Question

Question 1 (iii)

List five rational numbers between:
$\frac{-4}{5}and\frac{-2}{3}$

Answer 1

$\frac{-4}{5}and\frac{-2}{3}$
Let us write $\frac{-4}{5}and\frac{-2}{3}$ as rational numbers with the same denominators
$\Rightarrow \frac{-4}{5}=\frac{-36}{45}and\frac{-2}{3}=\frac{-30}{45}$
$\therefore \frac{-36}{45}$<$\frac{-35}{45}$<$\frac{-34}{45}$<$\frac{-33}{45}$<$\frac{-32}{45}$<$\frac{-31}{45}$<$\frac{-30}{45}$
$\Rightarrow \frac{-4}{5}$<$\frac{-7}{9}$<$\frac{-34}{45}$<$\frac{-11}{15}$<$\frac{-32}{45}$<$\frac{-31}{45}$<$\frac{-2}{3}$
Therefore, five rational numbers between $\frac{-4}{5}and\frac{-2}{3}$ would be
$\frac{-7}{9},\frac{-34}{45},\frac{-11}{15},\frac{-32}{45},\frac{-31}{45}$