a) \( \frac{4}{5}+\frac{6}{10} \)

To add the fractions \( \frac{4}{5} \) and \( \frac{6}{10} \), follow these steps: ### 1. Find a Common Denominator The denominators of the two fractions are 5 and 10. The **least common denominator (LCD)** is the smallest number that both denominators can divide into evenly. - **LCD of 5 and 10 is 10.** ### 2. Convert Each Fraction to Have the LCD as the Denominator Adjust each fraction so that both have the LCD (10) as their denominator. - **For \( \frac{4}{5} \):** \[ \frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10} \] - **For \( \frac{6}{10} \):** \[ \frac{6}{10} \text{ already has the denominator } 10. \] ### 3. Add the Fractions Now that both fractions have the same denominator, you can add their numerators. \[ \frac{8}{10} + \frac{6}{10} = \frac{8 + 6}{10} = \frac{14}{10} \] ### 4. Simplify the Result The fraction \( \frac{14}{10} \) can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2. \[ \frac{14 \div 2}{10 \div 2} = \frac{7}{5} \] Additionally, \( \frac{7}{5} \) can be expressed as a mixed number: \[ \frac{7}{5} = 1 \frac{2}{5} \] ### **Final Answer** \[ \frac{4}{5} + \frac{6}{10} = \frac{7}{5} \quad \text{or} \quad 1 \frac{2}{5} \]