To add the two mixed numbers, we follow these steps:

Step 1: Write the mixed numbers in expanded form.

$5 \frac{9}{10} = 5 + \frac{9}{10}, \quad 2 \frac{3}{10} = 2 + \frac{3}{10}$

Step 2: Add the whole numbers and the fractions separately.

• Whole numbers: $5 + 2 = 7$
• Fractions: $\frac{9}{10} + \frac{3}{10} = \frac{9 + 3}{10} = \frac{12}{10}$

Step 3: Simplify the fractional part.

$\frac{12}{10} = 1 \frac{2}{10} = 1 \frac{1}{5} \text{ (simplified by dividing numerator and denominator by 2)}.$

Step 4: Combine the whole number and fractional parts.

$7 + 1 \frac{1}{5} = 8 \frac{1}{5}.$

Final Answer:

$8 \frac{1}{5}$

Would you like a more detailed breakdown? Here are related questions for practice:

1. Add $4 \frac{7}{10} + 3 \frac{6}{10}$.
2. Subtract $6 \frac{9}{10} - 2 \frac{4}{10}$.
3. Multiply $5 \frac{9}{10} \times 2 \frac{3}{10}$.
4. Divide $7 \frac{3}{10} \div 2 \frac{5}{10}$.
5. Add $3 \frac{4}{5} + 2 \frac{7}{10}$.

Tip:

Always simplify fractions by dividing the numerator and denominator by their greatest common divisor (GCD).