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3 tháng 10 2018
Đặt \(A=\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}...\frac{899}{30^2}\)
\(\Rightarrow A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{29.31}{30.30}\)
\(\Rightarrow A=\frac{1.3.2.4.3.5...29.31}{2.2.3.3.4.4...30.30}\)
\(\Rightarrow A=\frac{\left(1.2.3...29\right).\left(3.4.5...31\right)}{\left(2.3.4...30\right).\left(2.3.4...30\right)}\)
\(\Rightarrow A=\frac{1}{30}.\frac{31}{2}=\frac{31}{60}\)
Vậy \(A=\frac{31}{60}\)
27 tháng 9 2016
Đặt \(A=\frac{\frac{2000}{11}+\frac{2000}{12}+...+\frac{2000}{100}}{\frac{1}{99}+\frac{2}{98}+\frac{3}{97}+...+\frac{98}{2}+\frac{99}{1}}\)
\(\Rightarrow A=\frac{2000.\left(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{100}\right)}{\left(1+\frac{1}{99}\right)+\left(1+\frac{2}{98}\right)+...+\left(1+\frac{98}{2}\right)+1}\)
\(\Rightarrow A=\frac{2000.\left(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{100}\right)}{\frac{100}{99}+\frac{100}{98}+...+\frac{100}{2}+\frac{100}{100}}\)
\(\Rightarrow A=\frac{2000.\left(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{100}\right)}{100.\left(\frac{1}{99}+\frac{1}{98}+...+\frac{1}{2}+\frac{1}{100}\right)}\)
\(\Rightarrow A=\frac{20.\left(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{100}\right)}{\frac{1}{99}+\frac{1}{98}+...+\frac{1}{2}+\frac{1}{100}}\)
\(\Rightarrow A=\frac{\frac{20}{11}+\frac{20}{12}+..+\frac{20}{100}}{\frac{1}{99}+\frac{1}{98}+..+\frac{1}{2}+\frac{1}{100}}\)
28 tháng 7 2019
b)\(\frac{-15.8+10.7}{5.6+20.3}=\frac{-15.8+10.7}{5.2.3+5.4.3}=\frac{-90+70}{5.3.\left(2+4\right)}=\frac{-20}{90}=-\frac{2}{9}\)
\(\frac{2^4.5^2.7}{2^3.5.7^2.11}=\frac{2.5.1}{1.1.7.11}=\frac{10}{77}\)
MSC:77.9=693
\(\frac{-2}{9}=\frac{-2.693}{9.693}=\frac{-1386}{6237}\)
\(\frac{10}{77}=\frac{10.693}{77.693}=\frac{6930}{53361}\)
VM
29 tháng 7 2019
a) \(\frac{4.5+4.11}{8.7+4.3}=\frac{4.\left(5+11\right)}{56+12}=\frac{4.16}{68}=\frac{64}{68}=\frac{16}{17}.\)
Mình chỉ làm câu a) thôi nhé.
Chúc bạn học tốt!
13 tháng 7 2017
f) \(\frac{25^2.20^4}{5^{10}.4^5}=\frac{\left(5^2\right)^5.\left(4.5\right)^4}{5^{10}.4^5}=\frac{5^{10}.5^4.4^4}{5^{10}.4^5}=\frac{5^{14}.4^4}{5^{10}.4^5}=\frac{5^4}{4}\)
i) \(\frac{9^{15}.81^4}{27^8.3^{20}}=\frac{\left(3^2\right)^{15}.\left(3^4\right)^4}{\left(3^3\right)^8.3^{20}}=\frac{3^{30}.3^{16}}{3^{24}.3^{20}}=\frac{3^{46}}{3^{44}}=3^2=9\)
13 tháng 7 2017
f) Ta có: \(\frac{25^2.20^4}{5^{10}.4^5}\)= \(\frac{\left(5^2\right)^2.\left(4.5\right)^4}{5^{10}.4^5}\)= \(\frac{5^4.4^4.5^4}{5^{10}.4^5}\)= \(\frac{5^8.4^4}{5^{10}.4^5}\)= \(\frac{1}{5^2.4}\)=\(\frac{1}{100}\).
i) Ta có: \(\frac{9^{15}.81^4}{27^8.3^{20}}\)= \(\frac{\left(3^2\right)^{15}.\left(3^4\right)^4}{\left(3^3\right)^8.3^{20}}\)= \(\frac{3^{30}.3^8}{3^{24}.3^{20}}\)= \(\frac{3^{38}}{3^{44}}\)=\(\frac{1}{3^6}\)= \(\frac{1}{729}\)
TT
2
M
18 tháng 9 2017
317.8111/2710.915
=317.(34)11/(33)10.(32)15
=317.344/330.330
=361/360
=3
13 tháng 7 2017
b) \(\frac{36^7}{2^{15}.27^5}=\frac{\left(2^2.3^2\right)^7}{2^{15}.\left(3^3\right)^5}=\frac{2^{14}.3^{14}}{2^{15}.3^{15}}=\frac{1.1}{2.3}=\frac{1}{6}\)
h) \(\frac{2^{18}.9^4}{6^6.8^4}=\frac{2^{18}.\left(3^2\right)^4}{\left(2.3\right)^6.\left(2^3\right)^4}=\frac{2^{18}.3^8}{2^6.3^6.2^{12}}=\frac{2^{18}.3^8}{2^{18}.3^6}=\frac{1.3^2}{1.1}=9\)
o) \(\frac{3^3+3.6^2+6^3}{13}=\frac{3^3+6^2\left(3+6\right)}{13}=\frac{3^3+6^2.3^2}{13}\)
\(=\frac{3^2\left(3+6^2\right)}{13}=\frac{9.3.13}{13}=\frac{9.3.1}{1}=27\)
Rút gọn :
\(\frac{9}{30}=\frac{9:3}{30:3}=\frac{3}{10}\)
\(\frac{98}{80}=\frac{98:2}{80:2}=\frac{49}{40}\)
\(\frac{15}{1000}=\frac{15:5}{1000:5}=\frac{3}{200}\)
Quy đồng :
\(\frac{3}{10}=\frac{3.20}{10.20}\frac{60}{200}\)
\(\frac{49}{40}=\frac{49.5}{40.5}=\frac{245}{200}\)
\(\frac{3}{200}=\frac{3}{200}\)
\(\frac{9}{30}=\frac{3}{10};\frac{98}{80}=\frac{49}{40};\frac{15}{1000}=\frac{3}{200}\)
MSC của \(\frac{3}{10};\frac{49}{40};\frac{3}{200}\)là :200
Có : \(\frac{3}{10}=\frac{60}{200}\)
\(\frac{49}{40}=\frac{245}{200}\)
\(\frac{3}{200}=\frac{3}{200}\)