Solve Fraction Addition: 2/3 + 7/9 Step-by-Step

To solve this problem, we will perform the following steps:

• Step 1: Find the Least Common Multiple (LCM) of the denominators 3 and 9.
• Step 2: Convert both fractions to have a common denominator.
• Step 3: Add the numerators of the converted fractions and write the result over the common denominator.
• Step 4: Simplify the resultant fraction if needed.

Let's work through each step:

Step 1:
The denominators of our fractions are 3 and 9. The LCM of 3 and 9 is 9, since 9 is the smallest number that both 3 and 9 divide evenly into.

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

- For $\frac{2}{3}$, multiply both the numerator and denominator by 3 (because $\frac{9}{3} = 3$):
$\frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9}$

- The second fraction $\frac{7}{9}$ already has a denominator of 9, so it remains the same:
$\frac{7}{9}$

Step 3:
Add the two fractions:
$\frac{6}{9} + \frac{7}{9} = \frac{6 + 7}{9} = \frac{13}{9}$

Step 4:
The fraction $\frac{13}{9}$ is in its simplest form because 13 is a prime number and does not divide evenly into 9.

Therefore, the solution to the problem is $\frac{13}{9}$.