Improper fractions

Last updated: 11 Nov 2008

A fraction in which the numerator is greater than the denominator is called an improper fraction. For example:

$mathematical expression$

In this case the numerator, 5, is greater than the denominator, 2. This will be true of any fraction which is greater than 1.

If we divide the numerator by the denominator we can split the improper fraction into its whole number and fraction parts:

$mathematical expression$

Therefore $mathematical expression$ is 2 wholes and 1 half left over or two and a half.

$mathematical expression$

Two and a half is a mixed fraction. I.e. a whole number added to a fraction. It is very unusual to see an improper fraction listed in the answers to a GMAT question, so you will often need to convert your answer into a mixed fraction.

Example

What is $mathematical expression$ written as a mixed fraction?

$mathematical expression$

Therefore $mathematical expression$ is 8 wholes with 4 sevenths left over, or eight and four sevenths.

$mathematical expression$

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Improper fractions

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