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1 tháng 6 2018
\(\frac{1414+1515+1616+1717+1818+1919}{2020+2121+2222+2323+2424+2525}\)
\(=\frac{101\times\left(14+15+16+17+18+19\right)}{101\times\left(20+21+22+23+24+25\right)}\)
\(=\frac{14+15+16+17+18+19}{20+21+22+23+24+25}\)
+) Tử số :
Số các số hạng là : ( 19 - 14 ) : 1 + 1 = 6 ( số )
Tổng là : ( 19 + 14 ) x 6 : 2 = 99
+) Mẫu số :
Số các số hạng là : ( 25 - 20 ) : 1 + 1 = 6 ( số )
Tổng là : ( 25 + 20 ) x 6 : 2 = 135
\(\Leftrightarrow\frac{99}{135}=\frac{11}{15}\)
6 tháng 6 2016
\(\frac{1414+1515+1616+1717+1818+1919}{2020+2121+2222+2323+2424+2525}\)
= \(\frac{\left(1414+1919\right)+\left(1515+1818\right)+\left(1616+1717\right)}{\left(2020+2525\right)+\left(2121+2424\right)+\left(2222+2323\right)}\)
= \(\frac{3333+3333+3333}{4545+4545+4545}=\frac{3333}{4545}=\frac{11}{15}\)
t i c k nhé!! 45435436457
N
18 tháng 7 2017
\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}\)
\(=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)
\(=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{15}\right)\)
\(=\frac{1}{2}.\frac{14}{15}\)
\(=\frac{7}{15}\)
TN
18 tháng 7 2017
a) \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}+\frac{1}{13.15}\)
\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{15}\right)=\frac{1}{2}.\frac{14}{15}\)\(=\frac{7}{15}\)
b)\(\frac{1414+1515+...+1919}{2020+2121+...+2525}\)
\(\Rightarrow\frac{101\left(14+15+16+17+18+19\right)}{101\left(20+21+22+23+24+25\right)}\)
\(=\frac{14+15+16+17+18+19}{20+21+22+23+24+25}\)
\(=\frac{\left(19+14\right).6:2}{\left(25+20\right).6:2}=\frac{19+14}{25+20}=\frac{33}{45}=\frac{11}{15}\)
19 tháng 7 2020
\(\left(2020\frac{2018}{2021}-2019\frac{20182018}{20212021}\right):\frac{2018}{2021}\)
\(=\left(2020\frac{2018}{2021}-2019\frac{2018}{2021}\right):\frac{2018}{2021}\)
\(=1:\frac{2018}{2021}=\frac{2021}{2018}\)
NN
1
19 tháng 8 2017
\(\frac{10}{2000}:\frac{10}{2000}.\frac{4}{5}+\frac{1}{5}+20\%+80\%\)
=\(1.\frac{4}{5}+\frac{1}{5}+\frac{1}{5}+\frac{4}{5}\)
=\(\frac{4}{5}.2+\frac{1}{5}.2\)
=\(\frac{8}{5}+\frac{2}{5}\)
=\(\frac{10}{5}=2\)
=
16 tháng 9 2017
\(\frac{1010+1111+1212+1313+1414+1515+1616+1717}{2020+2121+2222+2323+2424+2525+2626+2727}\)
\(=\frac{101.10+101.11+...+101.17}{101.20+101.21+...+101.27}\)
\(=\frac{101.\left(10+11+...+17\right)}{101.\left(20+21+...+27\right)}\)
\(=\frac{108}{188}\)
\(=\frac{27}{47}\)
16 tháng 9 2017
\(2>\left(\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{4}{96}\right)\cdot5.y>\frac{5}{6}\)
\(\Rightarrow2>\left(\frac{1}{6}+\frac{2}{15}+\frac{3}{40}+\frac{1}{24}\right):5.y>\frac{5}{6}\)
\(\Rightarrow2>\left(\frac{20}{120}+\frac{16}{120}+\frac{9}{120}+\frac{5}{120}\right):5.y>\frac{5}{6}\)
\(\Rightarrow2>\frac{5}{12}:5.y>\frac{5}{6}\)
\(\Rightarrow2>\frac{1}{12}.y>\frac{5}{6}\)
Đặt :\(\frac{1}{12}.y=2\Rightarrow y=2:\frac{1}{12}=24\)
\(\frac{1}{12}.y=\frac{5}{6}\Rightarrow y=\frac{5}{6}:\frac{1}{12}=10\)
\(\Rightarrow24>y>10\)
\(\Rightarrow y\in\left\{11;12;...;23\right\}\)
TH
22 tháng 5 2018
a) \(\left(\frac{4}{3}-\frac{4}{6}\right)+\left(\frac{4}{6}-\frac{4}{9}\right)+\left(\frac{4}{9}-\frac{4}{10}\right)+\left(\frac{4}{12}-\frac{4}{15}\right)\)
\(=\frac{4}{15}-\frac{4}{3}=\frac{-16}{15}\)
C) bạn chỉ ần bỏ các số giống nhau thôi nhé
= 1
b)
TH
8 tháng 8 2017
a ) \(\frac{2016\cdot12+2003+2000\cdot2015+2015}{2015+2015\cdot502+504\cdot2015}\)
\(=\frac{\left(2015+1\right)\cdot12+2003+2000\cdot2015+2015}{2015\cdot\left(1+502+504\right)}\)
\(=\frac{2015\cdot12+12\cdot1+2003+2000\cdot2015+2015}{2015\cdot1007}\)
\(=\frac{2015\cdot12+\left(12\cdot1+2003\right)+2000\cdot2015+2015}{2015\cdot1007}\)
\(=\frac{2015\cdot12+2015+2000\cdot2015+2015}{2015\cdot1007}\)
\(=\frac{2015\cdot\left(12+1+2000+1\right)}{2015\cdot1007}\)
\(=\frac{2015\cdot2014}{2015\cdot1007}\)
\(=2\)
b ) \(\frac{1978\cdot1979+1980\cdot21+1958}{1980\cdot1979-1978\cdot1979}\)
\(=\frac{1978\cdot1979+\left(1979+1\right)\cdot21+1958}{\left(1980-1978\right)\cdot1979}\)
\(=\frac{1979\cdot1978+1979\cdot21+21\cdot1+1958}{2\cdot1979}\)
\(=\frac{1978\cdot1979+1979\cdot21+1979}{2\cdot1979}\)
\(=\frac{\left(1978+21+1\right)\cdot1979}{2\cdot1979}\)
\(=\frac{2000\cdot1979}{2\cdot1979}\)
\(=1000\)
27 tháng 5 2017
Đặt biểu thức trên là A ta có:
A = \(\frac{1}{3}\)+ \(\frac{1}{6}\)+ \(\frac{1}{12}\)+ \(\frac{1}{24}\)+ \(\frac{1}{48}\)+ \(\frac{1}{96}\)
A x 3 = \(1\)+ \(\frac{1}{2}\)+ \(\frac{1}{4}\)+ \(\frac{1}{8}\)+ \(\frac{1}{16}\)+ \(\frac{1}{32}\)
A x 3 = \(1\)+ \(1\)- \(\frac{1}{2}\)+ \(\frac{1}{2}\)- \(\frac{1}{4}\)+ \(\frac{1}{4}\)- \(\frac{1}{8}\)+ \(\frac{1}{8}\)- \(\frac{1}{16}\)+ \(\frac{1}{16}\)- \(\frac{1}{32}\)
A x 3 = 2 - \(\frac{1}{32}\)= \(\frac{63}{32}\)
A = \(\frac{63}{32}\): 3 = \(\frac{63}{96}\)
\(=\frac{77211}{70261}\)