# 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

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