Question

Write three rational number that lie between the two given number.

${\displaystyle \frac{4}{5},\frac{2}{3}}$

Answer 1

The given numbers are ${\displaystyle \frac{4}{5} \text{and} \frac{2}{3}}$

Let us convert these numbers into fractions with equal denominators.

${\displaystyle \frac{4}{5}=\frac{4\times 6}{5\times 6}=\frac{24}{30}}$

${\displaystyle \frac{2}{3}=\frac{2\times 10}{3\times 10}=\frac{20}{30}}$

We know that,

20 < 21 < 22 < 23 < 24

∴ ${\displaystyle \frac{20}{30}<\frac{21}{30}<\frac{22}{30}<\frac{23}{30}<\frac{24}{30}}$

${\displaystyle \Rightarrow \frac{2}{3}<\frac{21}{30}<\frac{22}{30}<\frac{23}{30}<\frac{4}{5}}$

Hence, 3 rational numbers between ${\displaystyle \frac{2}{3} \text{and} \frac{4}{5}}$ are:

${\displaystyle \frac{21}{30},\frac{22}{30} \text{and} \frac{23}{30}}$.