Dividing a fraction by another fraction is equivalent to multiplying the first fraction by the reciprocal of the second fraction.

The reciprocal of $\dfrac{\color{blue}1}{\color{red}12}$ is $\dfrac{\color{red}12}{\color{blue}1}.$ So we have

\[ \dfrac 1 4 \div \dfrac{\color{blue}1}{\color{red}12} = \dfrac 1 4 \times \dfrac{\color{red}12}{\color{blue}1} \]

Now, we multiply fractions. We multiply the numerators, and we multiply the denominators:

\[ \dfrac 1 {4} \times \dfrac{12}{1} = \dfrac {1\times 12} {4\times 1} = \dfrac{12}{4} \]

Finally, we simplify:

\[ 12 \div 4=3 \]

Dividing a fraction by another fraction is equivalent to multiplying the first fraction by the reciprocal of the second fraction.

The reciprocal of $\dfrac{\color{blue}1}{\color{red}6}$ is $\dfrac{\color{red}6}{\color{blue}1}.$ So we have

\[ \dfrac 1 3 \div \dfrac{\color{blue}1}{\color{red}6} = \dfrac 1 3 \times \dfrac{\color{red}6}{\color{blue}1} \]

Now, we multiply fractions. We multiply the numerators, and we multiply the denominators:

\[ \dfrac 1 {3} \times \dfrac{6}{1} = \dfrac {1\times 6} {3\times 1} = \dfrac{6}{3} \]

Finally, we simplify:

\[ 6\div 3=2 \]

Dividing a fraction by another fraction is equivalent to multiplying the first fraction by the reciprocal of the second fraction.

The reciprocal of $\dfrac{\color{blue}3}{\color{red}5}$ is $\dfrac{\color{red}5}{\color{blue}3}.$ So we have

\[ \dfrac 3 {8} \div \dfrac{\color{blue}3}{\color{red}5} = \dfrac 3 {8} \times \dfrac{\color{red}5}{\color{blue}3} \]

Now, we multiply fractions. We multiply the numerators, and we multiply the denominators:

\[ \dfrac 3 {8} \times \dfrac{5}{3} = \dfrac {3 \times 5} {8 \times 3} = \dfrac{15}{24} \]

Finally, we simplify:

\[\dfrac{15}{24} = \dfrac{15\div 3}{24\div 3} = \dfrac{\color{blue}5}{8} \]

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

Dividing a fraction by another fraction is equivalent to multiplying the first fraction by the reciprocal of the second fraction.

The reciprocal of $\dfrac{\color{blue}2}{\color{red}5}$ is $\dfrac{\color{red}5}{\color{blue}2}.$ So we have

\[ \dfrac 4 {7} \div \dfrac{\color{blue}2}{\color{red}5} = \dfrac 4 {7} \times \dfrac{\color{red}5}{\color{blue}2} \]

Now, we multiply fractions. We multiply the numerators, and we multiply the denominators:

\[ \dfrac 4 {7} \times \dfrac{5}{2} = \dfrac {4\times 5} {7\times 2} = \dfrac{20}{14} \]

Finally, we simplify:

\[\dfrac{20}{14} = \dfrac{20\div 2}{14\div 2} = \dfrac{\color{blue}10}{7} \]

Therefore, the missing number is ${\color{blue}{10}}.$

Dividing a fraction by another fraction is equivalent to multiplying the first fraction by the reciprocal of the second fraction.

The reciprocal of $\dfrac{\color{blue}3}{\color{red}4}$ is $\dfrac{\color{red}4}{\color{blue}3}.$ So we have

\[ \dfrac 1 {16} \div \dfrac{\color{blue}3}{\color{red}4} = \dfrac 1 {16} \times \dfrac{\color{red}4}{\color{blue}3} \]

Now, we multiply fractions. We multiply the numerators, and we multiply the denominators:

\[ \dfrac 1 {16} \times \dfrac{4}{3} = \dfrac {1\times 4} {16\times 3} = \dfrac{4}{48} \]

Finally, we simplify:

\[\dfrac{4}{48} = \dfrac{4\div 4}{48\div 4} = \dfrac{1}{12} \]

Dividing a fraction by another fraction is equivalent to multiplying the first fraction by the reciprocal of the second fraction.

The reciprocal of $\dfrac{\color{blue}2}{\color{red}3}$ is $\dfrac{\color{red}3}{\color{blue}2}.$ So we have

\[ \dfrac 1 {6} \div \dfrac{\color{blue}2}{\color{red}3} = \dfrac 1 {6} \times \dfrac{\color{red}3}{\color{blue}2} \]

Now, we multiply fractions. We multiply the numerators, and we multiply the denominators:

\[ \dfrac 1 {6} \times \dfrac{3}{2} = \dfrac {1\times 3} {6\times 2} = \dfrac{3}{12} \]

Finally, we simplify:

\[\dfrac{3}{12} = \dfrac{3\div 3}{12\div 3} = \dfrac{1}{4} \]

Dividing a fraction by another fraction is equivalent to multiplying the first fraction by the reciprocal of the second fraction.

The reciprocal of $\dfrac{\color{blue}2}{\color{red}7}$ is $\dfrac{\color{red}7}{\color{blue}2}.$ So we have

\[ \dfrac 1 {3} \div \dfrac{\color{blue}2}{\color{red}7} = \dfrac 1 {3} \times \dfrac{\color{red}7}{\color{blue}2} \]

Now, we multiply fractions. We multiply the numerators, and we multiply the denominators:

\[ \dfrac 1 {3} \times \dfrac{7}{2} = \dfrac {1\times 7} {3\times 2} = \dfrac{7}{6} \]

Finally, we write the resulting improper fraction as a mixed number:

\[ \dfrac{7}{6} =1\,\textrm{R} 1 = 1\,\dfrac 1 {6}\]

Dividing a fraction by another fraction is equivalent to multiplying the first fraction by the reciprocal of the second fraction.

The reciprocal of $\dfrac{\color{blue}3}{\color{red}19}$ is $\dfrac{\color{red}19}{\color{blue}3}.$ So we have

\[ \dfrac 1 {2} \div \dfrac{\color{blue}3}{\color{red}19} = \dfrac 1 {2} \times \dfrac{\color{red}19}{\color{blue}3} \]

Now, we multiply fractions. We multiply the numerators, and we multiply the denominators:

\[ \dfrac 1 {2} \times \dfrac{19}{3} = \dfrac {1\times 19} {2\times 3} = \dfrac{19}{6} \]

Finally, we write the resulting improper fraction as a mixed number:

\[ \dfrac{19}{6} =3\,\textrm{R} 1 = 3\,\dfrac 1 {6}\]