Question

Insert three rational numbers between 3/4 and 1/5. Pls solve with steps!​

Answer 1

Given:

• Two rational numbers 3/4 and 1/5

To find:

• Three rational numbers between them

Solution:

Let us start by making the denominators of both the rational numbers same.

LCM of 4 and 5 = 20

So,

$\sf{\dfrac{3}{4}=\:\dfrac{3\times5}{4\times5}=\:\dfrac{15}{20}}$

$\sf{\dfrac{1}{5}=\:\dfrac{1\times4}{5\times4}=\:\dfrac{4}{20}}$

We can easily obtain the required rational numbers now by choosing any three numbers between 4 and 15.

$\sf{Three\:rational\:numbers\:are\:\dfrac{5}{15},\dfrac{6}{15},\:\dfrac{7}{15}}$

$\sf{=\dfrac{1}{3},\:\dfrac{2}{5},\:\dfrac{7}{15}}$

$\bf{Therefore\:three\:rational\:numbers\:between\:\dfrac{3}{4}\:and\:\dfrac{1}{5}\:are\:\dfrac{1}{3},\:\dfrac{2}{5}\:and\:\dfrac{7}{15}.}$