# Convert between a mixed number and an improper fraction

We know a mixed number is a whole number (integer) and a fraction.

Improper fractions are fractions with a bigger number on the top than the bottom.

**Example**

Mixed number is `2\2/3`

Improper fraction is `8/3`

But to convert between `2\2/3` to `8/3` remember that `2\2/3` really means:

Mixed number think addition.

So `2\2/3` is really `2+2/3`

`4\3/8` is really `4+3/8`

`12\3/13` is really `12+3/13`

To convert between a mixed number and an improper number do exactly what it says

i.e. ADD THEM

**Example 1**

Convert `2\2/3` to an improper fraction

`2\2/3=2+2/3`

And in adding think `1/2`

we know `1/2+1/2=1`

which must be `(1+1)/2=1`

If adding is the aim the bottom number must be the same

Therefore `2+2/3=2/1+2/3=2/1times3/3+2/3times1/1`

`2/1times3/3+2/3times1/1=6/3+2/3`

`6/3+2/3=(6+2)/3=8/3`

**Answer:** `2\2/3=8/3`

**Example 2**

Convert `4\1/3` to an improper fraction.

We know `4\1/3=4+1/3`

And in adding think `1/2` i.e. `1/2+1/2=1`

which must be `(1+1)/2` (the bottom number must be the same)

therefore `4+1/3=4/1+1/3=4/1times3/3+1/3times1/1`

`4/1times3/3+1/3times1/1=12/3+1/3`

`12/3+1/3=(12+1)/3=13/3`

**Answer:** `4\1/3=13/3`

**Example 3**

Convert `2\5/6` to an improper fraction.

We know `2\5/6=2+5/6`

And in adding think `1/2` i.e. `1/2+1/2=1`

which must be `(1+1)/2` (the bottom number must be the same)

therefore `2+5/6=2/1+5/6=2/1times6/6+5/6times1/1`

`2/1times6/6+5/6times1/1=12/6+5/6`

`12/6+5/6=(12+5)/6=17/6`

**Answer:** `2\5/6=17/6`