Number Systems — Question 2

Since we want six rational numbers, we write 3 and 4 as rational numbers with denominator 3 + 4 = 7,

i.e.,

$3 = \dfrac{3 \times 7}{7} = \dfrac{21}{7}$

and

$4 = \dfrac{4 \times 7} {7} = \dfrac{28}{7}$

∴ Rational numbers between 3 and 4 are, $\dfrac{22}{7}$, $\dfrac{23}{7}$, $\dfrac{24}{7}$, $\dfrac{25}{7}$, $\dfrac{26}{7}$, $\dfrac{27}{7}$