Fractions are an invention of the human mind to go beyond counting

Fractions are invented by the human mind and then applied to geometry or applications involving objects in space, like pizza.

Counting by whole numbers does not work for many applications. So we invent a new object, the fraction and apply it.  The invention is stimulated by the application, but the application does not create the properties of fractions.

Man wanted to communicate over distance and so telegraphy and telephony were invented.  But the principles of telegraphy and telephony do not follow from the existence of spatial separation.

We do not tell students, people dwell apart and therefore the electric force between two charges falls of as the square of the distance.

The rule for the electric between two particles is not derived from people dwelling apart.  To tell students it comes from that would be to confuse them.  This is obvious for the laws of electricity but not for the rules for fractions.





About New Math Done Right

Author of Pre-Algebra New Math Done Right Peano Axioms. A below college level self study book on the Peano Axioms and proofs of the associative and commutative laws of addition. President of Mathematical Finance Company. Provides economic scenario generators to financial institutions.
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