# Mathematical Theory.

Mathematical theory includes the study of fractions, analytic geometry etc. These topics will allow to understand better a material and will answer questions in your math problems.

Divisibility rules
Divisibility by 2
Divisibility by 3
Divisibility by 4
Divisibility by 5
Divisibility by 6
Divisibility by 9
Divisibility by 10

Fraction
Forms of fractions
The basic property of fraction
Simplifying fractions
Least common denominator of fractions
Converting improper fractions (composed fractions) to mixed numbers
Converting mixed numbers to improper fractions (composed fractions)
Addition and Subtraction of fractions
Multiplication of fractions
Division of fractions
Comparing fractions
Convert Decimals to Common Fractions

Percent
Percent Definition. Main information
Decimal to Percent. Percent to Decimal
The method of solving problems with percentage
Find P percent of A
B is P percent of what?
B is what percent of A?
Find the number which is greater (less) than a given number by P percent.

Factoring: Some special cases
Square of the sum
Square of the difference
Difference of squares
Cube of sum
Cube of difference
Sum of cubes
Difference of cubes

Vectors
Vectors Definition. Main information
Component form of a vector with initial point and terminal point
Length of a vector
Direction cosines of a vector
Equal vectors
Orthogonal vectors
Collinear vectors
Coplanar vectors
Angle between two vectors
Vector projection
Addition and subtraction of vectors
Scalar-vector multiplication
Dot product of two vectors
Cross product of two vectors (vector product)
Scalar triple product (mixed product)
Linearly dependent and linearly independent vectors
Decomposition of the vector in the basis

Matrix
Matrix Definition. Main information
System of linear equations - matrix form
Types of matrices
Matrix scalar multiplication
Addition and subtraction of matrices
Matrix multiplication
Transpose matrix
Elementary matrix operations
Determinant of a matrix
Minors and cofactors of a matrix
Inverse matrix
Linearly dependent and independent rows
Rank of a matrix

Analytic geometry
Distance between two points
Midpoint. Coordinates of midpoint
Equation of a line
Equation of a plane
Distance from point to plane
Distance between two planes
Distance from a point to a line - 2-Dimensional
Distance from a point to a line - 3-Dimensional
Angle between two planes
Angle between line and plane

I will add new theoretical material in this section gradually.

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