\(\frac{51.52.53...100}{1.3.5...99}\)

\(=\frac{\left(2.4.6...100\right).\left(51.52.53...100\right)}{\left(2.4.6...100\right).\left(1.3.5...99\right)}\)

\(=\frac{\left(2.4.6...100\right).\left(51.52.53...100\right)}{1.2.3.4.5.6...99.100}\)

\(=\frac{2.4.6...100}{1.2.3...50}\)

\(=\frac{\left(2.2...2\right).\left(1.2.3...50\right)}{1.2.3...50}\)

\(=2.2.2...2\)

\(=2^{50}\)

sao hỏi khó zzzzzzzzậy

Xét tử : \(1.3.5.....99\)

\(=\frac{1.2.3.4.....98.99.100}{2.4.6.....100}\) 

\(=\frac{\left(1.2.3.....50\right)\left(51.52.....99.100\right)}{\left(1.2\right).\left(2.2\right).....\left(50.2\right)}\)

\(=\frac{\left(1.2.3.....50.\right).\left(51.52.....100\right)}{\left(1.2.3.....50\right).2.2.....2}\)

\(=\frac{51.52.....100}{2.2....2}\)

\(=\frac{51}{2}.\frac{52}{2}.....\frac{100}{2}\)

Ta được phân số\(\frac{\frac{51}{2}.\frac{52}{2}.....\frac{100}{2}}{51.52.....100}\)

\(=\frac{\frac{51}{2}.\frac{52}{2}.....\frac{100}{2}}{\frac{51}{2}.\frac{52}{2}.....\frac{100}{2}.2.2.....2}\)

\(=\frac{1}{2.2.....2}\)

\(=\frac{1}{2^{50}}\)

Ta có \(1.3.5...99=\frac{1.2.3.4.5...100}{2.4.6...100}=\frac{1.2.3.4.5....100}{2^{50}.1.2.3.4...50}=\frac{51.52.53...100}{2^{50}}\left(\text{đpcm}\right)\)

Ta có : \(1.3.5....99=\frac{1.2.3.4.5....100}{2.4.6...100}=\frac{1.2.3.4.5....1000}{2^{50}.1.2.3.4....50}=\frac{51.51.53....100}{2^{50}}\)( đpcm )

5/13

\(\dfrac{5}{13}\)

= 5/13

\(\frac{100}{244}=\frac{25\cdot4}{4\cdot61}=\frac{25}{61}\)

\(\frac{49}{315}=\frac{7\cdot7}{7\cdot45}=\frac{7}{45}\)

100 / 244 = 25 / 61

49 / 325 = 7 / 45

Chúc bn hok tốt!!

\(\frac{100}{244}=\frac{25}{61}\)

\(\frac{49}{315}=\frac{7}{45}\)

chúc bạn học tốt !

Rút gọn 55/100 : 11/20 .

\(\frac{55}{100}\)\(=\frac{55:5}{100:5}\)\(=\frac{11}{20}\)

\(\frac{11}{20}\)nha vì bn lấy 55 : 5 = 11 , 100 : 5 = 20