Mixed numbers and improper fractions

2\frac{1}{2}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, \frac{5}{2}. This is equivalent to the mixed number, but in this case the number 2\frac{1}{2} has been written as 5 halves. Improper fractions have numerators which are bigger than the denominators.

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 3\frac{1}{2} into an improper fraction.

Change 3\frac{1}{2} into halves. 3 whole ones is 3 \times 2 = 6 halves.

There is another half in the fraction part of 3\frac{1}{2}, so altogether there are 7 halves, meaning that 3\frac{1}{2} is the same as \frac{7}{2}.

Turning 3 1/2 into an improper fraction equals 7/2

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 3 = \frac{6}{2}
  2. Add on the fraction part: \frac{6}{2} + \frac{1}{2} = \frac{7}{2}

So 3\frac{1}{2} = \frac{7}{2}

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 \frac{7}{5} into a mixed number.

7 \div 5 = 1 (whole one), and remainder 2.

Write \frac{7}{5} as 1 \frac{2}{5}.

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, 3 \frac{1}{4} (mixed number) is equal to \frac{13}{4} (improper fraction).