Dividing a whole number by a fraction is equivalent to multiplying the whole number by the reciprocal of the fraction.

The reciprocal of $\dfrac{1}{\color{blue}8}$ is $\color{blue}8.$

So, we have

\[ 3\div \dfrac1{\color{blue}8} = 3 \times {\color{blue}8} =24. \]

Dividing a whole number by a fraction is equivalent to multiplying the whole number by the reciprocal of the fraction.

The reciprocal of $\dfrac{1}{\color{blue}11}$ is $\color{blue}11.$

So, we have \[ 4 \div \dfrac{1}{\color{blue}11} = 4 \times {\color{blue}11} = \bbox[3pt,Gainsboro]{\color{blue}44}. \]

Dividing a whole number by a fraction is equivalent to multiplying the whole number by the reciprocal of the fraction.

First, we write $5$ as an improper fraction:

\[ 5=\dfrac{5}{1} \]

Next, we note that the reciprocal of $\dfrac{\color{blue}2}{\color{red}3}$ is $\dfrac{\color{red}3}{\color{blue}2}.$

So, we have

\[ 5\div \dfrac 2 3 = \dfrac 5 1 \div \dfrac{\color{blue}2}{\color{red}3} = \dfrac 5 1 \times \dfrac{\color{red}3}{\color{blue}2}. \]

Now, we multiply our fractions.

\[ \dfrac 5 {1} \times \dfrac{3}{2} = \dfrac {5\times 3} {1\times 2} = \dfrac{15}{2} \]

Dividing a whole number by a fraction is equivalent to multiplying the whole number by the reciprocal of the fraction.

First, we write $2$ as an improper fraction: \[ 2 = \dfrac{2}{1} \]

Next, we note that the reciprocal of $\dfrac{\color{blue}5}{\color{red}9}$ is $\dfrac{\color{red}9}{\color{blue}5}.$

So, we have \[ 2 \div \dfrac{5}{9} = \dfrac{2}{1} \div \dfrac{\color{blue}5}{\color{red}9} = \dfrac{2}{1} \times \dfrac{\color{red}9}{\color{blue}5}. \]

Now, we multiply our fractions. \[ \dfrac{2}{1} \times \dfrac{9}{5} = \dfrac{2 \times 9}{1 \times 5} = \dfrac{18}{5} \]

Finally, we write the resulting improper fraction as a mixed number: \[ \dfrac{18}{5} = 3\,\textrm{R} \, 3 = \bbox[3pt,Gainsboro]{\color{blue}3\,\dfrac{3}{5}} \]

Dividing a whole number by a fraction is equivalent to multiplying the whole number by the reciprocal of the fraction.

First, we write $4$ as an improper fraction: \[ 4 = \dfrac{4}{1} \]

Next, we note that the reciprocal of $\dfrac{\color{blue}4}{\color{red}5}$ is $\dfrac{\color{red}5}{\color{blue}4}.$

So, we have \[ 4 \div \dfrac{4}{5} = \dfrac{4}{1} \div \dfrac{\color{blue}4}{\color{red}5} = \dfrac{4}{1} \times \dfrac{\color{red}5}{\color{blue}4}. \]

Now, we multiply our fractions.

\[ \dfrac{4}{1} \times \dfrac{5}{4} = \dfrac{4 \times 5}{1\times 4} = \dfrac{20}{4} \]

Finally, we simplify: \[ 20 \div 4 = \bbox[3pt,Gainsboro]{\color{blue}5} \]

Dividing a whole number by a fraction is equivalent to multiplying the whole number by the reciprocal of the fraction.

First, we write $4$ as an improper fraction:

\[ 4=\dfrac{4}{1} \]

Next, we note that the reciprocal of $\dfrac{\color{blue}2}{\color{red}7}$ is $\dfrac{\color{red}7}{\color{blue}2}.$

So, we have

\[ 4\div \dfrac 2 7 = \dfrac {4} 1 \div \dfrac{\color{blue}2}{\color{red}7} = \dfrac {4} 1 \times \dfrac{\color{red}7}{\color{blue}2}. \]

Now, we multiply our fractions. Note that we can simplify the process by swapping the denominators first.

\begin{align*} \dfrac41 \times \dfrac72 &= \dfrac42\times\dfrac71\\[5pt] &=2\times 7 \\[5pt] &=\bbox[3pt,Gainsboro]{\color{blue}14} \end{align*}

Dividing a whole number by a fraction is equivalent to multiplying the whole number by the reciprocal of the fraction.

First, we write $6$ as an improper fraction:

\[ 6=\dfrac{6}{1} \]

Next, we note that the reciprocal of $\dfrac{\color{blue}8}{\color{red}11}$ is $\dfrac{\color{red}11}{\color{blue}8}.$

So, we have

\[ 6\div \dfrac 8 {11} = \dfrac 6 1 \div \dfrac{\color{blue}8}{\color{red}11} = \dfrac 6 1 \times \dfrac{\color{red}11}{\color{blue}8}. \]

Now, we multiply our fractions. Note that we can simplify the process by swapping the denominators first.

\begin{align*} \dfrac 6 {1} \times \dfrac{11}{8} &= \dfrac{6}{8} \times \dfrac{11}{1} \\[5pt] &=\dfrac34 \times 11 \\[5pt] &=\bbox[3pt,Gainsboro]{\color{blue}\dfrac{33}{4}} \end{align*}

Dividing a whole number by a fraction is equivalent to multiplying the whole number by the reciprocal of the fraction.

First, we write $2$ as an improper fraction:

\[2=\dfrac{2}{1} \]

Next, we note that the reciprocal of $\dfrac{\color{blue}6}{\color{red}7}$ is $\dfrac{\color{red}7}{\color{blue}6}.$

So, we have \[ 2\div \dfrac 6 {7} = \dfrac 2 1 \div \dfrac{\color{blue}6}{\color{red}7} = \dfrac 2 1 \times \dfrac{\color{red}7}{\color{blue}6}. \]

Now, we multiply our fractions. Note that we can simplify the process by swapping the denominators first.

\begin{align*} \dfrac21\times \dfrac{7}{6} &=\dfrac{2}{6}\times\dfrac{7}{1} \\[5pt] &=\dfrac{1}{3}\times7 \\[5pt] &=\dfrac{7}{3} \end{align*}

Finally, we convert our result to a mixed number:

\[ \dfrac{7}{3} = 2\,\textrm R \,1 = \bbox[3pt,Gainsboro]{\color{blue}2\,\dfrac13} \]