Solve the Fraction Subtraction: 2/3 minus 4/9

To solve this problem, we'll perform the following steps:

• Step 1: Find the Least Common Denominator (LCD) of $3$ and $9$.
• Step 2: Convert each fraction to have the LCD as its denominator.
• Step 3: Subtract the numerators of the converted fractions.
• Step 4: Simplify the resulting fraction if needed.

Let's proceed with the steps:

Step 1: The denominators of the given fractions are $3$ and $9$. The LCD of $3$ and $9$ is $9$ since $9$ is the smallest multiple that both $3$ and $9$ divide into evenly.

Step 2: Convert each fraction to have a denominator of $9$.

$\frac{2}{3}$ can be converted to an equivalent fraction with the denominator $9$ by multiplying the numerator and denominator by 3:

$\frac{2}{3} \times \frac{3}{3} = \frac{6}{9}$

The second fraction $\frac{4}{9}$ already has the denominator $9$, so it remains unchanged.

Step 3: Subtract the fractions: $\frac{6}{9} - \frac{4}{9}$.

Since the denominators are now the same, subtract the numerators:

$6 - 4 = 2$

The resulting fraction is $\frac{2}{9}$.

Step 4: Check if there is a need to simplify. The fraction $\frac{2}{9}$ is already in its simplest form.

Thus, the solution to the problem is $\frac{2}{9}$.