Algebra Foundations Study Notes

Study Notes

Algebra Foundations Study Notes

Distributive Property: This property states that multiplying a number by a sum is the same as multiplying each addend individually and then summing the results. Represented mathematically as A(B + C) = AB + AC.
Equivalent Expressions: These are expressions that yield the same numerical value for all variable assignments, indicating they represent the same mathematical relationship or quantity.
Algebraic Expression: A type of mathematical phrase that includes at least one variable, and may also incorporate numbers and operation symbols, such as addition or multiplication.
Numeric Expression: A mathematical sentence comprised solely of numbers and one or more operation symbols, excluding any variables.
Commutative Property: This property indicates that the order of addition or multiplication does not affect the sum or product. For addition, it is expressed as a + b = b + a.
Associative Property: This property reveals that the way numbers are grouped in addition or multiplication does not change their sum or product. For addition, shown as (a + b) + c = a + (b + c).
Variable: A variable is a symbol (typically a letter) representing a quantity that can vary or change in value.
Formula: A mathematical expression that combines numbers and symbols to convey a specific calculation or relationship between quantities.
Square Number: A number resulting from multiplying a number by itself, such as 4 (which is 2 squared).
Square Root: The square root of a number is the value that, when multiplied by itself, returns the original number; for example, the square root of 9 is 3.
Pythagorean Theorem: A fundamental principle in geometry that relates the lengths of the sides of a right triangle, expressed mathematically as a² + b² = c², where c represents the hypotenuse.
Hypotenuse: In a right triangle, the hypotenuse is the longest side, opposite the right angle.
Cubic Number: This refers to a number that comes from multiplying a number by itself twice. For example, 27 is a cubic number since it is derived from 3 x 3 x 3.
Cube Root: The cube root of a number is the value that, when multiplied by itself three times, gives the original number; for example, the cube root of 64 is 4.
Exponent: An exponent indicates how many times a base number is to be multiplied by itself. For example, in 2^3 (2 raised to the power of 3), 2 is multiplied by itself three times (2 x 2 x 2).

Description

Explore the foundational concepts of algebra with this study guide. Learn about key properties such as the distributive, commutative, and associative properties, as well as different types of expressions. Perfect for reinforcing your understanding of algebraic fundamentals.