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 Description  
 Fraction:  A number that can be written as a quotient of two quantities.
Different Meanings of Fractions and Ratios


Numbers such as can have different meanings depending on the context in which whether they represent fractions or ratios. The following are three possible meanings for fractions and/or ratios.

Part-Part

In this meaning, a ratio represents a relationship between one part of a whole and another part of the whole. For example, the ratio of eighth graders at Smith Middle School who are in the school band (40) to those who are not (110) can be represented by the part-part ratio 40/110.

Part-Whole

In this meaning, fraction represents a relationship between a part and its whole. The numerator indicates the number of parts of the whole to be considered. For example, if a cake is cut into 12 equal pieces and 5 pieces remain, we can represent this situation using the part-whole meaning of fraction as 5/12. Using the example about band members at Smith Middle School, we can represent the number of bands members out of the total number of eighth graders at the school using a part-whole representation: 40/150.


Whole-Part


In this meaning, a ratio represents a relationship between a part and its whole. For example, the ratio of all eighth graders at Smith Middle School to those eighth graders in the school band could be represented by the whole-part ratio: 150/40. Using the cake example, we could represent that whole-part ratio of the number of pieces originally cut to the number of pieces that were left over as 12/5.