Multiplying Mixed Numbers

Example 1. Find ${2}\frac{{4}}{{5}}\cdot\frac{{7}}{{8}}$.

First number is mixed: convert it into improper fraction: ${2}\frac{{4}}{{5}}=\frac{{14}}{{5}}$.

$\frac{{14}}{{5}}\cdot\frac{{7}}{{8}}=\frac{{{14}\cdot{7}}}{{{5}\cdot{8}}}=\frac{{98}}{{40}}$.

Now, reduce fraction: $\frac{{98}}{{40}}=\frac{{49}}{{20}}$.

Convert to mixed number: $\frac{{49}}{{20}}={2}\frac{{9}}{{20}}$.

Answer: $\frac{{49}}{{20}}={2}\frac{{9}}{{20}}$.

Example 2. Find ${3}\frac{{8}}{{9}}\cdot{2}\frac{{1}}{{5}}$.

Convert both numbers into improper fractions: ${3}\frac{{8}}{{9}}=\frac{{35}}{{9}}$ and ${2}\frac{{1}}{{5}}=\frac{{11}}{{5}}$.

Now, multiply fractions: $\frac{{35}}{{9}}\cdot\frac{{11}}{{5}}=\frac{{{35}\cdot{11}}}{{{9}\cdot{5}}}=\frac{{385}}{{45}}$

Reduce fraction: $\frac{{385}}{{45}}=\frac{{77}}{{9}}$.

Convert to mixed number: $\frac{{77}}{{9}}={8}\frac{{5}}{{9}}$.

Answer: $\frac{{77}}{{9}}={8}\frac{{5}}{{9}}$.

Example 3. Find ${2}\frac{{1}}{{3}}\cdot{\left(-{3}\frac{{1}}{{4}}\right)}$.

Convert both numbers into fractions: ${2}\frac{{1}}{{3}}=\frac{{7}}{{3}}$ and $-{3}\frac{{1}}{{4}}=-\frac{{13}}{{4}}$.

Multiply fractions: $\frac{{7}}{{3}}\cdot{\left(-\frac{{13}}{{4}}\right)}=\frac{{{7}\cdot{\left(-{13}\right)}}}{{{3}\cdot{4}}}=-\frac{{91}}{{12}}$.

Fraction is irreducible.

Convert to mixed number: $-\frac{{91}}{{12}}=-{7}\frac{{7}}{{12}}$.

Answer: $-\frac{{91}}{{12}}=-{7}\frac{{7}}{{12}}$.