Mixed Number Sum 5Ed60E

1. **State the problem:** We need to calculate the sum of the mixed numbers $1 \frac{2}{7}$ and $2 \frac{2}{3}$ and express the answer as a mixed number in simplest form. 2. **Convert mixed numbers to improper fractions:** $$1 \frac{2}{7} = \frac{1 \times 7 + 2}{7} = \frac{7 + 2}{7} = \frac{9}{7}$$ $$2 \frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3}$$ 3. **Find a common denominator:** The denominators are $7$ and $3$. The least common denominator (LCD) is $21$. 4. **Convert fractions to have the LCD:** $$\frac{9}{7} = \frac{9 \times 3}{7 \times 3} = \frac{27}{21}$$ $$\frac{8}{3} = \frac{8 \times 7}{3 \times 7} = \frac{56}{21}$$ 5. **Add the fractions:** $$\frac{27}{21} + \frac{56}{21} = \frac{27 + 56}{21} = \frac{83}{21}$$ 6. **Convert the improper fraction back to a mixed number:** Divide $83$ by $21$: $$83 \div 21 = 3 \text{ remainder } 20$$ So, $$\frac{83}{21} = 3 \frac{20}{21}$$ 7. **Simplify the fraction if possible:** The fraction $\frac{20}{21}$ is already in simplest form because $20$ and $21$ have no common factors other than $1$. **Final answer:** $$3 \frac{20}{21}$$