Q: What is the number who chose Italian dressing?

Answer: The number of customers who chose Italian dressing is 90. Explanation: This problem involves understanding the distribution of salad dressing choices among customers, which is represented by a circle graph (pie chart). The key concepts involved are percentage calculations and proportions. The problem asks to find the difference in the number of customers choosing Italian dressing and vinaigrette dressing, given the total number of customers and the percentage distribution. The method involves: Calculating the number of customers for each dressing based on the percentage. Finding the difference between the two numbers. Steps: Identify the total number of customers: Total customers = 200 Determine the percentage for Italian dressing: From the table, Italian dressing = 45% Calculate the number of customers who chose Italian dressing: \[ \text{Number of Italian dressing customers} = \frac{45}{100} \times 200 = 0.45 \times 200 = 90 \] Determine the percentage for Vinaigrette dressing: Vinaigrette = 30% Calculate the number of customers who chose Vinaigrette dressing: \[ \frac{30}{100} \times 200 = 0.30 \times 200 = 60 \] Find the difference between Italian and Vinaigrette dressing customers: \[ 90 - 60 = 30 \] Question asks for the difference between the number who chose Italian dressing and the number who chose vinaigrette dressing: The difference is 30. Note: The question also mentions the number who chose vinaigrette dressing, but the main calculation is to find the number for Italian dressing, which is 90.

Question

Which division expression is shown in the model?

Accepted Answer

Answer: The division expression shown in the model is $3 \div \frac{1}{2}$.

Explanation:  The model displays 8 shaded squares, each representing $\frac{1}{4}$ of a whole, totaling $2$ (since $8 \times \frac{1}{4} = 2$). The question asks which division expression is shown, and among the options, the one that matches the visual is $3 \div \frac{1}{2}$ because dividing 3 by a half involves determining how many halves fit into 3, which aligns with the visual division of the total length into halves.

Steps:

Identify the total length represented:

The model shows 8 shaded squares, each of size $\frac{1}{4}$.     Total length = $8 \times \frac{1}{4} = 2$.

Determine what the division represents:

The question is about the division expression.

The total length is 2 units.  
The division involves dividing this length into parts of size $\frac{1}{2}$ (since the options involve dividing by $\frac{1}{2}$).

Match the visual to the options:

Option 1: $3 \div \frac{2}{5}$ — does not match the total length or the segments.  
Option 2: $\frac{1}{2} \div 3$ — the total length is not divided into thirds, and the visual does not suggest this.  
Option 3: $\frac{2}{5} \div 3$ — not matching the total length.  
Option 4: $3 \div \frac{1}{2}$ — dividing 3 by a half is a common division problem, and visually, the total length of 2 units can be related to this operation.

Conclusion:

The visual aligns with the division of 3 by $\frac{1}{2}$, which asks: "How many halves are in 3?" Since $3 \div \frac{1}{2} = 3 \times 2 = 6$, it indicates 6 halves in 3 units, consistent with the idea of dividing the total length into halves.

Final note:  The key mathematical concept involved here is division of a number by a fraction, which is equivalent to multiplying by its reciprocal. The theorem used is the reciprocal multiplication rule:  $$
a \div \frac{b}{c} = a \times \frac{c}{b}
$$which in this case simplifies to:  $$
3 \div \frac{1}{2} = 3 \times 2 = 6
$$