Symmetry of multiplication and division in relation to a point "unit" allow to present dividing as multiplying by a number reverse to any number:

**а : b = a x 1/b**

Just, multiplying by a number reverse to any number, it is possible to present as dividing by any number:

**а х 1/b = a : b**

Traditional determination of prime fractional number as a result of division of two integers of

**p**and

**q**interchangebly to the result of increase of integer of p on a number reverse to the integer of

**q**:

**p : q = p x 1/q**

In further exposition term a "multiplication" will imply an increase and division in the generally accepted sense because of their complete symmetry and relativity of these concepts.

Multiplication is this co-operation of two different units of measurements at right angles in a point "zero". As a result of co-operation new unit of measurement appears with beginning in a point "zero", that causes the quality change of interactive units of measurements. A mathematical action opposite on sense to the multiplication is decomposition on factors. Decomposition is executed through trigonometric functions that can have numerical and not numerical (

**0**and

**1/0**) values. Simplest similarity of decomposition under a corner in

**45**degrees - this square root. Decomposition and trigonometric functions are more detailed will be considered additionally.

An area

*(for example, area of rectangle)*is a result of co-operation of two perpendicular units of measurements of length. The multiplication of parallel units of measurements is not possible

*(at the multiplication of lengths of two parallel parties of rectangle, measured in meters, it is possible to get meters square, but it is impossible to get an area)*. Mathematical properties of units of measurements will be considered additionally.

*As in mathematics it is accepted to distinguish the separate sets of numbers that is partly included in a concept "Any number", it is at a desire possible to set forth mathematically exact determinations for some from them. For example:*

unit and all numbers that can be got addition of units are named natural;

all numbers that can be got addition or deduction of units are named integers (at deduction of the same amount of units, that is present, numbers apply in a zero);

numbers being not whole are named a fractional.

unit and all numbers that can be got addition of units are named natural;

all numbers that can be got addition or deduction of units are named integers (at deduction of the same amount of units, that is present, numbers apply in a zero);

numbers being not whole are named a fractional.

**Expl for blondes:**Now a turn came to look, as numbers and units co-operate in mathematics. This piece I named quantity.
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