# Mixed numbers and improper fractions

is an example of a mixed number. A mixed number has a whole number part and a fraction part.

The same fraction can also be shown as an improper fraction, . This is equivalent to the mixed number, but in this case the number has been written as 5 halves. Improper fractions have which are bigger than the .

## Converting mixed numbers to improper fractions

To convert a mixed number into an improper fraction, look at the denominator of the fraction part first. This will be the denominator of the improper fraction.

### Example

Convert into an improper fraction.

Change into halves. 3 whole ones is halves.

There is another half in the fraction part of , so altogether there are 7 halves, meaning that is the same as .

To convert any mixed number to an improper fraction:

1. Change the whole number part to a fraction using the denominator of the fraction part. So
2. Add on the fraction part:

So

## Converting improper fractions to mixed numbers

To convert an improper fraction to a mixed number, work out how many whole numbers there are by dividing the numerator by the denominator. Make the remainder the new numerator and leave the denominator as it was.

### Example

Convert into a mixed number.

= 1 (whole one), and remainder 2.

Write as .

Mixed numbers and improper fractions are worth the same amount as one another (if they are equivalent) but are written differently. Mixed numbers are made up of a whole number and a separate fraction. Improper fractions do not show whole numbers separately and the numerator is bigger than the denominator. For example, (mixed number) is equal to (improper fraction).