Algebra Review Sections R.3 - R.7 Vocabulary

Vocabulary flashcards generated from lecture notes covering algebraic expression definitions, properties of real numbers, exponent laws, order of operations, and basic equation concepts.

Equivalent Expressions

Two expressions that have the same value for all allowable replacements.

Equivalent Fractional Expression

A quotient which has the same value as its initial form.

Commutative Law of Addition

A law of algebra stating that for any numbers $a$ and $b$, $a + b = b + a$.

Commutative Law of Multiplication

A law of algebra stating that for any numbers $a$ and $b$, $ab = ba$.

Associative Law of Addition

A law of algebra stating that for any numbers $a$, $b$, and $c$, $a + (b + c) = (a + b) + c$.

Associative Law of Multiplication

A law of algebra stating that for any numbers $a$, $b$, and $c$, $a \times (b \times c) = (a \times b) \times c$.

Distributive Law

A law of algebra stating that for any numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.

Factoring Out Common Factors

A technique achieved by applying the distributive law in reverse; formally, if $N = ab$, then $a$ and $b$ are factors of $N$.

Product Rule for Exponents

An exponent property stating that for any number $a$ and any integers $m$ and $n$, $a^m \times a^n = a^{m+n}$, provided the bases are the same.

Quotient Rule for Exponents

An exponent property stating that for any non-zero number $a$ and any integers $m$ and $n$, $\frac{a^m}{a^n} = a^{m-n}$.

Power Rule for Exponents

An exponent property stating that for any real number $a$ and any integers $m$ and $n$, $(a^m)^n = a^{mn}$.

Raising a Product to a Power Rule

An exponent property stating that for any real numbers $a$ and $b$ and any integer $n$, $(ab)^n = a^n b^n$.

Raising a Quotient to a Power Rule

An exponent property stating that for any real numbers $a$ and $b$ ($b \neq 0$) and any integer $n$, (\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}).

BEDMAS

An acronym representing the required order of operations: Brackets, Exponents, Division, Multiplication, Addition, and Subtraction.

Rule for Negative Exponents

An exponent rule stating that for any non-zero real number $a$ and any integer $n$, $\frac{1}{a^n} = a^{-n}$.

Term (Algebraic)

An expression containing a number or combination of numbers and variables where the last operation in evaluating the expression would be multiplication or division.

Coefficient

A numerical value that is multiplied by a variable.

Like Terms

Terms in an algebraic expression containing identical variables.

Property of "-1"

An algebraic law stating that for any number $a$, $-1 \times a = -a$, which also implies $-(a - b) = b - a$ for any numbers $a$ and $b$.

Algebraic Expression

A mathematical expression that differs from a numerical expression by containing variables (letters) in addition to numbers.

Naming Algebraic Expressions

The rule of naming an algebraic expression based on the last operation to be performed in the expression (e.g., sum, difference, product, quotient).

Evaluating Algebraic Expressions

Finding the value of an algebraic expression, which depends on substituting specific values for the variables.

Equation

A statement of equality of two expressions (algebraic expressions connected with an $=$ sign).

Satisfying an Equation

When substituting a specific value for a variable results in equal values on both sides of the equation, making it a true statement.