# Dividing Mixed Numbers

## Related calculator: Fractions Calculator

To divide **mixed numbers**, convert them to improper fractions and then divide fractions.

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 5/12` by `5 3/7`.

Convert mixed numbers to improper fractions: `2 5/12=29/12` and `5 3/7=38/7`.

Perform division: `29/12-:38/7=(29*7)/(38*12)=203/456`.

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

**Answer**: `203/456`.

Next example.

**Example 2.** Divide `1 5/11` by `8/3`.

We convert `1 5/11` into improper fraction: `1 5/11=16/11`. Second number is already fraction.

Now, divide numbers: `(16/11)/(8/3)=(16*3)/(11*8)=48/88`.

Reduce fraction: `48/88=6/11`.

**Answer**: `6/11`.

Next example.

**Example 3.** Divide `5 4/7` by `- 2 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 4/7=39/7` and `2 1/2=7/2`.

Divide numbers: `(39/7)/(5/2)=(39*2)/(5*7)=78/35`.

Convert to mixed number if needed: `78/35=2 8/35`.

Don't forget that result should be negative.

**Answer**: `-78/35=-2 8/35`.

Now, it is time to practice.

**Exercise 1.** Divide `3 2/5` by `7 1/2`.

**Answer**: `34/75`.

Next exercise.

**Exercise 2.** Divide -15 by `3 5/7` .

**Answer**: `-105/26=-4 1/26`. Hint: `-15=-15/1`.

Next example.

**Exercise 3.** Divide `-4 1/5` by `- 7/4`.

**Answer**: `12/5=2 2/5`.