Question

Find five rational numbers between:

(i) $\frac{2}{3}$ and $\frac{4}{5}$

(ii) $\frac{-3}{2}$ and $\frac{5}{3}$

(iii) $\frac{1}{4}$ and $\frac{1}{2}$

Answer 1

(i) We can represent $\frac{2}{3}$ as $\frac{30}{45}$ and $\frac{4}{5}$ as $\frac{36}{45}$ respectively.

Therefore; $5$ rational numbers between $\frac{2}{3}$ and $\frac{4}{5}$ are $\frac{31}{45},\frac{32}{45},\frac{33}{45},\frac{34}{45},\frac{35}{45}$

(ii) We can represent $\frac{-3}{2}$ as $\frac{-9}{6}$ and $\frac{5}{3}$ as $\frac{10}{6}$

Therefore, $5$ rational numbers between $\frac{-3}{2}$ and $\frac{5}{3}$ are $\frac{-8}{6},\frac{-7}{6},-1,\frac{-5}{6},\frac{-4}{6}$

(iii) We can represent $\frac{1}{4}$ as $\frac{8}{32}$ and $\frac{1}{2}$ as $\frac{16}{32}$ respectively.

Therefore, $5$ rational numbers are $\frac{9}{32},\frac{10}{32},\frac{11}{32},\frac{12}{32},\frac{13}{32}$