Comparaison

Complétez,sans utiliser la calculatrice, par < ou > :

Question

a.\(\frac{1}{3,15} \cdots \frac{1}{\pi}\)

Solution

\(\pi<3,15\) \(\Longleftrightarrow \frac{1}{3,15} <\frac{1}{\pi}\)

Question

b.\(\frac{1}{\sqrt{2}+1} \cdots \frac{1}{\sqrt{2}}\)

Solution

\(\sqrt{2} < \sqrt{2}+1\) \(\Longleftrightarrow \frac{1}{\sqrt{2}+1} < \frac{1}{\sqrt{2}}\)

Question

c.\(\frac{1}{-25} \cdots \frac{1}{-26}\)

Solution

\(-26<-25\) \(\Longleftrightarrow\)\( \frac{1}{-25} <\frac{1}{-26}\)

Question

d.\(\frac{-1}{2}\dots\frac{-1}{3}\)

Solution

-3<-2 \(\Longleftrightarrow \frac{1}{-2}<\frac{1}{-3} \Longleftrightarrow \frac{-1}{2}<\frac{-1}{3}\)

Question

e.\(\frac{3}{7}\dots\frac{3}{5}\)

Solution

5<7

\(\Longleftrightarrow \frac{1}{7}<\frac{1}{5}\)

\(\Longleftrightarrow 3\times \frac{1}{7}<3\times \frac{1}{5}\)

\(\Longleftrightarrow \frac{3}{7}<\frac{3}{5}\)