Algebraic Expressions and Real Number System Terms

Vocabulary flashcards covering core algebraic concepts, laws, and number sets from the lecture transcript.

Algebraic Expressions

Mathematical phrases that can contain numbers, variables, and operational symbols.

Commutative Law of Addition

A mathematical law stating that changing the order of addends does not change the sum, expressed as $a + b = b + a$.

Associative Law of Addition

A mathematical law stating that changing the grouping of addends does not change the sum, expressed as $(a + b) + c = a + (b + c)$.

Additive Inverse

The number that, when added to a given number, yields a sum of zero; also known as the opposite of a number.

Subtraction of Real Numbers

An operation defined as adding the additive inverse of the number being subtracted, expressed as $a - b = a + (-b)$.

Opposite of a Sum or a Difference

A rule stating that taking the opposite of a sum or difference changes the sign of each term, such as $-(a + b) = -a - b$ and $-(a - b) = -a + b$.

Product

The result obtained by multiplying two or more numbers or algebraic expressions together.

Distributive Law of Multiplication over Addition

A law stating that multiplying a sum by a number gives the same result as multiplying each addend individually and adding the products, expressed as $a(b + c) = ab + ac$.

Parentheses

Grouping symbols used in algebraic expressions to indicate operations that should be performed first.

Distributive Law of Multiplication over Subtraction

A law stating that multiplying a difference by a number gives the same result as multiplying each term individually and subtracting the products, expressed as $a(b - c) = ab - ac$.

Equivalent Fractions

Fractions that represent the exact same value or proportion, even though they have different numerators and denominators.

Opposite Operations

Mathematical operations that reverse or undo the effect of each other, such as addition and subtraction.

Base

The number or variable in an exponential expression that is raised to a power.

Exponent

A number that indicates how many times the base is to be multiplied by itself in an exponential expression.

Exponential Expression

A mathematical expression consisting of a base and an exponent, written in the form $x^n$.

Irrational Numbers

Real numbers that cannot be expressed as a simple fraction or ratio of two integers, having non-terminating and non-repeating decimal expansions.

Rational Numbers

Real numbers that can be written as a ratio or fraction $\frac{a}{b}$ of two integers, where $b \neq 0$.

Integers

The set of whole numbers and their opposites, including positive whole numbers, negative whole numbers, and zero.

Sets

Well-defined collections of distinct objects or numbers grouped together within braces.