Question

Express the following fractions in ascending order:

$\frac{2}{3}$, $\frac{12}{7}$, $\frac{5}{21}$: ___, ___, ___

• A. $\frac{5}{21}$
• B. $\frac{2}{3}$, $\frac{12}{7}$

Answer 1

• Step 1: The least common denominator (LCD) of $3$, $7$ and $21$ is $21$. Make the denominator as $21$ for all the fractions.

$\frac{2}{3}=\frac{2\times 7}{3\times 7}=\frac{14}{21}$;

$\frac{12}{7}=\frac{12\times 3}{7\times 3}=\frac{36}{21}$;

$\frac{5}{21}=\frac{5\times 1}{21\times 1}=\frac{5}{21}$

• Step 2: Now each fraction has the same denominator $21$. Arrange the fractions in ascending order by arranging numerators in ascending order.

$\frac{5}{21}$, $\frac{14}{21}$, $\frac{36}{21}$

• Hence, the fractions in ascending order are $\frac{5}{21}$, $\frac{2}{3}$, $\frac{12}{7}$.