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More Fractions

Fractions - The Basics explained what a fraction actually was, how not all numbers can be represented as fractions, and how to add, subtract, multiply and divide fractions. This article builds on this work to show you how to handle more complicated fractions.

Different Types Of Fractions

The first type of fraction we need to be able to recognise is the proper fraction. Here are a couple of proper fractions…

Graph

These are proper fractions because the numerator (the number on the top) is smaller than the denominator (the number on the bottom). Note that a proper fraction always represents a number smaller than 1.

The next type of fraction is where the numerator is larger than the denominator. This type is called an improper fraction. Here are a couple of examples…

Graph

Note that an improper fraction always represents a number greater than 1.

The final type we need to be able to recognise is the mixed number fraction. A mixed number fraction contains a fractional part and a whole number part. For example:

Graph or Graph

A mixed number fraction also (obviously) represents a number greater than one - just like an improper fraction does. In fact, we can convert mixed number fractions into improper fractions (and vice versa), as you will see in the next section.

The tools that we learnt in Fractions - The Basics -where we looked at how to add, subtract, multiply and divide fractions - we can also use with improper fractions. However, they don't work with mixed number fractions. If you are given a mixed number fraction you will need to convert it into an improper fraction. The next section explains how.

Converting Mixed Number Fractions Into Improper Fractions

Given a fraction like Graph it is fairly easy to turn it into an improper fraction.

First, you have to take the whole number, in this case 2, and convert it alone into a fraction. To do this is simple, multiply it by the denominator (number 'on the bottom') of the fraction it is with, and put it over that number also. In this case, it is 3.

Written down this is:

Graph

So we have converted the whole number to a fraction. Now we must add the fraction we already had, which was Graph:

Graph

So the mixed number Graph is exactly the same as the improper fraction Graph.