The problem asks to order the given fractions, $\frac{9}{12}$, $\frac{1}{2}$, and $\frac{1}{3}$, from smallest to largest.

1. Problem Description

The problem asks to order the given fractions, $\frac{9}{12}$, $\frac{1}{2}$, and $\frac{1}{3}$, from smallest to largest.

2. Solution Steps

To compare the fractions, we can find a common denominator. The least common multiple (LCM) of 12, 2, and 3 is

1

2. So, we will convert each fraction to an equivalent fraction with a denominator of

1

2.

$\frac{9}{12}$ is already in the desired form.

To convert $\frac{1}{2}$ to a fraction with a denominator of 12, we multiply the numerator and denominator by 6:

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

To convert $\frac{1}{3}$ to a fraction with a denominator of 12, we multiply the numerator and denominator by 4:

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

Now we have the fractions $\frac{9}{12}$, $\frac{6}{12}$, and $\frac{4}{12}$. Comparing the numerators, we have 4 < 6 <

9. Thus,

$\frac{4}{12} < \frac{6}{12} < \frac{9}{12}$.

Replacing the fractions with their original forms:

$\frac{1}{3} < \frac{1}{2} < \frac{9}{12}$.

3. Final Answer

$\frac{1}{3}, \frac{1}{2}, \frac{9}{12}$