The problem asks us to order the fractions $\frac{2}{3}$, $\frac{5}{6}$, and $\frac{4}{9}$ from smallest to largest.

1. Problem Description

The problem asks us to order the fractions $\frac{2}{3}$, $\frac{5}{6}$, and $\frac{4}{9}$ from smallest to largest.

2. Solution Steps

To compare the fractions, we need to find a common denominator.

The least common multiple (LCM) of the denominators 3, 6, and 9 is

1

8. Now, we convert each fraction to an equivalent fraction with a denominator of

1

8. $\frac{2}{3} = \frac{2 \times 6}{3 \times 6} = \frac{12}{18}$

$\frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18}$

$\frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18}$

Now we can compare the fractions easily since they have the same denominator.

We compare the numerators: 8 < 12 <

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5. So, $\frac{8}{18} < \frac{12}{18} < \frac{15}{18}$.

Replacing the fractions with the original fractions, we have $\frac{4}{9} < \frac{2}{3} < \frac{5}{6}$.

3. Final Answer

The fractions in order from smallest to largest are $\frac{4}{9}$, $\frac{2}{3}$, $\frac{5}{6}$.