Question

a.
\\(\frac{1}{3}\\) \\(\frac{1}{3}\\) \\(\frac{1}{3}\\)
\\(\frac{1}{9}\\) \\(\frac{1}{9}\\) \\(\frac{1}{9}\\)
\\(\frac{1}{1}\times\frac{9}{3}=\frac{9}{3}=3\\)
b.

Explanation:

Step1: Analyze the first row

The first row has three equal parts, each labeled $\frac{1}{3}$. So the total of the first row is $3\times\frac{1}{3} = 1$.

Step2: Analyze the second row

The second row has some parts labeled $\frac{1}{9}$. Let's see how many $\frac{1}{9}$ make 1. Since $\frac{1}{9}\times9 = 1$, we need 9 parts of $\frac{1}{9}$ to make 1. Currently, there are 3 parts of $\frac{1}{9}$, so we need $9 - 3 = 6$ more parts. But maybe the question is about relating $\frac{1}{3}$ and $\frac{1}{9}$. Notice that $\frac{1}{3}=\frac{3}{9}$, so one $\frac{1}{3}$ is equal to three $\frac{1}{9}$. Let's check the first row's $\frac{1}{3}$ and the second row's $\frac{1}{9}$. Each $\frac{1}{3}$ in the first row can be divided into three $\frac{1}{9}$ in the second row. So if we take one $\frac{1}{3}$ (from the first row) and multiply by 3 (to get the number of $\frac{1}{9}$ in it), we have $\frac{1}{3}\times3=\frac{3}{3} = 1$? Wait, no. Wait, $\frac{1}{3}\div\frac{1}{9}=\frac{1}{3}\times\frac{9}{1}=3$. So $\frac{1}{3}$ is three times $\frac{1}{9}$. Let's verify with the diagram. Each $\frac{1}{3}$ block in the first row is the same height as three $\frac{1}{9}$ blocks in the second row (since the width of the $\frac{1}{3}$ block is three times the width of the $\frac{1}{9}$ block, assuming equal height). So $\frac{1}{3}=\frac{3}{9}$, so $\frac{1}{3}\div\frac{1}{9}=3$.

Step3: Check the written equation

The written equation is $\frac{1}{1}\times\frac{9}{3}=\frac{9}{3}=3$. Wait, maybe the question is to show that $\frac{1}{3}\div\frac{1}{9}=3$. Let's do that. Dividing by a fraction is multiplying by its reciprocal. So $\frac{1}{3}\div\frac{1}{9}=\frac{1}{3}\times\frac{9}{1}=\frac{9}{3}=3$. So that equation is correct.

Answer:

The equation $\frac{1}{3}\div\frac{1}{9}=3$ (or the written equation $\frac{1}{1}\times\frac{9}{3}=3$) is correct, showing that one - third divided by one - ninth is three. If the question was about how many $\frac{1}{9}$ are in $\frac{1}{3}$, the answer is 3.