Solve. How many hours will it take Wendy to make \( 4 \frac{2}{3} \) batches of cookies if she can make \( 1 \frac{1}{3} \) batches in 1 hour?

To determine how many hours Wendy will need to make \( 4 \frac{2}{3} \) batches of cookies when her rate is \( 1 \frac{1}{3} \) batches per hour, follow these steps: ### Step 1: Convert Mixed Numbers to Improper Fractions First, convert both mixed numbers to improper fractions for easier calculation. - \( 4 \frac{2}{3} \) can be converted as follows: \[ 4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3} \] - \( 1 \frac{1}{3} \) can be converted as follows: \[ 1 \frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{3 + 1}{3} = \frac{4}{3} \] ### Step 2: Set Up the Division Problem The time required is equal to the total number of batches divided by the rate of batches per hour: \[ \text{Time} = \frac{\text{Total Batches}}{\text{Rate}} \] Plugging in the values: \[ \text{Time} = \frac{\frac{14}{3}}{\frac{4}{3}} \] ### Step 3: Divide the Fractions Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{\frac{14}{3}}{\frac{4}{3}} = \frac{14}{3} \times \frac{3}{4} \] Simplify the multiplication: \[ \frac{14 \times 3}{3 \times 4} = \frac{42}{12} = \frac{7}{2} \] ### Step 4: Convert the Result to Hours and Minutes \(\frac{7}{2}\) hours can be converted to a mixed number: \[ \frac{7}{2} = 3 \frac{1}{2} \text{ hours} = 3 \text{ hours and } 30 \text{ minutes} \] ### **Final Answer** Wendy will need **3 and a half hours** to make \( 4 \frac{2}{3} \) batches of cookies.