Ch.1 The tools of algebra
Properties
Statements that are true for any number or variable. Ex:Distributive Property,Commutative Property................
Algebra
The branch of mathematics that involves expressions with variables.
Distributive Property
To multiply a sum by a number,multiply each addend of the sum by the number outside the parentheses. Ex:2(4+1)=(2x4)+(2x1)
Variable
A Placeholder,usually a letter ,used to represent a unspecified value in mathematical expressions or sentences.
Algebraic Expression
A combination of variables,numbers,and at least one operation.
Equation
A mathematical sentence that contains an equals sign. Ex:6+2=8
Function
A relation in which each element of the input is paired with exactly one element of the output according to specified rule.
Arithmetic Sequence
A sequence in which each term is found by adding the same number to the previous term. Ex: 2,(+2)4(+2),6,(+2)8,
Function Table
A table used to organize the input numbers,output numbers ,and the function rule.
Solution
A value for the variable that makes an equation true. The solution of 12=m+7 is 5.
Defining the Variable
Choosing a variable to represent an unknown value in a problem,and using it to write an expression or equation to solve the problem. Ex:The number of cats=c number of dogs=d
Term
Each number in a sequence Ex:7,8,9
Equivalent Expressions
Expressions that have the same value.
Exponents
In a power the number that tells how many times the base is used as a factor.
Base
In a power the number used as a factor.
Perfect Squares
Numbers with square roots that are whole numbers EX:25 is a perfect square because the square root of 25 is 5.
Standard Form
Numbers written without exponents. Ex:8,9,6,5
Square Roots
One of the two equal factors of a number. The square root of 9 is three.
Powers
The numbers expressed using exponents The power of 3^2 is read three to the power or three squared.
Coefficient
The numerical factor of a term that contains a variable. Ex:4m=12
Function Rule
The operation performed on the input of a function.
Commutative Properties
The order in which two numbers are added or multiplied dose not change their sum or product. Ex:6x5=5x6 , 5+6=6+5
Solving an Equation
The process of finding an solution to an equation.
Cubed
The product in which a number is a factor three times. Ex: two cubed is 8 because 2x2x2=8
squared
The product of a number and itself.36 is the square of 6. EX. ^6 =6
Domain
The set of input values for a function.
Identity Properties
The sum of an addend and 0 is the addend.The product of a factor and 1 is the the factor. Ex: 5+0=5 5x1=5
Radical Sign
The symbol used to indicate a nonnegative square root.
Associative Properties
The way in which three numbers are grouped when they are added or multiplied does not change their sum or product. Ex:5+(8+9)=(5+8)+9 , 5x(8x9)=(5x8)x9
Evaluate
Two find the value of an expression.
Factors
Two or more numbers that are multiplied together to form a product.
Exponential Form
numbers written with exponents.