1. **State the problem:** Grayson wants to make 5 servings of trail mix. The original recipe makes 15 servings and calls for 5 2/3 cups of almonds. We need to find how many cups of almonds Grayson needs for 5 servings. 2. **Write down the given quantities:** - Almonds in original recipe: $5 \frac{2}{3}$ cups - Servings in original recipe: 15 - Desired servings: 5 3. **Convert mixed number to improper fraction:** $$5 \frac{2}{3} = \frac{5 \times 3 + 2}{3} = \frac{15 + 2}{3} = \frac{17}{3}$$ 4. **Set up the proportion:** The amount of almonds is proportional to the number of servings. $$\frac{\text{Almonds for 5 servings}}{\text{Almonds for 15 servings}} = \frac{5}{15}$$ Let $x$ be the cups of almonds needed for 5 servings. $$\frac{x}{\frac{17}{3}} = \frac{5}{15}$$ 5. **Solve for $x$:** Multiply both sides by $\frac{17}{3}$: $$x = \frac{5}{15} \times \frac{17}{3}$$ Simplify $\frac{5}{15}$: $$\frac{5}{15} = \frac{\cancel{5}}{\cancel{15}} = \frac{1}{3}$$ So, $$x = \frac{1}{3} \times \frac{17}{3} = \frac{17}{9}$$ 6. **Convert improper fraction to mixed number:** Divide 17 by 9: $$17 \div 9 = 1 \text{ remainder } 8$$ So, $$\frac{17}{9} = 1 \frac{8}{9}$$ 7. **Final answer:** Grayson needs $1 \frac{8}{9}$ cups of almonds for 5 servings.