Solve: Adding Fractions 4/9 + 1/2 Step by Step

To solve the problem of adding $\frac{4}{9}$ and $\frac{1}{2}$, we'll proceed step-by-step:

• Step 1: Determine a common denominator.
• Step 2: Convert each fraction to an equivalent fraction with this common denominator.
• Step 3: Add the numerators of these converted fractions.
• Step 4: Simplify the resulting fraction if necessary.

Now, let's perform these steps in detail:

Step 1: Determine the common denominator.
The denominators are 9 and 2. The least common denominator (LCD) can be found by multiplying these because they have no common factors other than 1:
$\text{LCD} = 9 \times 2 = 18$.

Step 2: Convert each fraction to have the common denominator of 18.

• Convert $\frac{4}{9}$: $\frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18}$
• Convert $\frac{1}{2}$: $\frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18}$

Step 3: Add the numerators of the converted fractions:
$\frac{8}{18} + \frac{9}{18} = \frac{8+9}{18} = \frac{17}{18}$

Step 4: Simplification (if needed):
The fraction $\frac{17}{18}$ is already in its simplest form.

Therefore, the sum of $\frac{4}{9}$ and $\frac{1}{2}$ is $\frac{17}{18}$.