1. **State the problem:** Nike was given 1 whole cake plus \frac{1}{2} pieces of cake, and Mary was given 1 whole cake plus \frac{1}{3} pieces of cake. We need to find the total amount of cake given to both. 2. **Write the amounts given:** - Nike's cake: $1 + \frac{1}{2}$ - Mary's cake: $1 + \frac{1}{3}$ 3. **Add the amounts:** $$\text{Total} = \left(1 + \frac{1}{2}\right) + \left(1 + \frac{1}{3}\right)$$ 4. **Combine like terms:** $$= 1 + 1 + \frac{1}{2} + \frac{1}{3} = 2 + \frac{1}{2} + \frac{1}{3}$$ 5. **Find common denominator for fractions:** The denominators are 2 and 3, so the common denominator is 6. 6. **Convert fractions:** $$\frac{1}{2} = \frac{3}{6}, \quad \frac{1}{3} = \frac{2}{6}$$ 7. **Add fractions:** $$\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$$ 8. **Add whole number and fraction:** $$2 + \frac{5}{6} = \frac{12}{6} + \frac{5}{6} = \frac{17}{6}$$ 9. **Convert to mixed number:** $$\frac{17}{6} = 2 \frac{5}{6}$$ **Final answer:** The total amount of cake given to both Nike and Mary is $2 \frac{5}{6}$ pieces of cake.