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