See a solution process below: Explanation: First we need to convert the two mixed numbers into improper fractions: \displaystyle{1}\frac{{1}}{{2}}\div{1}\frac{{4}}{{5}}\Rightarrow{\left({1}+\frac{{1}}{{2}}\right)}\div{\left({1}+\frac{{4}}{{5}}\right)}\Rightarrow ...

\displaystyle{6}\frac{{2}}{{5}} Explanation: Given - \displaystyle\frac{{4}}{{5}}\div\frac{{1}}{{8}} \displaystyle\frac{{4}}{{5}}\times\frac{{8}}{{1}}=\frac{{32}}{{5}}={6}\frac{{2}}{{5}}

\displaystyle{2} Explanation: The value of 1 is the same as \displaystyle\frac{{2}}{{2}} So write \displaystyle{1}\frac{{1}}{{2}} as \displaystyle{1}+\frac{{1}}{{2}}\ \text{ }\ \to\ \text{ }\ \frac{{2}}{{2}}+\frac{{1}}{{2}}\ \text{ }\ \to\ \text{ }\ \frac{{3}}{{2}} ...

\displaystyle{1}\frac{{1}}{{2}}\div\frac{{3}}{{8}}={4} Explanation: To divide by a fraction, you can multiply by its reciprocal, formed by swapping the numerator and denominator... \displaystyle{1}\frac{{1}}{{2}}\div\frac{{3}}{{8}}=\frac{{3}}{{2}}\div\frac{{3}}{{8}}=\frac{{\cancel{{{\left({3}\right)}}}}}{{2}}\times\frac{{8}}{{\cancel{{{\left({3}\right)}}}}}=\frac{{8}}{{2}}={4}

See a solution process below: Explanation: First, convert each mixed number to an improper fraction: \displaystyle{2}\frac{{1}}{{2}}={2}+\frac{{1}}{{2}}={\left(\frac{{2}}{{2}}\times{2}\right)}+\frac{{1}}{{2}}=\frac{{4}}{{2}}+\frac{{1}}{{2}}=\frac{{{4}+{1}}}{{2}}=\frac{{5}}{{2}} ...

\displaystyle{2}\frac{{1}}{{2}} Explanation: Convert the mixed numbers into improper fractions \displaystyle{4}\frac{{1}}{{2}}=\frac{{9}}{{2}} and \displaystyle{1}\frac{{4}}{{5}}=\frac{{9}}{{5}} ...