


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.
PartPart
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 partpart ratio 40/110.
PartWhole
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 partwhole 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 partwhole representation: 40/150.
WholePart
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 wholepart ratio: 150/40. Using the cake example, we could
represent that wholepart ratio of the number of pieces originally cut to the
number of pieces that were left over as 12/5.


