Mixed numbers and improper fractions
\(2 \frac{1}{2}\) is an example of a mixed number. This is when whole numbers and fractions are written together.
The same fraction can also be shown as an improper fraction, \(\frac{5}{2}\). This is worth the same amount as the mixed number, but does not separate between whole numbers and parts. Improper fractions have The top part of a fraction. For â…ť , the numerator is 5. which are bigger than the The bottom part of a fraction. For â…ť, the denominator is 8, which represents 'eighths'..
Improper fractions are sometimes called top-heavy fractions.
Converting mixed numbers to improper fractions
To turn mixed numbers into improper fractions, look at the denominator of the fraction first. This will be the denominator of the improper fraction.
Example
Turn \(3 \frac{1}{2}\) into an improper fraction.
The fraction in the mixed number has 2 as its denominator, so the improper fraction will also have 2 as its denominator. 3 whole ones are 6 halves. There is also another half left over. In total, this is 7 halves or \(\frac{7}{2}\).
To convert any mixed number to an improper fraction:
- multiply the whole number by the denominator
- add on the numerator
\(3 = 3 \times \frac{2}{2} = \frac{6}{2}~so~3\frac{1}{2} = \frac{7}{2}\)
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
Turn \(\frac{7}{5}\) into a mixed number.
\(7 \div 5\) = 1 whole one, and 2 remaining.
Write \(\frac{7}{5}\) as \(1 \frac{2}{5}\).
Mixed numbers and improper fractions are worth the same amount as one another but are written differently. Mixed numbers show whole numbers separate to the fractions. 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).