Question

insert three rational numbers between
4/13 and 1/13​

Answer 1

In this case we can't simply write the numbers-3/13, 2/13 because we need 3 and they are two.

So, here we will multiply both the denominators by 10,20 or any number you want and as we will multiply the denominator we will also have to multiply the numerator, here I am multiplying with 10

$\frac{4}{13}\left *} \atop {*}} \right. \frac{10}{10} \left{=} \atop {=}} \right.\frac{40}{130}$

Same with 1/13

$\frac{1}{13}\left *} \atop {*}} \right. \frac{10}{10} \left{=} \atop {=}} \right.\frac{10}{130}$

Now, we know 40/130 is equivalent to 10/130, So we can easily insert three rational numbers between 40/130 and 10/130 like 39/130, 38/130, 37/130 etc.