Question

which equation is represented by the model? answer
$\frac{1}{5} \div 11 = 2\frac{1}{5}$
$2\frac{1}{5} \div \frac{1}{5} = 11$
$11 \div \frac{1}{5} = 2\frac{1}{5}$
$\frac{1}{5} \div 2\frac{1}{5} = 11$

Explanation:

Step1: Analyze the model

The model shows a total length (let's assume the total number of \(\frac{1}{5}\) segments) and we need to relate it to the equation. First, let's find how many \(\frac{1}{5}\) segments are there. From the model, if we count the blue and white parts, but looking at the options, we know that \(2\frac{1}{5}=\frac{11}{5}\), and if we consider the relationship between the number of \(\frac{1}{5}\) parts and the total. Let's check the options:

We know that \(2\frac{1}{5}=\frac{11}{5}\), so if we have a total of 11 (in terms of \(\frac{1}{5}\) units, since \(\frac{11}{5}\) means 11 times \(\frac{1}{5}\)) and we divide by \(\frac{1}{5}\), we get \(11\div\frac{1}{5}=\frac{11}{\frac{1}{5}} = 11\times5 = 55\)? Wait, no, wait. Wait, \(2\frac{1}{5}=\frac{11}{5}\), so if we have a number \(x\) such that \(x\times\frac{1}{5}=2\frac{1}{5}\), but no, the options are division. Wait, let's re - express the options:

Option 1: \(\frac{1}{5}\div11 = 2\frac{1}{5}\)? No, \(\frac{1}{5}\div11=\frac{1}{55}
eq\frac{11}{5}\)

Option 2: \(2\frac{1}{5}\div\frac{1}{5}=11\). Let's compute \(2\frac{1}{5}=\frac{11}{5}\), then \(\frac{11}{5}\div\frac{1}{5}=\frac{11}{5}\times5 = 11\). That makes sense. Let's check the other options:

Option 3: \(11\div\frac{1}{5}=2\frac{1}{5}\)? \(11\div\frac{1}{5}=55
eq\frac{11}{5}\)

Option 4: \(\frac{1}{5}\div2\frac{1}{5}=11\)? \(\frac{1}{5}\div\frac{11}{5}=\frac{1}{11}
eq11\)

So the correct equation is \(2\frac{1}{5}\div\frac{1}{5}=11\)

Step2: Verify the calculation

We know that dividing by a fraction is multiplying by its reciprocal. So \(2\frac{1}{5}=\frac{11}{5}\), and \(\frac{11}{5}\div\frac{1}{5}=\frac{11}{5}\times\frac{5}{1}=11\). So this equation holds.

Answer:

\(2\frac{1}{5}\div\frac{1}{5}=11\) (the fourth option in the original list, but in the options provided, it's the one with \(2\frac{1}{5}\div\frac{1}{5}=11\))