Rút gọn: 24 . 48 . 816
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a)
`6/9=2/3`
`6/24=1/4`
`48/96=1/2`
`42/98=3/7`
b)
`24/36=2/3`
`18/30=3/5`
`15/120=1/8`
`80/240=1/3`
a)\(\dfrac{6}{9}=\dfrac{6:3}{9:3}=\dfrac{2}{3}\)
\(\dfrac{6}{24}=\dfrac{6:6}{24:6}=\dfrac{1}{4}\)
\(\dfrac{48}{96}=\dfrac{48:48}{96:48}=\dfrac{1}{2}\)
\(\dfrac{42}{98}=\dfrac{42:14}{98:14}=\dfrac{3}{7}\)
b)\(\dfrac{24}{36}=\dfrac{24:12}{36:12}=\dfrac{2}{3}\)
\(\dfrac{18}{30}=\dfrac{18:6}{30:6}=\dfrac{3}{5}\)
\(\dfrac{15}{120}=\dfrac{15:15}{120:15}=\dfrac{1}{8}\)
\(\dfrac{80}{240}=\dfrac{80:80}{240:80}=\dfrac{1}{3}\)
\(\dfrac{5}{15}=\dfrac{5:5}{15:5}=\dfrac{1}{3}\\ \dfrac{28}{56}=\dfrac{28:28}{56:28}=\dfrac{1}{2}\\ \dfrac{48}{96}=\dfrac{48:48}{96:48}=\dfrac{1}{2}\\ \dfrac{15}{120}=\dfrac{15:15}{120:15}=\dfrac{1}{8}\\ \dfrac{60}{80}=\dfrac{60:20}{80:20}=\dfrac{3}{4}\)
\(\dfrac{6}{9}\) = \(\dfrac{6:3}{9:3}\) = \(\dfrac{2}{3}\) \(\dfrac{24}{36}\) = \(\dfrac{24:12}{36:12}\) = \(\dfrac{2}{3}\)
\(\dfrac{80}{240}\) = \(\dfrac{80:80}{240:80}\) = \(\dfrac{1}{3}\) \(\dfrac{75}{100}\) = \(\dfrac{75:25}{100:25}\) = \(\dfrac{3}{4}\)
\(\dfrac{123123}{103103}\) = \(\dfrac{123123:1001}{103013:1001}\) = \(\dfrac{123}{103}\)
\(\dfrac{2121}{3232}\) = \(\dfrac{2121:101}{3232:101}\) = \(\dfrac{21}{32}\)
b: \(=\dfrac{3}{7}\cdot\dfrac{5}{7}\cdot\dfrac{6}{7}=\dfrac{90}{343}\)
c: \(=\dfrac{4}{9}\cdot\dfrac{5}{9}\cdot\dfrac{3}{7}=\dfrac{20}{189}\)
d: \(=\dfrac{1}{3}\cdot\dfrac{5}{12}\cdot\dfrac{5}{12}=\dfrac{25}{432}\)
Theo thứ tự : 5/6 ; 2/3 ; 2/3 ; 3/2 ; 2/3 ; 3/8 ; 3/1(hay là 3)
\(\dfrac{10}{12}=\dfrac{5}{6}\) \(\dfrac{8}{12}=\dfrac{2}{3}\) \(\dfrac{10}{15}=\dfrac{2}{3}\) \(\dfrac{27}{18}=\dfrac{3}{2}\) \(\dfrac{24}{36}=\dfrac{4}{6}=\dfrac{2}{3}\)
\(\dfrac{18}{48}=\dfrac{3}{8}\) \(\dfrac{42}{14}=\dfrac{6}{2}=\dfrac{3}{1}\)
\(=\dfrac{7^{48}\cdot5^{30}\cdot2^8-5^{30}\cdot7^{49}\cdot2^{10}}{3^2\cdot2^2\cdot5^2\cdot7^{48}}\)
\(=\dfrac{7^{48}\cdot5^{30}\cdot2^8\left(1+7\cdot4\right)}{3^2\cdot2^2\cdot5^2\cdot7^{48}}=\dfrac{5^{28}\cdot2^6\cdot12}{3^2}=\dfrac{5^{28}\cdot2^8}{3}\)
\(2^4.4^8.8^{16}=2^4.2^{16}.2^{48}=2^{68}\)
24.48.816=24.(22)8.(23)16=24.216.248=24+16+48=268