Question

the model below represents a division problem. which equation is represented by the model? answer options: \\(\frac{1}{4} \div 15 = 3\frac{3}{4}\\), \\(15 \div \frac{1}{4} = 3\frac{3}{4}\\), \\(3\frac{3}{4} \div \frac{1}{4} = 15\\), \\(\frac{1}{4} \div 3\frac{3}{4} = 15\\)

Explanation:

Step1: Analyze the model

The model has segments of $\frac{1}{4}$. Let's count the number of $\frac{1}{4}$ segments in the blue part. From the number line, we can see that from 0 (implicit) to the end of the blue part, we have 15 segments of $\frac{1}{4}$? Wait, no, let's check the length. Wait, the blue part: let's see, the value of the blue part is $3\frac{3}{4}$? Wait, no, wait. Wait, $3\frac{3}{4}$ is $\frac{15}{4}$. Wait, each segment is $\frac{1}{4}$. So if we have a number divided by $\frac{1}{4}$ equals 15? Wait, no. Wait, let's think about division of fractions. The equation $3\frac{3}{4}\div\frac{1}{4}$: $3\frac{3}{4}=\frac{15}{4}$, so $\frac{15}{4}\div\frac{1}{4}=\frac{15}{4}\times4 = 15$. So the equation $3\frac{3}{4}\div\frac{1}{4}=15$ is correct. Let's check the options:

Option 1: $\frac{1}{4}\div15 = 3\frac{3}{4}$ → No, because $\frac{1}{4}\div15=\frac{1}{60}
eq3\frac{3}{4}$.

Option 2: $3\frac{3}{4}\div\frac{1}{4}=15$ → Let's compute $3\frac{3}{4}=\frac{15}{4}$, $\frac{15}{4}\div\frac{1}{4}=\frac{15}{4}\times4 = 15$. Correct.

Option 3: $15\div\frac{1}{4}=3\frac{3}{4}$ → $15\div\frac{1}{4}=15\times4 = 60
eq3\frac{3}{4}$.

Option 4: $\frac{1}{4}\div3\frac{3}{4}=15$ → $\frac{1}{4}\div\frac{15}{4}=\frac{1}{15}
eq15$.

So the correct equation is $3\frac{3}{4}\div\frac{1}{4}=15$.

Answer:

$3\frac{3}{4}\div\frac{1}{4}=15$ (the option with this equation, assuming the options are labeled, e.g., if it's the bottom - right option, but based on the calculation, the equation is $3\frac{3}{4}\div\frac{1}{4}=15$)