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what are the new things that you learned about the nature of mathematics​

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NATURE OF MATHEMATIC

Commutative, distributive, and associative are the three characteristics shared by all mathematical computation processes. There are variances between the three qualities. Associative nature refers to grouping, commutative nature refers to exchange, and distributive nature refers to spread. It is important to comprehend these three characteristics since they are likely to serve as standards for education at all levels.

  1. Commutative
    Commutative Nature does not apply to Subtractions and Divisions. The commutative nature does not apply to integer subtraction and division operations, since the result of the exchange of numbers against such operations does not produce the same value.
    The commutative properties of the summation operation can be formulated as follows,
    [tex]a+b=b+a=c[/tex]
    The commutative properties of multiplication operations can be formulated as follows,
    [tex]a*b=b*a=c[/tex]
  2. Distributive
    With two different count operations, one of which acts as a deployment action and the other of which is employed to propagate numbers grouped in parenthesis, count operations by nature have distributive qualities. Distributive law is another name for distributive nature.
    Distributive multiplication to summation. The distributive properties of multiplication to the summation operation can be formulated as follows,
    [tex]a * (b + c) = (a * b) + (a * c) = d[/tex]
    The distributive nature of multiplication to subtraction operations can be formulated as follows,
    [tex]a * (b - c) = (a * b) - (a * c) = d[/tex]
  3. Associative
    When an operation calculates three or more integers, associative characteristics are necessary so that the outcome is independent of how the numbers were grouped. This commutative property can be thought of as a counting operation facilitated by the grouping of two numbers since it is performed on three numbers. By instructing parenthesis to be calculated first, followed by the addition of other numbers, the two numbers can be grouped. Like commutative properties, associative properties also apply only to the calculation operations of addition and multiplication only.
    A + B + C = (A + B) + C = A + (B + C) = D
    Or
    A x B x C = (A x B) x C = A x (B x C) = D

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