Question

Insert three rational number between $\frac{7}{3}$ and $\frac{3}{4}$.

Answer 1

Given ,
Rational number = $\frac{7}{3}$,$\frac{3}{4}$.
To find the rational number between $\frac{7}{3}$ and $\frac{3}{4}$.
Since the denominators of the rational numbers are different.
To make the denominator same, we take LCM of the given denominators.
So LCM of 4 and 3 is 12.
So,
$\frac{7}{3}$× $\frac{4}{4}$ = $\frac{28}{12}$
Also,
$\frac{3}{4}$× $\frac{3}{3}$ = $\frac{9}{12}$

Let's multiply the numerator and denominator of each rational number by (n+1) where 'n' is the number of rational number to be inserted in between $\frac{7}{3}$,$\frac{3}{4}$.
Since, n=3
n+1=3+1
= 4
So,
$\frac{28}{12}$× $\frac{4}{4}$ = $\frac{112}{48}$
Also,
$\frac{9}{12}$× $\frac{4}{4}$ = $\frac{36}{48}$
So the three rational numbers between $\frac{7}{3}$ and $\frac{3}{4}$. are $\frac{37}{48}$, $\frac{38}{48}$, $\frac{40}{48}$.