Question

Express the following fractions in ascending order:

$\frac{3}{10}$, $\frac{10}{3}$, $\frac{2}{21}$: ___, ___, ___

• A. $\frac{2}{21}$
• B. $\frac{3}{10}$, $\frac{10}{3}$

Answer 1

• Step 1: The least common denominator (LCD) of $3$, $10$ and $21$ is $210$. Make the denominator as $210$ for all the fractions.

$\frac{3}{10}=\frac{3\times 21}{10\times 21}=\frac{63}{210}$;

$\frac{10}{3}=\frac{10\times 70}{3\times 70}=\frac{700}{210}$;

$\frac{2}{21}=\frac{2\times 10}{21\times 10}=\frac{20}{210}$

• Step 2: Now each fraction has the same denominator $210$. Arrange the fractions in ascending order by arranging numerators in ascending order.

$\frac{20}{210}$, $\frac{63}{210}$, $\frac{700}{210}$

• Hence, the fractions in ascending order are $\frac{2}{21}$, $\frac{3}{10}$, $\frac{10}{3}$.