Question

Find a rational number between $\frac{3}{7}$ and $\frac{2}{3}$.

• A. 1
• B. 2
• C. $\frac{11}{21}$
• D. $\frac{9}{21}$

Answer 1

The correct option is C $\frac{11}{21}$

First let's make denominator of both $\frac{2}{3}$ and $\frac{3}{7}$ equal.

LCM of 3 and 7 is 21.

Multiplying both numerator and denominator of $\frac{3}{7}$ by 3 we get $\frac{9}{21}$.

Similarly, multiplying both numerator and denominator of $\frac{2}{3}$ by 7, we get $\frac{14}{21}$.

So, we have to choose a rational number between $\frac{9}{21}$ and $\frac{14}{21}$.

Now, $1=\frac{21}{21}$

$2=\frac{2\times 21}{1\times 21}=\frac{42}{21}$

Now, consider $\frac{14}{21}$, $\frac{9}{21}$, $\frac{21}{21}$, $\frac{42}{21}$ and $\frac{11}{21}$.

$\frac{9}{21}$ < $\frac{11}{21}$ < $\frac{14}{21}$ < $\frac{21}{21}$ < $\frac{42}{21}$

$\Rightarrow$ $\frac{3}{7}$ < $\frac{11}{21}$ < $\frac{2}{3}$ < $1$ < $2$

Hence, $\frac{11}{21}$ lies between $\frac{3}{7}$ and $\frac{2}{3}$.