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What do we mean by fractions? | Models
of fractions |
A fraction is a number that can be written as a/b ( an indicated quotient), where a is an integer and b is an integer other than zero. Some examples of fractions are:
Numbers such as 11, -13 and 0 are also fractions. They can be written in this way: 11/1 , -13/1, 0/1 or 0/4. Not all numbers are fractions: the square root of 2 is not a fraction and neither is pi (although it is often approximated by 22/7). The word fraction comes from a Latin word meaning to break, suggesting that initially a fraction may have been viewed as part of a broken whole. This early view of the meaning of a fraction is evident when fractions are thought of as expressing a part to whole relationship, where the whole is divided into parts of equal value. There are other meanings for fractions but this way of making sense of them is the one usually used in primary school mathematics. When representing fractions based on this meaning with materials or diagrams the object for the whole may be one single object or area of a figure. However, the whole can also be made up a collection of objects or areas of several figures together. The models of fractions below illustrate some of these examples. In either case, the number represented by some part of the whole is always done in reference to the unit. The fraction 2/5, for example, indicates that the reference unit (the "whole") has been divided into 5 equal parts and 2 of these parts make up this fraction.
We can use different models to represent fractions. A whole and therefore a unit can be,
"Can I have a quarter of your sandwich?"
"I need to cut that piece of wood into 3 equal lengths, that is, into thirds"
"I have 18 tennis balls to be shared equally among 6 children. Each will get one sixth of the tennis balls."
When the whole equals one, the unit also equals one. Example 1: A fraction as a part to whole relationship when the whole is one unit. Show two thirds, 2/3, of a rectangle?
When the whole is more than one, we think of the whole as being made up of more than one unit. Example 2: A fraction as a part to whole relationship when the whole is more than one unit. Describe two thirds (2/3) of 2 rectangles? We want to find 2/3 of 2 rectangles, so in this case "the whole" is 2 rectangles and we will call each rectangle "a unit".
Answer: 2/3 of 2 rectangles is 1 1/3 rectangles. The example above demonstrates the importance of distinguishing the whole and the units that are used to describe the whole. Any quantity can be interpreted as "the whole" (as in this case, two rectangles).
To view the quiz answers, click here. |
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| © University of Melbourne 2003 |
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