Properties Of Operations With Real Numbers In Addition And Multiplication

The real numbers They are those numbers that cover all the possible combinations that exist.

1. Natural numbers
2. Integer numbers
3. Rational numbers
4. Irrational numbers

Thus the real numbers are the grouping of the different numbers that exist marked above.

The properties of operations with real numbers in addition and multiplication are as follows:

Example of operations with real numbers in addition and multiplication:

1. Lock, the addition or multiplication of two real numbers always gives a real number. Example: Let a, b and R
   a + b e R (a) (b) e R
   
2. Commutative, The order in which the addends or factors are grouped does not alter the result of the operation. Example: Yes you have to:
   a, b € R a + b = b + a (a) (b) = (b) (a)
   
3. Associative. The addition or the multiplication, are not altered, by the way in which the addends or factors are grouped, respectively.
   Example: Let a, b, c e R Then: a + (b + c) = (a + b) + c
   a (b c) = (a b) c
   
4. Neutral additive. It is defined with this name to the number zero, since when it is added with any real number, the result is the same number.
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   Example: Yes a e R
   then: there exists an element 0/0 e R such that: a + 0 = 0 + a = a
   
5. Multiplicative neutral. It is defined with this name, the number one, since every number multiplied by one, gives the same number.
   Example: Yes a e R
   then: there is an element 1/1 eR
   such that: (1) (a) = (a) (1) = a
   
6. Distributive of multiplication with respect to sum: When a sum is multiplied by the same factor, the result obtained is the same, as if each sum is multiplied by the common factor and then added.
   Example: Let a, b, c e R Then: a (b + c) = ab + ac