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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.
9th-10th Foundation

### Foundation of Algebra with Numerical Arithmetics

Welcome to the revolutionary and ingenious formal foundation of algebra with Numerical Arithmetics.

Algebra is based on the following basics of numerical arithmetics.

•  PEMA Precedence Order (Parenthesis, Exponent, Multiplication, and Addition)
Division is inverse of Multiplication
Root and Logarithm are two inverses of Exponent

•  CADI Properties of Addition and Multiplication (Closure, Commutative, Associative, Distributive, Identity, Inverse).

•  Numerical Expressions are statement of a value

•  Value of a Numerical Expression does not change when modified per PEMA / CADI

•  Equations are statements of equality of two expressions

•  And statement of equality does not change ...(explained in the lesson)

•  And so for In-equations
(click for the list of lessons in this topic)

Numerical Arithmetics: Laws and Properties for Algebra

Formal foundation in Algebra is established with laws and properties of Numerical Arithmetics.

•  Comparison : Trichotomy and transitivity properties.

•  Subtraction : Handled as inverse of addition, and holds properties of addition. eg: Commutative property a-b = a+(-b) = -b+a (!=b-a)
•  Division : Handled as inverse of multiplication, and holds properties of multiplication. eg: a-:b(c+d) = a xx (1/b)xx(c+d) = axx (c/b + d/b) != a-:(bc+bd)
The above is exemplary and ingenious foundation in learning algebra. For example, x+(y+x) is simplified using the commutative law = x+(x+y) and the associative law = 2x+y.