Question

Which of the following rational number lies between $\frac{2}{3}$ and $\frac{4}{5}$?

• A. $\frac{8}{15}$
• B. $\frac{17}{15}$
• C. $\frac{9}{15}$
• D. $\frac{11}{15}$

Answer 1

The correct option is D $\frac{11}{15}$

Changing the given fractions to equivalent fractions,
$\frac{2\times 5}{3\times 5}=\frac{10}{15}$,
$\frac{4\times 3}{5\times 3}=\frac{12}{15}$

Now, plotting them on the number line:


So, $\frac{10}{15}<\frac{11}{15}<\frac{12}{15}$
$\Rightarrow \frac{11}{15}$ lies between $\frac{2}{3}$ and $\frac{4}{5}$.