Given:
Two rational numbers are [tex]-\dfrac{2}{5}[/tex] and [tex]-\dfrac{2}{7}[/tex].
To find:
The three rational numbers between the given two numbers.
Solution:
Two rational numbers are [tex]-\dfrac{2}{5}[/tex] and [tex]-\dfrac{2}{7}[/tex]. First we need to make denominators common.
[tex]-\dfrac{2}{5}=-\dfrac{2\times 7}{5\times 7}[/tex]
[tex]-\dfrac{2}{5}=-\dfrac{14}{35}[/tex]
and,
[tex]-\dfrac{2}{7}=-\dfrac{2\times 5}{7\times 5}[/tex]
[tex]-\dfrac{2}{7}=-\dfrac{10}{35}[/tex]
Now, we have same denominators. Numerators are -14 and -10.
So, three numbers between -14 and -10 are -11, -12 ,13.
[tex]-14<-13<-12<-11<-10[/tex]
[tex]\dfrac{-14}{35}<\dfrac{-13}{35}<\dfrac{-12}{35}<\dfrac{-11}{35}<\dfrac{-10}{35}[/tex]
[tex]\dfrac{-2}{7}<\dfrac{-13}{35}<\dfrac{-12}{35}<\dfrac{-11}{35}<\dfrac{-2}{5}[/tex]
Therefore, the three rational numbers between [tex]-\dfrac{2}{5}[/tex] and [tex]-\dfrac{2}{7}[/tex] are [tex]\dfrac{-13}{35},\dfrac{-12}{35},\dfrac{-11}{35}[/tex].
