# Adding Mixed Numbers

## Related calculator: Fractions Calculator

Adding mixed numbers is quite easy.

We know that mixed number consists of integer part and fractional part.

To **add mixed numbers** three steps are needed:

- Convert each mixed number to improper fraction.
- Add improper fractions (using addition of fractions with unlike denominators)
- Convert improper fraction to mixed number if needed (and if possible).

**Example 1.** Find `1 3/5+2 4/9`.

Convert each mixed number into improper fraction: `1 3/5=8/5` and `2 4/9=22/9`.

Now add fractions: `8/5+22/9=(8*9)/(5*9)+(22*5)/(9*5)=72/45+110/45=182/45`.

Convert fraction to mixed number: `182/45=4 2/45`.

**Answer**: `4 2/45`.

Next example.

**Example 2.** Find `-2 1/6+3 1/2`.

Convert each mixed number into improper fraction: `-2 1/6=-13/6` and `3 1/2=7/2`.

Now add fractions: `-13/6+7/2=-13/6+(7*3)/(2*3)=-13/6+21/6=8/6`.

Reduce fraction: `8/6=4/3`.

Convert fraction to mixed number: `4/3=1 1/3`.

**Answer**: `4/3=1 1/3`.

Next example.

**Example 3.** Find `2+5 8/11`.

Since first number has no fractional part, we can easier add numbers.

Add integer parts: `2+5=7` and fractional part leave the same.

**Warning.** This works only when we add either both positive numbers or both negative numbers.

**Answer**: `7 8/11=85/11`.

Now, take pen and paper and do following exercises.

**Exercise 1**. Find `5 1/6+3 7/8`.

**Answer**: `217/24=9 1/24`.

Next exercise.

**Exercise 2**. Find `7 4/9+(-2 5/6)`.

**Answer**: `83/18=4 11/18`.

Next exercise.

**Exercise 3**. Find `-5 1/6+(-3 7/8)`.

**Answer**: `-217/24=-9 1/24`.

Next exercise.

**Exercise 4**. Find `3 5/6+5/7`.

`3 5/6+5/7=23/6+5/7=161/42+30/42=191/42=4 23/42`.

**Answer**: `191/42=4 23/42`.

Next exercise.

**Exercise 5**. Find `-5 1/6+7`.

Here we just can't add fractional parts to obtain `2 1/6`. This is not correct, because one of the addends is negative and another is positive.

We do it as always.

`-5 1/6+7=-31/6+42/6=11/6=1 5/6`.

**Answer**: `11/6=1 5/6`.

If you are not sure whether it is possible to add integer parts, use the three-step method. It guarantees correct answer.