Question

The ascending arrangement of $\frac{2}{3},\frac{6}{7},\frac{13}{21}$ is:

• A. $\frac{6}{7},\frac{2}{3},\frac{13}{21}$
• B. $\frac{13}{21},\frac{2}{3},\frac{6}{7}$
• C. $\frac{6}{7},\frac{13}{21},\frac{2}{3}$
• D. $\frac{2}{3},\frac{6}{7},\frac{13}{21}$

Answer 1

The correct option is B

$\frac{13}{21},\frac{2}{3},\frac{6}{7}$

Correct option: (b) $\frac{13}{21},\frac{2}{3},\frac{6}{7}$

Explanation

$\frac{2}{3},\frac{6}{7},\frac{13}{21}$

On taking $LCM$of $21,3,7$ we get

$LCM\left(21,3,7\right)=21$

We will change each of the given fractions into an equivalent fraction having $21$ as the denominator.

$$\begin{gathered} \frac{2}{3}=\frac{2\times 7}{3\times 7}=\frac{14}{21} \\ \frac{6}{7}=\frac{6\times 3}{7\times 3}=\frac{18}{21} \\ \frac{13}{21}=\frac{13\times 1}{21\times 1}=\frac{13}{21} \end{gathered}$$

Then we arrange the fractions

$\frac{13}{21}<\frac{14}{21}<\frac{18}{21}$

Hence,

$\frac{13}{21}<\frac{2}{3}<\frac{6}{7}$

Hence, the given fractions in ascending order are $\frac{13}{21},\frac{2}{3},\frac{6}{7}$

Hence, the correct option is (b)