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\(2\frac{1}{2}\)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.

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 \(\frac{7}{2}\).

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 \(3\frac{1}{2} = \frac{7}{2}\)

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).