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.