Thank you for the clarification. Let's work with the correct fractions, \( \frac{3}{10} \) and \( \frac{1}{5} \).

### Step 1: Identify the Denominators
The fractions given are \( \frac{3}{10} \) and \( \frac{1}{5} \).
- The denominators are 10 and 5.

### Step 2: Find Common Denominators
Here are three possible common denominators:

1. **Least Common Denominator (LCD):**
   - The least common denominator is the smallest number that both 10 and 5 divide into. In this case, 10 is the LCD.
   - So, 10 is a common denominator.

2. **Multiples of 10:**
   - **20**: The next possible common denominator is \( 2 \times 10 = 20 \).
   - **30**: Another possible common denominator is \( 3 \times 10 = 30 \).

### Step 3: Add the Fractions for Each Denominator
We will convert each fraction to the respective common denominator and add them.

1. **Using 10 as the denominator:**
   \[
   \frac{3}{10} \text{ is already over 10.}
   \]
   \[
   \frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}
   \]
   \[
   \frac{3}{10} + \frac{2}{10} = \frac{5}{10}
   \]
   The sum \( \frac{5}{10} \) can be reduced:
   \[
   \frac{5}{10} = \frac{1}{2}
   \]

2. **Using 20 as the denominator:**
   \[
   \frac{3}{10} = \frac{3 \times 2}{10 \times 2} = \frac{6}{20}
   \]
   \[
   \frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20}
   \]
   \[
   \frac{6}{20} + \frac{4}{20} = \frac{10}{20}
   \]
   The sum \( \frac{10}{20} \) can be reduced:
   \[
   \frac{10}{20} = \frac{1}{2}
   \]

3. **Using 30 as the denominator:**
   \[
   \frac{3}{10} = \frac{3 \times 3}{10 \times 3} = \frac{9}{30}
   \]
   \[
   \frac{1}{5} = \frac{1 \times 6}{5 \times 6} = \frac{6}{30}
   \]
   \[
   \frac{9}{30} + \frac{6}{30} = \frac{15}{30}
   \]
   The sum \( \frac{15}{30} \) can be reduced:
   \[
   \frac{15}{30} = \frac{1}{2}
   \]

### Final Answer:
In all cases, the reduced answer is \( \frac{1}{2} \).

Would you like more details or have any questions about this process?

Here are 5 related questions to explore further:
1. How can you determine if two fractions are equivalent?
2. What are some strategies for finding common denominators quickly?
3. How does finding a common denominator help in comparing fractions?
4. What happens if the fractions have a common factor in the numerator and denominator?
5. How would you multiply or divide fractions like \( \frac{3}{10} \) and \( \frac{1}{5} \)?

**Tip:** Always look for the smallest common denominator first, as it often simplifies calculations and reduces the need for further simplification.

Learn how to add fractions \( \frac{3}{10} \) and \( \frac{1}{5} \) with a detailed step-by-step solution. Understand the concept of common denominators and fraction addition. Suitable for students in Grades 4-6.

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