Question

a recipe for one batch of blueberry muffins uses the ingredients shown in the table. use this information for problems 4–7. 4. complete the double number line representing the amounts of sour cream and flour. sour cream (cups) 0 flour (cups) 0 ingredient amount blueberries 2\frac{1}{4} cups sour cream 1 cup salt \frac{1}{2} tsp flour 2 cups baking powder 3 tsp sugar 1 cup

Explanation:

Step 1: Identify batch quantities

From the table, 1 batch of muffins uses:

• Sour cream: $1$ cup
• Flour: $2$ cups

Step 2: Analyze the number line structure

The double number line has 4 equal intervals (segments) between $0$ and the end (representing 1 batch).

Step 3: Divide sour cream into intervals

For sour cream ($1$ cup total):
Each interval = $\frac{1}{4}$ cup (since $1 \div 4 = \frac{1}{4}$).
Thus, the sour cream number line ticks: $0, \frac{1}{4}, \frac{2}{4} = \frac{1}{2}, \frac{3}{4}, 1$ (at the end).

Step 4: Divide flour into intervals

For flour ($2$ cups total):
Each interval = $\frac{2}{4} = \frac{1}{2}$ cup (since the ratio of flour to sour cream is $2:1$, so each sour cream interval of $\frac{1}{4}$ cup corresponds to a flour interval of $\frac{1}{2}$ cup).
Thus, the flour number line ticks: $0, \frac{1}{2}, 1, \frac{3}{2}, 2$ (at the end).

So the completed number lines are:

• Sour cream (cups): Ticks at $0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1$ (end).
• Flour (cups): Ticks at $0, \frac{1}{2}, 1, \frac{3}{2}, 2$ (end).

Answer:

To complete the double number line:

• Sour cream (cups): Each tick mark represents $\frac{1}{4}$ cup (since 1 cup is the total for 1 batch, and the number line has 4 intervals? Wait, no—wait, the table says 1 cup of sour cream for 1 batch. Wait, the number line for sour cream has 0, then 4 intervals? Wait, no, looking at the number line: the sour cream number line has 0, then 4 small ticks? Wait, no, the original number line for sour cream (cups) has 0, then 4 segments? Wait, no, the problem is to represent the amounts for 1 batch. Wait, 1 batch uses 1 cup of sour cream and 2 cups of flour. So the double number line should show the relationship between sour cream and flour. For 1 batch: sour cream = 1 cup, flour = 2 cups. So the number line for sour cream: 0, 1 (at the end). For flour: 0, 2 (at the end). But the number line has 4 intervals? Wait, maybe the number line is divided into 4 equal parts? Wait, no—wait, the table: 1 cup sour cream, 2 cups flour. So the ratio of sour cream to flour is 1:2. So for each unit of sour cream, flour is 2 units. So if the sour cream number line has 0, then 1 (at the 4th tick? Wait, maybe the number line is divided into 4 parts, but 1 cup is the total. Wait, no, let's re-express:

For 1 batch:

• Sour cream: 1 cup (so the end of the sour cream number line is 1 cup).
• Flour: 2 cups (so the end of the flour number line is 2 cups).

Assuming the number line has 4 equal intervals (since there are 4 ticks after 0? Wait, the original number line for sour cream (cups) has 0, then 4 small ticks? Wait, the image shows the sour cream number line with 0, then 4 segments (5 ticks: 0, then 4 intervals). Wait, maybe the number line is for multiple batches? Wait, no—Problem 4 is to complete the double number line representing the amounts of sour cream and flour for 1 batch? Wait, no, the table is for 1 batch. So 1 batch: sour cream = 1 cup, flour = 2 cups. So the sour cream number line: 0, then 1 (at the end). The flour number line: 0, then 2 (at the end). But the number line has 4 intervals? Wait, maybe the number line is divided into 4 parts, so each part is 0.25 cups for sour cream (1 cup / 4 = 0.25) and 0.5 cups for flour (2 cups / 4 = 0.5). So:

Sour cream (cups) number line:

• 0, 0.25, 0.5, 0.75, 1 (at the end).

Flour (cups) number line:

• 0, 0.5, 1, 1.5, 2 (at the end).

So the completed number lines would have:

Sour cream (cups): 0, 0.25, 0.5, 0.75, 1 (the last tick is 1).

Flour (cups): 0, 0.5, 1, 1.5, 2 (the last tick is 2).