Solve the Fraction Addition: 1/5 + 3/10 Step-by-Step

Solve the following exercise:

$\frac{1}{5}+\frac{3}{10}=\text{?}$

To solve this problem, let's break it down into clear, manageable steps:

• Step 1: Identify the common denominator. Here, the denominators are 5 and 10. The least common denominator (LCD) is 10.
• Step 2: Convert $\frac{1}{5}$ to an equivalent fraction with a denominator of 10. This means multiplying both the numerator and denominator by 2. Thus, $\frac{1}{5} = \frac{2}{10}$.
• Step 3: We already have $\frac{3}{10}$ with a denominator of 10, so no conversion is necessary.
• Step 4: Add the two fractions: $\frac{2}{10} + \frac{3}{10} = \frac{2 + 3}{10} = \frac{5}{10}$.
• Step 5: Verify if the fraction can be simplified. Here, $\frac{5}{10}$ is already in its simplest form equivalent to $\frac{1}{2}$, but, as part of the answer choices, it appears as $\frac{5}{10}$.

Therefore, the correct answer is $\frac{5}{10}$.