Question

what division number sentence is represented by the model shown?
options:
\\(\frac{13}{4} \times \frac{3}{4}\\)
\\(4 div \frac{3}{4}\\)
\\(\frac{13}{4} div \frac{3}{4}\\)
\\(\frac{13}{4} div 4\\)

Explanation:

Step1: Analyze the model's total and groups

The model likely represents a total of \(\frac{13}{4}\) (from the shaded parts) being divided into groups of \(\frac{3}{4}\)? Wait, no—wait, looking at the options, the third option is \(\frac{13}{4} \div \frac{3}{4}\)? Wait, no, let's re-examine. Wait, the model: let's see, the total number of fourths? Wait, maybe the total is \(\frac{13}{4}\) (since 3 wholes (12/4) plus 1/4 is 13/4) and we are dividing by \(\frac{3}{4}\)? Wait, no, the third option is \(\frac{13}{4} \div \frac{3}{4}\)? Wait, no, the options: first is multiplication, second is \(4 \div \frac{3}{4}\), third is \(\frac{13}{4} \div \frac{3}{4}\), fourth is \(\frac{13}{4} \div 4\). Wait, maybe the model has a total of \(\frac{13}{4}\) (13 fourths) and is divided into groups of \(\frac{3}{4}\)? No, wait, maybe the total is \(\frac{13}{4}\) and we are dividing by \(\frac{3}{4}\)? Wait, no, let's think again. Wait, the model: suppose we have a total of \(\frac{13}{4}\) (since 3 wholes (each is 4/4, so 3*4/4=12/4) plus 1/4 is 13/4) and we are dividing by \(\frac{3}{4}\)? Wait, no, the third option is \(\frac{13}{4} \div \frac{3}{4}\)? Wait, no, the options: let's check the division. Wait, the question is about the division number sentence. Let's analyze the options:

Option 1: Multiplication, so eliminate.

Option 2: \(4 \div \frac{3}{4}\) – 4 is 16/4, not 13/4.

Option 3: \(\frac{13}{4} \div \frac{3}{4}\) – 13/4 is 3 and 1/4, which matches the model (3 wholes and 1/4).

Option 4: \(\frac{13}{4} \div 4\) – dividing by 4, but the model's groups seem to be in thirds? Wait, no, maybe the model shows dividing 13/4 into groups of 3/4? Wait, no, maybe the model has 13 fourths (13/4) and is divided into groups of 3 fourths (3/4), so the division is 13/4 ÷ 3/4.

Step2: Confirm the correct option

Among the options, the third one (\(\frac{13}{4} \div \frac{3}{4}\)) matches the total (13/4) and the divisor (3/4) as per the model's representation.

Answer:

C. \(\boldsymbol{\frac{13}{4} \div \frac{3}{4}}\) (assuming the third option is labeled C; if the options are A, B, C, D with A: \(\frac{13}{4} \times \frac{3}{4}\), B: \(4 \div \frac{3}{4}\), C: \(\frac{13}{4} \div \frac{3}{4}\), D: \(\frac{13}{4} \div 4\))