Dividing Mixed Numbers

Related calculator: Fractions Calculator

After this you, possibly, need to reduce fraction.

Also, you can convert improper fraction back to mixed number.

Note! Rules for determining sign of the result are same as when dividing integers.

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

Next example.

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

Next example.

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

Now, it is time to practice.

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

Answer: $\frac{{34}}{{75}}$.

Next exercise.

Exercise 2. Divide -15 by ${3}\frac{{5}}{{7}}$.

Answer: $-\frac{{105}}{{26}}=-{4}\frac{{1}}{{26}}$. Hint: $-{15}=-\frac{{15}}{{1}}$.

Next example.

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

Answer: $\frac{{12}}{{5}}={2}\frac{{2}}{{5}}$.