Tính nhanh :
\(\frac{327x412+400}{328x412-12}\)
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a) \(15\times\left(\frac{212121}{434343}+\frac{333333}{353535}\right)=15\times\left(\frac{21\times10101}{43\times10101}+\frac{33\times10101}{35\times10101}\right)\)
\(=15\times\left(\frac{21}{43}+\frac{33}{35}\right)=\frac{6462}{301}\)
b) \(\frac{639\times721721}{721\times639639}=\frac{639\times721\times1001}{721\times639\times1001}=1\)
c) \(\frac{327\times412+400}{328\times412-12}=\frac{\left(328-1\right)\times412+400}{328\times412-12}=\frac{328\times412-412+400}{328\times412-12}\)
\(=\frac{328\times412-12}{328\times412-12}=1\)
d) \(9\times\left(\frac{151515}{171717}+\frac{131313}{181818}\right)=9\times\left(\frac{15\times10101}{17\times10101}+\frac{13\times10101}{18\times10101}\right)=9\times\left(\frac{15}{17}+\frac{13}{18}\right)\)
\(=9\times\frac{491}{306}=\frac{491}{34}\)
\(\frac{327\cdot412+400}{328\cdot412-12}\)
\(=\frac{327\cdot412+400}{\left(327+1\right)\cdot412-12}\)
\(=\frac{327\cdot412+400}{327\cdot412+\left(412-12\right)}\)
\(=\frac{327\cdot412+400}{327\cdot412+400}\)
\(=1\)
\(\frac{327\cdot412+400}{328\cdot412-12}=\frac{327\cdot412+400}{\left(327+1\right)\cdot412-12}=\)\(\frac{327\cdot412+400}{327\cdot412+1\cdot412-12}=\frac{327\cdot412+400}{327\cdot412+412-12}=\)\(\frac{327\cdot412+400}{327\cdot412+400}=\frac{1}{1}=1\)
\(\frac{327.412+400}{328.412-12}\) = \(\frac{328.412-412+400}{328.412-12}\)= \(\frac{328.412-\left[412-400\right]}{328.412-12}\) = \(\frac{328.412-12}{328.412-12}\) = 1
\(=1+\frac{1}{3}+1+\frac{1}{15}+...+1+\frac{1}{399}.\)
\(=10+\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{19.21}\)
=\(10+\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{21}\right)\)
=\(10+\frac{1}{2}\left(1-\frac{1}{21}\right)=10+\frac{1}{2}.\frac{20}{21}=\frac{220}{21}\)
\(12400:50=248\cdot50:50=248\)
\(360:15=24\cdot15:15=24\)
\(23800:25=952\cdot25:25=952\)
a ] 12 400 : 50 = 248
b ] 360 : 15 = 24
c ] 23800 : 25 = 952
Rút gọn biểu thức cho 3 ta được biểu thức mới là
\(\frac{4}{28}+\frac{4}{70}+\frac{4}{130}+...\frac{4}{700}\)
= \(\frac{4}{4.7}+\frac{4}{7.10}+\frac{4}{10.13}+...+\frac{4}{25.28}\)
=\(\frac{4}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{25.28}\right)\)
= \(\frac{4}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)
= \(\frac{4}{3}\left(\frac{1}{4}-\frac{1}{28}\right)\)
= \(\frac{4}{3}.\frac{3}{14}\)
= \(\frac{2}{7}\)
học lâu giờ quên rùi
\(\frac{327.412+400}{328.412-12}=\frac{327.412+400}{\left(327+1\right).412-12}=\frac{327.412+400}{327.412+412-12}=\frac{327.412+400}{327.412+400}=1\)