9. \( \frac{5}{6}+\frac{2}{5} \)

To add the fractions \( \frac{5}{6} \) and \( \frac{2}{5} \), follow these steps: ### Step 1: Find a Common Denominator To add two fractions, they must have the same denominator. The denominators here are 6 and 5. - **Least Common Denominator (LCD)** of 6 and 5 is 30. ### Step 2: Convert Both Fractions to Equivalent Fractions with the LCD Convert each fraction to an equivalent fraction with the denominator of 30. - For \( \frac{5}{6} \): \[ \frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30} \] - For \( \frac{2}{5} \): \[ \frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30} \] ### Step 3: Add the Equivalent Fractions Now that both fractions have the same denominator, you can add them directly: \[ \frac{25}{30} + \frac{12}{30} = \frac{25 + 12}{30} = \frac{37}{30} \] ### Step 4: Simplify the Result (If Needed) The result \( \frac{37}{30} \) is an improper fraction. It can also be expressed as a mixed number: \[ \frac{37}{30} = 1 \frac{7}{30} \] ### **Final Answer** \[ \frac{5}{6} + \frac{2}{5} = \frac{37}{30} \quad \text{or} \quad 1 \frac{7}{30} \]