# Subtracting Mixed Numbers

## Related calculator: Fractions Calculator

Subtracting mixed numbers is quite easy.

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

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

- Convert each mixed number to improper fraction.
- Subtract improper fractions (using subtraction 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 subtract fractions: `8/5-22/9=(8*9)/(5*9)-(22*5)/(9*5)=72/45-110/45=-38/45`.

Convert fraction to mixed number: can't convert because fraction is proper.

**Answer**: `-38/45`.

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 subtract fractions: `-13/6-7/2=-13/6-(7*3)/(2*3)=-13/6-21/6=-34/6`.

Reduce fraction: `-34/6=-17/3`.

Convert fraction to mixed number: `-17/3=-5 2/3`.

**Answer**: `-17/3=-5 2/3`.

Next example.

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

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

Subtract integer parts: `-2-5=-7` and fractional part leave the same.

**Warning.** This works only when we subtract either negative and positive numbers (this case) or positive and negative numbers (like `2-(-5 8/11)=7 8/11`).

**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**: `31/24=1 7/24`.

Next exercise.

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

**Answer**: `185/18=10 5/18`.

Next exercise.

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

**Answer**: `-31/24=-1 7/24`.

Next exercise.

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

`3 5/6-5/7=23/6-5/7=161/42-30/42=131/42=3 5/42`.

**Answer**: `131/42=3 5/42`.

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 both numbers are 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 subtract integer parts, use the three-step method. It guarantees correct answer.