Calculate \( 2 \frac{2}{3}+3 \frac{1}{6} \)

To calculate \( 2 \frac{2}{3} + 3 \frac{1}{6} \), follow these steps: ### 1. Convert Mixed Numbers to Improper Fractions **For \( 2 \frac{2}{3} \):** \[ 2 \frac{2}{3} = \frac{(2 \times 3) + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3} \] **For \( 3 \frac{1}{6} \):** \[ 3 \frac{1}{6} = \frac{(3 \times 6) + 1}{6} = \frac{18 + 1}{6} = \frac{19}{6} \] ### 2. Find a Common Denominator The denominators are 3 and 6. The Least Common Denominator (LCD) is **6**. Convert \(\frac{8}{3}\) to have the denominator 6: \[ \frac{8}{3} = \frac{8 \times 2}{3 \times 2} = \frac{16}{6} \] \[ \frac{19}{6} \text{ remains the same} \] ### 3. Add the Fractions \[ \frac{16}{6} + \frac{19}{6} = \frac{16 + 19}{6} = \frac{35}{6} \] ### 4. Convert Back to a Mixed Number \[ \frac{35}{6} = 5 \frac{5}{6} \] *(Because 6 goes into 35 five times with a remainder of 5.)* ### **Final Answer** \[ 2 \frac{2}{3} + 3 \frac{1}{6} = 5 \frac{5}{6} \]