Let's work through the addition of these two mixed numbers: $2 \frac{3}{10} + 3 \frac{3}{5}$.

Step 1: Convert mixed numbers to improper fractions

• For $2 \frac{3}{10}$: $2 \frac{3}{10} = \frac{2 \times 10 + 3}{10} = \frac{23}{10}$

• For $3 \frac{3}{5}$: $3 \frac{3}{5} = \frac{3 \times 5 + 3}{5} = \frac{18}{5}$

Step 2: Find a common denominator

The denominators are 10 and 5. The least common denominator (LCD) is 10.

• Rewrite $\frac{18}{5}$ with denominator 10: $\frac{18}{5} = \frac{18 \times 2}{5 \times 2} = \frac{36}{10}$

Step 3: Add the fractions

Now that both fractions have the same denominator, we can add them: $\frac{23}{10} + \frac{36}{10} = \frac{23 + 36}{10} = \frac{59}{10}$

Step 4: Convert the improper fraction back to a mixed number

$\frac{59}{10}$ is equal to: $\frac{59}{10} = 5 \frac{9}{10}$

Final Answer:

The sum is $5 \frac{9}{10}$.

Would you like further explanation or details on any of the steps?

Here are 5 related questions to deepen understanding:

1. How do you convert a mixed number to an improper fraction?
2. How do you find the least common denominator for fractions?
3. What is the process for converting improper fractions back to mixed numbers?
4. Can you subtract two mixed numbers in a similar way?
5. How would the addition change if the denominators were not factors of each other?

Tip: Always simplify fractions and mixed numbers at the end to make sure your answer is in the simplest form.