Question

State True or False.

The five rational numbers between $\frac{3}{5}$ and $\frac{4}{5}$ are $\frac{19}{30},\frac{20}{30},\frac{21}{30},\frac{22}{30},\frac{23}{30}$.

• A. True
• B. False

Answer 1

The correct option is A True

Since we want five numbers we write $\frac{3}{5}$ and $\frac{4}{5}$
So multiply in numerator and denominator by $5+1=6$ we get
$\Rightarrow \frac{3}{5}=\frac{3\times 6}{5\times 6}=\frac{18}{30}$

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

We know that $18<19<20<21<22<23<24$
$\Rightarrow \frac{18}{30}<\frac{19}{30}<\frac{20}{30}<\frac{21}{30}<\frac{22}{30}<\frac{23}{30}<\frac{24}{30}$

Hence 5 rational number between $\frac{3}{5}and\frac{4}{5}$are
$\frac{19}{30},\frac{20}{30},\frac{21}{30},\frac{22}{30},\frac{23}{30},$