Question

So sánh các phân số sau theo cách thuận tiện nhất:

a.\(\frac{17}{19}\)và \(\frac{19}{17}\)        

b.\(\frac{15}{7}\)và \(\frac{25}{12}\)

c.A=\(\frac{3^{10}+1}{3^9+1}\)và B= \(\frac{3^9+1}{3^8+1}\)

d.A=\(\frac{54.107-53}{53.107+54}\)và B=\(\frac{135.269-133}{134.269+135}\)

Answer 1

a.Vì \(\frac{17}{19}< 1\) và \(\frac{19}{17}>1\)

nên \(\frac{17}{19}< 1< \frac{19}{17}\)

hay \(\frac{17}{19}< \frac{19}{17}\)

b) \(\frac{15}{7}=2\frac{1}{7}\) và \(\frac{25}{12}=2\frac{1}{12}\)

Vì \(2\frac{1}{7}>2\frac{1}{12}\) nên \(\frac{15}{7}>\frac{25}{12}\)

Answer 2

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

\(\Leftrightarrow A=\frac{53.107+107-53}{53.107+54}\)

\(\Leftrightarrow A=\frac{53.107+54}{53.107+54}\)

\(\Leftrightarrow A=1\)

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

\(\Leftrightarrow B=\frac{134.269+269-133}{134.269+135}\)

\(\Leftrightarrow B=\frac{134.269+135}{134.269+135}\)

\(\Leftrightarrow B=1\)

Vì 1 = 1 nên A =B