Algebra 1 Unit 1 - Language of Algebra
Exponent
A number placed above and to the right of another number to show that it has been raised to a power.
Algebraic Expressions
A symbol or a combination of symbols used in algebra, containing one or more numbers, variables, and arithmetic operations.
Power
An expression that contains an exponent.
Commutative Property ()
Any operation ⊕ for which a⊕b = b⊕a for all values of a and b. Addition and multiplication are both commutative.
Distributive Property
Distributive Property states that the product of a number and a sum is equal to the sum of the individual products of the addends and the number.
Term
Parts of an expression or series separated by + or - signs; can be a number, a variable, or a product of numbers and variables.
Multiplicative Property of Zero
States that any number multiplied by zero will equal zero.
Variable
Symbols used to represent unknown numbers.
Like Terms
Terms which have the same variables and corresponding powers and or roots. Like terms can be combined using addition and subtraction. Terms that are not like cannot be combined using addition or subtraction.
Associative Property (Multiply or Add Only)
The associative property of a mathematical expression means that the order of the operations can be changed or regrouped so long as the operands (numbers or terms) are not changed.
Perimeter
The distance around an object.
Absolute Value
The distance number is away from zero on the number line. (distance is always positive)
Area
The measure of the surface enclosed by a geometric shape.
Reciprocal
The multiplicative inverse of a number. {Example: flip flop of a fraction ⅔ and 3/2.
Factor
The numbers or variables being multiplied together.
Coefficient
The numerical factor of a term. Example: 3 is the coefficient of 3x.
Integers
The set of whole numbers and their opposites {...-2, -1, 0, 1, 2 ....}
Substitution Property
The substitution property of equality that, if a = b, then b can be substituted or interchanged for a in any equation without changing the truth value of the equation.
Volume
The total amount of space enclosed in a solid.
Evaluate
To find the numerical value of an expression.
Simplify
To make simpler! Simplifying an algebraic expression means writing it in the most compact or efficient manner, without changing the value of the expression.
Opposites
Two integers are opposites if they are each the same distance away from zero, but on opposite sides of the number line. {Example: 2 and -2 are opposites.}
Multiplicative Inverses (Reciprocals)
a number "b" which when multiplied by "1/b" yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a.
Multiplicative Identity
an identity that when used to multiply a given element in a specified set leaves that element unchanged, as the number 1 for the real-number system.
Base
in the expression x^3, then x would be the base.
Order of Operations
is a rule used to clarify which procedures should be performed first in a given mathematical expression. (PEMDAS)
Subtraction
less, less than, subtracted from, difference, decreased by, minus
Product
product is the answer to multiplication problem.
Multiplication
product of, times, multiplied by, of
Division
quotient of, divided by, the ratio of
Additive Identity
states that the sum of the number and zero yields the same number.
Addition
sum, plus, added to, increased by, more than
Equivalent Expression
two algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are same.
Simplest Form
when an expression is in its most compact form, no parentheses or like terms are left.