{4}\)+ \(\frac{1}{4}\)* \(\frac{1}{5}\)+ \(\frac{1}{5}\)* \(\frac{1}{6}\)
=\(\frac{1}{2}\)* \(\frac{1}{6}\)= \(\frac{1}{12}\)
( Những phân số khác nhau bạn loại đi nhé tại mình ko làm được bước đó trên này bạn thông cảm nhé ! )
\(\frac{1}{2}\times\frac{1}{2}+\frac{1}{2}\times\frac{1}{3}+...+\frac{1}{5}\times\frac{1}{6}\)
\(=\frac{1}{4}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\)
\(=\frac{1}{4}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(=\frac{1}{4}+\frac{1}{2}-\frac{1}{6}\)
\(=\frac{7}{12}\)
Tìm x :
\(2\times x=\frac{1+2+3+...+9}{1-2+3-4+5-6+7-8+9}+\frac{25\times150-60\times5+20\times75}{1+2+3+...+99}\)
Ai nhanh mình tick cho nha !!! ( NHớ phải giải chi tiết nha @@@ )
\(2.x=\frac{1+2+3+...+9}{1-2+3-4+5-6+7-8+9}+\frac{25.150-60.5+20.75}{1+2+3+...+99}\)
\(2.x=\frac{\left(9+1\right).9:2}{\left(1-2\right)+\left(3-4\right)+\left(5-6\right)+\left(7-8\right)+9}+\frac{2.3.5^2.\left(5^2-2+2.5\right)}{\left(1+99\right).99:2}\)
\(2.x=\frac{45}{\left(-1\right)+\left(-1\right)+\left(-1\right)+\left(-1\right)+9}+\frac{2.3.5^2.33}{100.99.\frac{1}{2}}\)
\(2x=\frac{45}{5}+\frac{50.99}{50.2.99.\frac{1}{2}}=9+\frac{1}{2.\frac{1}{2}}=9+1=10\)
=> 2x = 10
x = 5
\(\frac{1}{1}\times\frac{1}{2}+\frac{1}{2}\times\frac{1}{3}+\frac{1}{3}\times\frac{1}{4}+\frac{1}{4}\times\frac{1}{5}+\frac{1}{5}\times\frac{1}{6}\)
\(=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\)
\(=\frac{30}{60}+\frac{10}{60}+\frac{5}{60}+\frac{3}{60}+\frac{2}{60}=\frac{50}{60}=\frac{5}{6}\)
=\(\frac{1}{2}\)+\(\frac{1}{6}\)+\(\frac{1}{12}\)+\(\frac{1}{20}\)+\(\frac{1}{30}\)=1-\(\frac{1}{2}\)+\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+\(\frac{1}{4}\)-\(\frac{1}{5}\)+\(\frac{1}{5}\)-\(\frac{1}{6}\)
=1-\(\frac{1}{6}\)
=\(\frac{5}{6}\)
C1:\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\)
\(\Rightarrow\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\)
\(\Rightarrow\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(\Rightarrow\frac{1}{1}-\frac{1}{6}\)
\(\Rightarrow\frac{5}{6}\)
C2:\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\)
\(\Rightarrow\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(\Rightarrow\frac{1}{1}-\frac{1}{6}\)
\(\Rightarrow\frac{5}{6}\)
Tìm số tự nhiên x biết:
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+.....+\frac{1}{x\times\left(x+1\right):2}=\frac{2001}{2003}\)
Giải chi tiết nha!!!!Ai nhanh mik tick liền!!!!
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right)\div2}=\frac{2001}{2003}\)
\(\frac{1}{2}\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right)\div2}\right)=\frac{1}{2}\cdot\frac{2001}{2003}\)
\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{x\left(x+1\right)}=\frac{2001}{4006}\)
\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{x\left(x+1\right)}=\frac{2001}{4006}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2001}{4006}\)
\(\frac{1}{2}-\frac{1}{x+1}=\frac{2001}{4006}\)
\(\frac{1}{x+1}=\frac{1}{2}-\frac{2001}{4006}\)
\(\frac{1}{x+1}=\frac{1}{2003}\)
\(\Rightarrow x+1=2003\)
\(x=2002\)
Vậy x = 2002
Bài 1 : tính theo cách hợp lý nhất
\(\frac{6}{11}+\frac{1}{3}+\frac{5}{11}\)
Bài 2 : Tính bằng cách nhanh nhất
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}\)
Bài 3 : Tính nhanh
a,\(\frac{3}{2}\times\frac{4}{5}\times\frac{2}{3}\)
b,\(\frac{6}{7}\times\subset\frac{5}{3}\times\frac{7}{6}\supset\)
Bài 4 : Tính nhanh
a,\(\frac{2}{5}\times\frac{1}{4}+\frac{3}{4}\times\frac{2}{5}\)
b,\(\frac{6}{11}\div\frac{2}{3}+\frac{5}{11}\div\frac{2}{3}\)
bài 1:
\(\frac{6}{11}+\frac{1}{3}+\frac{5}{11}\)
\(=\left(\frac{6}{11}+\frac{5}{11}\right)+\frac{1}{3}\)
\(=\frac{11}{11}+\frac{1}{3}=1+\frac{1}{3}=\frac{3}{3}+\frac{1}{3}=\frac{4}{3}\)
bài 2:
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}\)
\(=\left(\frac{1}{2}+\frac{1}{20}\right)+\left(\frac{1}{6}+\frac{1}{12}\right)\)
\(=\frac{11}{20}+\frac{1}{4}=\frac{11}{20}+\frac{5}{20}=\frac{15}{20}=\frac{3}{4}\)
bài 3:
a) \(\frac{3}{2}\cdot\frac{4}{5}\cdot\frac{2}{3}=\left(\frac{3}{2}\cdot\frac{2}{3}\right)\cdot\frac{4}{5}=1\cdot\frac{4}{5}=\frac{4}{5}\)
b) \(\frac{6}{7}\cdot\frac{5}{3}\cdot\frac{7}{6}=\left(\frac{6}{7}\cdot\frac{7}{6}\right)\cdot\frac{5}{3}=1\cdot\frac{5}{3}=\frac{5}{3}\)
bài 4:
a) \(\frac{2}{5}\cdot\frac{1}{4}+\frac{3}{4}\cdot\frac{2}{5}=\frac{2}{5}\cdot\left(\frac{1}{4}+\frac{3}{4}\right)=\frac{2}{5}\cdot1=\frac{2}{5}\)
b) \(\frac{6}{11}:\frac{2}{3}+\frac{5}{11}:\frac{2}{3}=\left(\frac{6}{11}+\frac{5}{11}\right):\frac{2}{3}=1:\frac{2}{3}=\frac{3}{2}\)
Bài 1:
6/11 + 1/3 + 5/11
= ( 6/11 + 5/11) + 1/3
= 11/11 + 1/3
= 1 + 1/3
= 3/3 +1/3
= 4/3
Bài 2:
1/2 + 1/6 + 1/12 + 1/20
= ( 1/2 + 1/6 + 1/12 ) + 1/20
= ( 6/12 + 2/12 + 1/12 ) + 1/20
=9/12 + 1/20
= 3/4 +1/20
= 15/20 + 1/20
= 16/20 = 4/5
Bài 3:
a) \(\frac{3}{2}\times\frac{4}{5}\times\frac{2}{3}\) \(=\left(\frac{3}{2}\times\frac{2}{3}\right)\times\frac{4}{5}\)\(=1\times\frac{4}{5}=\frac{4}{5}\)
b) \(\frac{6}{7}\times\left(\frac{5}{3}\times\frac{7}{6}\right)\) \(=\frac{6}{7}\times\frac{35}{18}\)\(=\frac{1\times5}{7\times3}=\frac{5}{21}\)
Bài 4:
a) 2/5 x 1/4 + 3/4 x 2/5
= 2/5 x ( 1/4 + 3/4)
= 2/5 x 1
= 2/5
b) 6/11 : 2/3 +5/11 : 2/3
= ( 6/11 + 5/11) x 3/2
= 11/11 x 3/2
= 1 x 3/2
= 3/2
....
1) Rút gọn biểu thức M:
\(\frac{\frac{2}{5}+\frac{2}{7}-\frac{2}{9}-\frac{2}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{9}-\frac{2}{11}}\)
2) Tính nhanh:
\(A=\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)\times....\times\left(1-\frac{1}{100}\right)\)
1, =\(\frac{2\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{9}-\frac{1}{11}\right)}{4\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{9}-\frac{1}{11}\right)}=\frac{1}{2}\)
2, A=\(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{99}{100}\)
= \(\frac{1\cdot2\cdot3\cdot....\cdot99}{2\cdot3\cdot4\cdot...\cdot100}=\frac{1}{100}\)
Vậy ......
hok tốt
6.b) A=\(\left(1+\frac{1}{2}\right)\times\left(1+\frac{1}{3}\right)+\left(1+\frac{1}{4}\right)\times..........\times\left(1+\frac{1}{99}\right)=\)Các bạn giúp mình nhanh và đúng nhé mình tick cho bạn đầu tiên nhé
\(\left(1+\frac{1}{2}\right)\left(1+\frac{1}{3}\right)\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{99}\right)\)
\(=\frac{3}{2}\times\frac{4}{3}\times...\times\frac{100}{99}\)
\(=\frac{100}{2}=50\)
B = \(\frac{(\frac{1}{5}-\frac{2}{7})\times\frac{3}{4}-\frac{3}{4}\times(\frac{1}{3}-\frac{2}{7})}{\frac{1}{5}\times\frac{2}{7}-\frac{1}{3}\times(\frac{2}{7}+\frac{3}{9})+\frac{3}{9}\times\frac{1}{5}}\)
ồ cuk dễ nhỉ
Nếu các bn thích thì ...........
cứ cho NTN này nhé !