We have $\dfrac{1}{5}$ on the left and $\dfrac{1}{15}$ on the right.

The division operation splits the shaded region on the left into $3$ equal parts. So the shaded part on the left is $3$ times larger than the shaded part on the right.

Therefore, the division problem shown is:

\[ \dfrac{1}{5} \div 3 = \dfrac{1}{15} \]

We have $\dfrac{1}{2}$ on the left and $\dfrac{1}{8}$ on the right.

The division operation splits the shaded region on the left into $4$ equal parts. So the shaded part on the left is $4$ times larger than the shaded part on the right.

Therefore, the division problem shown is

\[ \bbox[4pt,border: 1px solid lightgray]{\dfrac{1}{2}} \div 4 = \bbox[4pt,border: 1px solid lightgray]{\dfrac{1}{8}} \,. \]

We have $\dfrac{1}{8}$ on the left and $\dfrac{1}{16}$ on the right.

The division operation splits the shaded region on the left into $\color{blue}2$ equal parts. So the shaded part on the left is $\color{blue}2$ times larger than the shaded part on the right.

Therefore, the division problem shown is:

\[ \dfrac 1 8 \div \bbox[4pt,border: 1px solid lightgray]{2} = \dfrac{1}{16} \]

So, the missing number is $\bbox[4pt,border: 1px solid lightgray]{2}.$

We have $\dfrac{1}{2}$ on the left and $\dfrac{1}{10}$ on the right.

The division operation splits the shaded region on the left into $\color{blue}5$ equal parts. So the shaded part on the left is $\color{blue}5$ times larger than the shaded part on the right.

Therefore, the division problem shown is:

\[ \dfrac 1 2 \div {\color{blue}{5}} = \dfrac{1}{10} \]

So, the missing number is $\color{blue}5.$

We have $\dfrac{1}{4}$ on the left and $\dfrac{1}{28}$ on the right.

The division operation splits the shaded region on the left into $\color{blue}7$ equal parts. So the shaded part on the left is $\color{blue}7$ times larger than the shaded part on the right.

Therefore, the division problem shown is:

\[ \dfrac 1 4 \div \bbox[4pt,border: 1px solid lightgray]{7} = \dfrac{1}{28} \]

So, the missing number is $\bbox[4pt,border: 1px solid lightgray]{7}.$

Notice that in the model, we have $\dfrac{1}{4}$ on the left.

Since we need to divide by $\color{blue}2$, we split the whole into $\color{blue}2$ equal parts horizontally.

From the picture on the right, we obtain that the shaded part represents $\dfrac{1}{8}$ of the whole.

So, the missing picture is:

In the model, we have $\dfrac{1}{2}$ on the left.

Since we need to divide by $\color{blue}6$, we split the whole into $\color{blue}6$ equal parts horizontally.

From the picture on the right, we obtain that the shaded part represents $\dfrac{1}{12}$ of the whole.

The missing picture is:

Since we need to divide by $\color{blue}2$, we split the whole into $\color{blue}2$ equal parts horizontally.

From the picture on the right, we obtain that the shaded part represents $\dfrac{1}{4}$ of the whole.

Therefore, \[ \dfrac{1}{2} \div 2 = \bbox[4pt,border: 1px solid lightgray]{\dfrac{1}{4}}. \]

Since we need to divide by $\color{blue}6$, we split the whole into $\color{blue}6$ equal parts horizontally.

From the picture on the right, we obtain that the shaded part represents $\dfrac{1}{30}$ of the whole.

Therefore, \[ \dfrac{1}{5} \div 6 = \dfrac{1}{30}. \]

Since we need to divide by $\color{blue}7$, we split the whole into $\color{blue}7$ equal parts horizontally.

From the picture on the right, we obtain that the shaded part represents $\dfrac{1}{28}$ of the whole.

Therefore, \[ \dfrac{1}{4} \div 7 = \bbox[4pt,border: 1px solid lightgray]{\dfrac{1}{28}}. \]