Question

Identify five rational number between 1/5and1/3

Answer 1

To find:

• Five rational numbers between 1/5 and 1/3

Solution:

The first step is to find rational numbers equivalent to the ones given such that both of their denominators is equal.

LCM of 5 and 3 = 15

We could convert the rational numbers into ones with 15 as the denominator, but it is not certain that we will be able to get five rational numbers between them. We cannot choose the next common multiple, too since 15 x 2 = 30 and:

$\sf{\dfrac{1}{5}=\dfrac{1\times6}{5\times6}=\dfrac{6}{30}}$

$\sf{\dfrac{1}{3}=\dfrac{1\times10}{3\times10}=\dfrac{10}{30}$

We can only find 3 rational numbers between them.

Let us take 15 x 3 = 45 as the common multiple.

So,

$\sf{\dfrac{1}{5}=\dfrac{1\times9}{5\times9}=\dfrac{9}{45}}$

$\sf{\dfrac{1}{3}=\dfrac{1\times15}{3\times15}=\dfrac{15}{45}$

We can easily obtain the required numbers by choosing the five numbers between 9 and 15 as numerators.

$\sf{=\dfrac{10}{45},\:\dfrac{11}{45},\:\dfrac{12}{45},\:\dfrac{13}{45},\:\dfrac{14}{45}}$

Therefore, five rational numbers between 1/5 and 1/3 are 2/9, 11/45, 4/15, 13/45 and 14/45.