Question

so sánh các phân số 

A = 54.107−53 phần 53.107+54  và   B = 135 .269 -133 phần 134 .269 + 135

 

Answer 1

A=\(\frac{54.107-53}{53.107+54}\)

  = \(\frac{54.\left(106+1\right)-53}{53.107+53+1}\)

  = \(\frac{54.106+54-53}{53.\left(107+1\right)+1}\)

  = \(\frac{54.106+1}{53.108+1}\)

mà \(54.106=53.108\)

=> \(\frac{54.106+1}{53.108+1}=1\)

B = \(\frac{135.269-133}{134.269+135}\)

   = \(\frac{135.\left(268+1\right)-133}{134.269+134+1}\)

   = \(\frac{135.268+135-133}{134.\left(269+1\right)+1}\)

   = \(\frac{135.268+2}{134.270+1}\)

Mà \(135.268=134.270\)

=> \(\frac{135.268+2}{134.270+1}=\frac{135.268+1+1}{134.270+1}\)  

\(=\frac{135.268+1}{134.270+1}+\frac{1}{134.270+1}\)

  \(=1+\frac{1}{134.270+1}>1\) 

=> B > 1 

=> B > A