Question

Among the given numbers, select the number which lies between $\frac{1}{2}$ and $\frac{8}{9}$?

• A. $0$
• B. $\frac{5}{6}$
• C. $\frac{6}{5}$
• D. $\frac{1}{3}$

Answer 1

The correct option is B $\frac{5}{6}$

$\text{To find the rational number between}$
$\frac{1}{2}and\frac{8}{9},$ we need find the LCM of the denominators.
So, LCM of 2 and 9 =18
Now, convert both the rational numbers into their equivalent rational numbers having the common denominator 18.
$\frac{1}{2}$ = $\frac{1\times 9}{2\times 9}$ = $\frac{9}{18}$
Similarly, $\frac{8}{9}$ = $\frac{8\times 2}{9\times 2}$ = $\frac{16}{18}$
So, the given rational number should be between $\frac{9}{18}$ and $\frac{16}{18}$.

Now, when we covert $\frac{5}{6}$ to equivalent rational number with the denominator 18, we get
$\frac{5}{6}$ = $\frac{5\times 3}{6\times 3}$ = $\frac{15}{18}$, which is between $\frac{9}{18}$ and $\frac{16}{18}$.
So, $\frac{5}{6}$ lies between $\frac{1}{2}$ and $\frac{8}{9}$.