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Fractions As Operator

Fractions as transformersHow much is 10% of


That " % of" is a symbol of a fractions as operator.

A concept reportedly not much emphasized at school (Usiskin, 2007 in [1])

Fractions can be seen as a mathematical operator, like the sign "plus" or "times".

Fractions can be "transformers" which can "shrink or enlarge", "multiply or divide" , "lengthen or shorten" , "increase or decrease" something [2].

The symbol 2/3 means that we must act on a set of things, on a segment, on a geometrical picture and apply an operation on it.

two thirds

This new transformer is the operation of multiplication and division combined.

2/3 of 100 (yards, eggs, pixels, dollars) means

hundred times two divided by three: (100 x 2) : 3 = 66.666...(yards, eggs, pixels, dollars)


Example of fractions as operator

Let's take a piece of rod, or a segment:


To say 3/5 of that segment means that we must first take 3 of such pieces, or better we can say we make 3 copies of it, like this

3 times segment 1

and then we divide those "copies" by 5 (precisely we divide - we partition - them in five equal parts and take only one)

segment3 divided by 5

Fractions are used in this way continously in every day activities like calculating the percentage of a discount when buying something, preparing a meal for more people than the recipee indicates, calculating the length of a boat you want to reproduce in a 1:28 scale, and so forth.




1 Elementary and Middle School Mathematics: Teaching Developmentally (7th Edition)

2. Teaching Fractions And Ratios For Understanding: Essential Content Knowledge And Instructional...

Picture with Cortesy of LAIST,


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