Solve the Fraction Addition: 1/2 + 2/5 Step by Step

To solve the problem of adding the fractions $\frac{1}{2}$ and $\frac{2}{5}$, we will follow these steps:

• Step 1: Determine a common denominator for the fractions.
• Step 2: Convert each fraction to an equivalent fraction with this common denominator.
• Step 3: Add the resulting fractions.

Now, let’s explore each step in detail:

Step 1: The denominators are 2 and 5. A common denominator can be found by multiplying these two numbers: $2 \times 5 = 10$. Therefore, 10 is our common denominator.

Step 2: Convert each fraction to have the common denominator of 10.
- For $\frac{1}{2}$, multiply both the numerator and the denominator by 5:
$\frac{1}{2} \times \frac{5}{5} = \frac{5}{10}$.
- For $\frac{2}{5}$, multiply both the numerator and the denominator by 2:
$\frac{2}{5} \times \frac{2}{2} = \frac{4}{10}$.

Step 3: Add the fractions $\frac{5}{10}$ and $\frac{4}{10}$:
Combine the numerators while keeping the common denominator:
$5 + 4 = 9$.
Thus, $\frac{5}{10} + \frac{4}{10} = \frac{9}{10}$.

Therefore, the sum of $\frac{1}{2}$ and $\frac{2}{5}$ is $\frac{9}{10}$.