Number Systems — Question 3

Since we want five rational numbers, we write $\dfrac{3}{5}$ and $\dfrac{4}{5}$ as rational numbers with denominator 5 + 1 = 6, i.e.,

$\dfrac{3}{5} = \dfrac{3 \times 6} {5 \times 6} = \dfrac{18}{30}$

and

$\dfrac{4}{5} = \dfrac{4 \times 6} {5 \times 6} = \dfrac{24}{30}$

∴ Rational numbers between $\dfrac{3}{5}$ and $\dfrac{4}{5}$ are, $\dfrac{19}{30}$, $\dfrac{20}{30}$, $\dfrac{21}{30}$, $\dfrac{22}{30}$, $\dfrac{23}{30}$