Dividing Mixed Numbers

Example 1. Divide ${2}\frac{{5}}{{12}}$ by ${5}\frac{{3}}{{7}}$.

Convert mixed numbers to improper fractions: ${2}\frac{{5}}{{12}}=\frac{{29}}{{12}}$ and ${5}\frac{{3}}{{7}}=\frac{{38}}{{7}}$.

Perform division: $\frac{{29}}{{12}}\div\frac{{38}}{{7}}=\frac{{{29}\cdot{7}}}{{{38}\cdot{12}}}=\frac{{203}}{{456}}$.

Fraction is irreducible and also can't be converted to mixed number because it is proper.

Answer: $\frac{{203}}{{456}}$.

Example 2. Divide ${1}\frac{{5}}{{11}}$ by $\frac{{8}}{{3}}$.

We convert ${1}\frac{{5}}{{11}}$ into improper fraction: ${1}\frac{{5}}{{11}}=\frac{{16}}{{11}}$. Second number is already fraction.

Now, divide numbers: $\frac{{\frac{{16}}{{11}}}}{{\frac{{8}}{{3}}}}=\frac{{{16}\cdot{3}}}{{{11}\cdot{8}}}=\frac{{48}}{{88}}$.

Reduce fraction: $\frac{{48}}{{88}}=\frac{{6}}{{11}}$.

Answer: $\frac{{6}}{{11}}$.

Example 3. Divide ${5}\frac{{4}}{{7}}$ by $-{2}\frac{{1}}{{2}}$.

Result of dividing positive number by negative is negative.

So, ignore minus of the second number and convert both numbers to improper fractions: ${5}\frac{{4}}{{7}}=\frac{{39}}{{7}}$ and ${2}\frac{{1}}{{2}}=\frac{{7}}{{2}}$.

Divide numbers: $\frac{{\frac{{39}}{{7}}}}{{\frac{{5}}{{2}}}}=\frac{{{39}\cdot{2}}}{{{5}\cdot{7}}}=\frac{{78}}{{35}}$.

Convert to mixed number if needed: $\frac{{78}}{{35}}={2}\frac{{8}}{{35}}$.

Don't forget that result should be negative.

Answer: $-\frac{{78}}{{35}}=-{2}\frac{{8}}{{35}}$.