Question

So sánh các phân số sau bằng cách nhanh nhất:

3838/8383 và 383838/838383

3838/8383 và 2014/2016

Answer 1

a, Ta có \(\frac{3838}{8383}=\frac{3838\div101}{8383\div101}=\frac{38}{83}\)

\(\frac{383838}{838383}=\frac{383838\div10101}{838383\div10101}=\frac{38}{83}\)

Vì \(\frac{38}{83}=\frac{38}{83}\)nên \(\frac{3838}{8383}=\frac{383838}{838383}\)

b, \(\frac{3838}{8383}=\frac{38383\div101}{8383\div101}=\frac{38}{83}=1-\frac{45}{83}\)

\(\frac{2014}{2016}=\frac{2014\div2}{2016\div2}=\frac{1007}{1008}=1-\frac{1}{1008}=1-\frac{45}{45360}\)

Vì \(\frac{45}{83}>\frac{45}{45360}\)nên \(1-\frac{45}{83}< 1-\frac{45}{45360}\)hay \(\frac{38}{83}< \frac{1007}{1008}\)suy ra \(\frac{3838}{8383}< \frac{2014}{2016}\)

Answer 2

Ta có: 3838/8383 = 383838/838383  vì 3838/8383 = 38/83 = 383838/838383