Question

Insert three rational number between $\frac{4}{3}$ and $\frac{1}{4}$.

[ 2 Marks ]

Answer 1

Given ,
Rational number = $\frac{4}{3}$,$\frac{1}{4}$.
To find the rational number between $\frac{4}{3}$ and $\frac{1}{4}$.
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,
$\frac{4}{3}$× $\frac{4}{4}$ = $\frac{16}{12}$
Also,
$\frac{1}{4}$× $\frac{3}{3}$ = $\frac{3}{12}$

[ 0.5 Marks ]
​​​​​​​
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 $\frac{4}{3}$,$\frac{1}{4}$.
Since, n=3
n+1=3+1
= 4
So,
$\frac{16}{12}$× $\frac{4}{4}$ = $\frac{64}{48}$
Also,
$\frac{3}{12}$× $\frac{4}{4}$ = $\frac{12}{48}$

​​​​​​​[ 0.5 Marks ]

So the three rational numbers between $\frac{4}{3}$ and $\frac{1}{4}$. are $\frac{13}{48}$, $\frac{14}{48}$, $\frac{15}{48}$.

​​​​​​​[ 1 Mark ]