Question

7.3 fractional batches of ice cream
one batch of an ice cream recipe uses 9 cups of milk. a chef makes different amounts of ice cream on different days. here are the amounts of milk she used

• monday: 12 cups
• thursday: 16 cups
• tuesday: 22\frac{1}{2} cups
• friday: 7\frac{1}{2} cups

1. how many batches of ice cream did she make on each of the following days? write a division equation and draw a tape diagram for the question about each day. then answer the question.

a. monday
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b. tuesday
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Explanation:

Step1: Identify the formula

To find the number of batches, we use the formula: Number of batches = Amount of milk used / Milk per batch. Here, milk per batch is 9 cups. For Monday, the amount of milk used is 12 cups.

Step2: Set up the division equation

The division equation is $12 \div 9$. We can simplify this fraction by dividing numerator and denominator by their greatest common divisor, which is 3. So, $\frac{12}{9} = \frac{12\div3}{9\div3} = \frac{4}{3} = 1\frac{1}{3}$.

Step3: Tape diagram (brief description)

For the tape diagram, we can represent 1 batch as a segment of length 9 (for 9 cups). We need to show how many times 9 fits into 12. First, draw a segment for 9 (1 batch), then we have 12 - 9 = 3 cups left. Since 9 cups is 1 batch, 3 cups is $\frac{3}{9} = \frac{1}{3}$ of a batch. So total batches are $1 + \frac{1}{3} = 1\frac{1}{3}$.

Answer:

For Monday, the number of batches is $1\frac{1}{3}$. The division equation is $12 \div 9 = 1\frac{1}{3}$. (Tape diagram: Draw a tape divided into parts where one full part is 9 cups (1 batch) and then a part of $\frac{1}{3}$ of that length to represent the remaining 3 cups, totaling $1\frac{1}{3}$ batches.)