Question

Express the following fractions in ascending order:

$\frac{1}{2}$, $\frac{5}{4}$, $\frac{2}{3}$: ___, ___, ___

• A. $\frac{1}{2}$
• B. $\frac{2}{3}$, $\frac{5}{4}$

Answer 1

• Step 1: The least common denominator (LCD) of $2$, $3$ and $4$ is $12$. Make the denominator as $12$ for all the fractions.

$\frac{1}{2}=\frac{1\times 6}{2\times 6}=\frac{6}{12}$;

$\frac{5}{4}=\frac{5\times 3}{4\times 3}=\frac{15}{12}$;

$\frac{2}{3}=\frac{2\times 4}{3\times 4}=\frac{8}{12}$

• Step 2: Now each fraction has the same denominator $12$. Arrange the fractions in ascending order by arranging numerators in ascending order.

$\frac{6}{12}$, $\frac{8}{12}$, $\frac{15}{12}$

• Hence, the fractions in ascending order are $\frac{1}{2}$, $\frac{2}{3}$, $\frac{5}{4}$.