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?

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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.
Wendy will need 3 and a half hours to make $$ 4 \frac{2}{3} $$ batches of cookies.

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?

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