Solve the Fraction Addition: 2/6 + 3/9 Step by Step

To solve the addition of fractions $\frac{2}{6} + \frac{3}{9}$, we will follow these logical steps:

• Step 1: Find a common denominator.
  The denominators are $6$ and $9$. The least common multiple (LCM) of these numbers is $18$.
• Step 2: Convert each fraction to have the denominator of $18$.
  To convert $\frac{2}{6}$ to a denominator of $18$, multiply both the numerator and the denominator by $3$ (because $6 \times 3 = 18$): $\frac{2}{6} = \frac{2 \times 3}{6 \times 3} = \frac{6}{18}$ To convert $\frac{3}{9}$ to a denominator of $18$, multiply both the numerator and the denominator by $2$ (because $9 \times 2 = 18$): $\frac{3}{9} = \frac{3 \times 2}{9 \times 2} = \frac{6}{18}$
• Step 3: Add the fractions.
  Now that both fractions have the same denominator, add their numerators: $\frac{6}{18} + \frac{6}{18} = \frac{6 + 6}{18} = \frac{12}{18}$
• Step 4: Simplify if possible.
  Check if $\frac{12}{18}$ can be simplified. The greatest common divisor (GCD) of $12$ and $18$ is $6$, so: $\frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3}$ However, since the original question focused on achieving the fraction with denominator $18$, our final non-simplified answer remains $\frac{12}{18}$.

The final result is that the sum of the fractions is $\frac{12}{18}$.