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

The reciprocal of $\color{blue}3$ is $\dfrac{1}{{\color{blue}{3}}}.$ So, we have

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

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

\[ \dfrac 1 7 \times \dfrac{1}{3} = \dfrac {1\times 1} {7\times 3} = \dfrac{1}{21} \]

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

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

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

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

\[ \dfrac 1 7 \times \dfrac{1}{6} = \dfrac {1\times 1} {7\times 6} = \dfrac{1}{42} \]

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

The reciprocal of $\color{blue}3$ is $\dfrac{1}{{\color{blue}{3}}}.$ So, we have

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

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

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

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

The reciprocal of $\color{blue}5$ is $\dfrac{1}{{\color{blue}{5}}}.$ So, we have

\[ \dfrac 2 7\, {\color{red}\div} \, {\color{blue}5} = \dfrac 2 7\, {\color{red}\times} \,\dfrac{1}{\color{blue}5}. \]

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

\[ \dfrac 2 7 \times \dfrac{1}{5} = \dfrac {2\times 1} {7\times 5} = \dfrac{2}{35} \]

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

The reciprocal of $\color{blue}2$ is $\dfrac{1}{{\color{blue}{2}}}.$ So, we have

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

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

\[ \dfrac {4}{7} \times \dfrac{1}{2} = \dfrac {4\times 1} {7\times 2} = \dfrac{4}{14} \]

Finally, we simplify our result by dividing the numerator and denominator by $2\mathbin{:}$

\[ \dfrac{4}{14} = \dfrac{4\div 2}{14\div 2} = \dfrac{2}{7} \]

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

The reciprocal of $\color{blue}5$ is $\dfrac{1}{{\color{blue}{5}}}.$ So, we have

\[ \dfrac {10}{11} \, {\color{red}\div} \, {\color{blue}5} = \dfrac {10}{11}\, {\color{red}\times} \,\dfrac{1}{\color{blue}5}. \]

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

\[ \dfrac {10}{11} \times \dfrac{1}{5} = \dfrac {10\times 1} {11\times 5} = \dfrac{10}{55} \]

Finally, we simplify our result by dividing the numerator and denominator by $5\mathbin{:}$

\[ \dfrac{10}{55} = \dfrac{10\div 5}{55\div 5} = \dfrac{2}{11} \]