1. **Problem Statement:** Exercise #1: Given a recipe with 1/4 cup sugar and 3/4 cup flour, find the ratio of sugar to flour as a complex fraction, simplify it, and interpret the unit rates. Exercise #2: A bucket fills 3/5 in 1/4 hour. Find the filling rate per hour as a mixed number. Exercise #3: Joe's Pizzeria sells 3 3/8 pizzas in 1 1/4 hours. Find the rate of pizzas sold per hour. --- 2. **Exercise #1 (a): Write and simplify the complex fraction** The ratio of sugar to flour is $$\frac{\frac{1}{4}}{\frac{3}{4}}$$. To simplify, multiply numerator by reciprocal of denominator: $$\frac{1}{4} \div \frac{3}{4} = \frac{1}{4} \times \frac{4}{3} = \frac{1 \times 4}{4 \times 3} = \frac{4}{12} = \frac{1}{3}$$. --- 3. **Exercise #1 (b): Ratio in simplest form** The simplest form of the ratio sugar to flour is $$\frac{1}{3}$$. This means for every 1 part sugar, there are 3 parts flour. --- 4. **Exercise #1 (c): Interpret unit rates** - Cups of sugar per 1 cup of flour: Since sugar:flour = 1:3, for 3 cups flour there is 1 cup sugar. So for 1 cup flour, sugar = $$\frac{1}{3}$$ cup. - Cups of flour per 1 cup of sugar: Invert the ratio: flour:sugar = 3:1. So for 1 cup sugar, flour = 3 cups. --- 5. **Exercise #2: Rate of bucket filling per hour** Given filling 3/5 bucket in 1/4 hour, rate per hour is: $$\frac{3/5}{1/4} = \frac{3}{5} \times \frac{4}{1} = \frac{12}{5} = 2 \frac{2}{5}$$ buckets per hour. --- 6. **Exercise #3 (a): Rate of pizzas sold per hour** Convert mixed numbers to improper fractions: $$3 \frac{3}{8} = \frac{27}{8}, \quad 1 \frac{1}{4} = \frac{5}{4}$$. Set up ratio as complex fraction: $$\frac{\frac{27}{8}}{\frac{5}{4}} = \frac{27}{8} \times \frac{4}{5} = \frac{108}{40} = \frac{27}{10} = 2 \frac{7}{10}$$ pizzas per hour. --- **Final answers:** - Exercise #1 (a): $$\frac{1}{3}$$ - Exercise #1 (b): $$\frac{1}{3}$$ - Exercise #1 (c): Sugar per cup flour = $$\frac{1}{3}$$ cup; Flour per cup sugar = 3 cups - Exercise #2: $$2 \frac{2}{5}$$ buckets per hour - Exercise #3 (a): $$2 \frac{7}{10}$$ pizzas per hour