Select the group of fractions in an ascending order:

The correct option is $\frac{1}{4}<\frac{1}{3}<\frac{1}{2}$.

To arrange fractions in ascending order (from smallest to largest), we can compare their values by finding a common denominator or by converting them into decimal form.

Method 1: Comparing with a common denominator
The given fractions are $\frac{1}{4}$, $\frac{1}{3}$, and $\frac{1}{2}$.
The Least Common Multiple (LCM) of the denominators 4, 3, and 2 is 12.

Convert each fraction into an equivalent fraction with a denominator of 12:

$\frac{1}{4}=\frac{1\times 3}{4\times 3}=\frac{3}{12}$

$\frac{1}{3}=\frac{1\times 4}{3\times 4}=\frac{4}{12}$

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

Since 3 < 4 < 6, comparing the numerators gives:
$\frac{3}{12}<\frac{4}{12}<\frac{6}{12}$

Replacing them with their original fraction forms, we get:
$\frac{1}{4}<\frac{1}{3}<\frac{1}{2}$

Method 2: Comparing decimal values
Convert each fraction to its decimal equivalent:

$\frac{1}{4}=0.25$

$\frac{1}{3}\approx 0.333$

$\frac{1}{2}=0.5$

Arranging these decimal values from smallest to largest:
0.25 < 0.333 < 0.5

Thus, in ascending order, the fractions are:
$\frac{1}{4}<\frac{1}{3}<\frac{1}{2}$