To solve $2 \frac{3}{5} + 1 \frac{9}{10}$, we will first convert the mixed numbers to improper fractions and then find the sum.

Step-by-Step Solution:

1. Convert $2 \frac{3}{5}$ to an improper fraction: $2 \frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5}$

2. Convert $1 \frac{9}{10}$ to an improper fraction: $1 \frac{9}{10} = \frac{1 \times 10 + 9}{10} = \frac{10 + 9}{10} = \frac{19}{10}$

3. Add $\frac{13}{5}$ and $\frac{19}{10}$:

   • To add these fractions, we need a common denominator. The least common multiple of 5 and 10 is 10.
   • Convert $\frac{13}{5}$ to a fraction with a denominator of 10: $\frac{13}{5} = \frac{13 \times 2}{5 \times 2} = \frac{26}{10}$
   • Now we can add $\frac{26}{10}$ and $\frac{19}{10}$: $\frac{26}{10} + \frac{19}{10} = \frac{26 + 19}{10} = \frac{45}{10}$

4. Simplify $\frac{45}{10}$: $\frac{45}{10} = \frac{9}{2}$

5. Convert $\frac{9}{2}$ back to a mixed number: $\frac{9}{2} = 4 \frac{1}{2}$

Final Answer:

$2 \frac{3}{5} + 1 \frac{9}{10} = 4 \frac{1}{2}$

Would you like more details on any part of this solution, or have any questions?

Further Questions:

1. How do you find the least common multiple of two numbers?
2. What is the process to convert mixed numbers into improper fractions?
3. How can you simplify an improper fraction?
4. How do you convert an improper fraction back into a mixed number?
5. Why is it important to have a common denominator when adding fractions?

Tip:

When working with fractions, always remember to simplify your final answer if possible.