1. **Problem:** Add the proper fraction to the mixed number with the same denominator. 2. **Formula:** To add a mixed number and a proper fraction with the same denominator, add the whole number part and the fractional parts separately: $$\text{Mixed Number} + \text{Proper Fraction} = \left(\text{Whole Number} + 0\right) + \left(\frac{a}{d} + \frac{b}{d}\right) = \text{Whole Number} + \frac{a+b}{d}$$ If the numerator of the fraction sum is greater than or equal to the denominator, convert the improper fraction to a mixed number and add to the whole number. --- ### Example 1a) $2 \frac{2}{8} + \frac{6}{8}$ 3. Add the fractional parts: $$\frac{2}{8} + \frac{6}{8} = \frac{2+6}{8} = \frac{8}{8}$$ 4. Since $\frac{8}{8} = 1$, add this to the whole number: $$2 + 1 = 3$$ 5. **Final answer:** $$2 \frac{2}{8} + \frac{6}{8} = 3$$ --- ### Example 1b) $2 \frac{3}{6} + \frac{5}{6}$ 6. Add the fractional parts: $$\frac{3}{6} + \frac{5}{6} = \frac{3+5}{6} = \frac{8}{6}$$ 7. Simplify $\frac{8}{6}$ by dividing numerator and denominator by 2: $$\frac{8}{6} = \frac{\cancel{8}^4}{\cancel{6}^3} = \frac{4}{3}$$ 8. Convert $\frac{4}{3}$ to a mixed number: $$\frac{4}{3} = 1 \frac{1}{3}$$ 9. Add this to the whole number: $$2 + 1 \frac{1}{3} = 3 \frac{1}{3}$$ 10. **Final answer:** $$2 \frac{3}{6} + \frac{5}{6} = 3 \frac{1}{3}$$