Question

Find five rational numbers between $\frac{1}{3}\text{and}\frac{3}{5}$. $\left[2\text{Marks}\right]$

Answer 1

We need to make the denominators of both the numbers same which will be the LCM of denominators of both the values. Now, LCM(3, 5) $=15$
On multiplying and dividing by 5, we get-
$\frac{1}{3}=\frac{5}{15}$

And similarly, on multiplying and dividing by 3, we get-
$\frac{3}{5}=\frac{9}{15}$

Now, the rational numbers in between will be,
$\frac{5}{15},\frac{6}{15},\frac{7}{15},\frac{8}{15},\frac{9}{15}$.

$\left[1\text{Mark}\right]$

But here we are getting 3 numbers only.
To get more numbers we can now make the denominator different, likewise if we again multiply and divide the no. by 2, we get-
$\frac{5}{15}=\frac{10}{30}\text{and}\frac{9}{15}=\frac{18}{30}$.

Therefore, the five numbers can be,
$\frac{11}{30},\frac{12}{30},\frac{13}{30},\frac{14}{30},\frac{15}{30}$

$\left[1\text{Mark}\right]$