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Commutative

Associative

Distributive

Reflexive

"order"... Ex:... 2+3=3+2

"grouping"... Ex:... 2+(x+3)=(2+x)+3

"can't touch this"... Ex:... 5(x+2)=5x+10

"mirror" - What you see is what you get... Ex:... 5=5

Commutative

"order"... Ex:... 2+3=3+2

Associative

"grouping"... Ex:... 2+(x+3)=(2+x)+3

associative property of addition

associative property of multiplication

identity property of multiplication

inverse property of addition

(-7+4)+1 = -7+(4+1)

8(9x11) = (8x9)11

1x10 = 10

-0.3+0.3 = 0

associative property of addition

(-7+4)+1 = -7+(4+1)

associative property of multiplication

8(9x11) = (8x9)11

Additive inverse

Additive Identity

Multiplicative Inverse

Multiplicative Identity

+3 - 3 = 0 Add opposites get 0

X+0= X Adding 0 to a problem doesn't change the problem

1/2 (2/1) = 1 Multiplying by the reciprocal to get 1.

5(1)=5 Multiplying a # by 1 will not change the problem.

Additive inverse

+3 - 3 = 0 Add opposites get 0

Additive Identity

X+0= X Adding 0 to a problem doesn't change the problem

Commutative property of Addition

Associative Property of Addition

Commutative property of Multiplication

Associative property of Multiplication

7 + 2x + 3 + 4x= 2x + 7 + 3 + 4x

(2x + 7) + 3 + 4x = 2x + (7 + 3) +4x

5y*7 + 6 = 5*7y + 6

5(7y) + 6 = (5*7)y + 6

Commutative property of Addition

7 + 2x + 3 + 4x= 2x + 7 + 3 + 4x

Associative Property of Addition

(2x + 7) + 3 + 4x = 2x + (7 + 3) +4x

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

Changing the order of the addends does not change the sum.... a+…

Changing the order when multiplying does not affect the produ…

Changing the grouping when multiplying does not affect the pr…

Changing the grouping when multiplying does not affect the pr…

Commutative Property of Addition

Changing the order of the addends does not change the sum.... a+…

Commutative Property of Multiplication

Changing the order when multiplying does not affect the produ…

Commutative property of addition

Commutative property of multiplication

Associative property of addition

Associative property of multiplication

a + b + c = c + b + a

a x b = b x a

a + (b + c) = (a + b) + c

a x (b x c) = (a x b) x c

Commutative property of addition

a + b + c = c + b + a

Commutative property of multiplication

a x b = b x a

Commutative property of __________

Associative property of __________

Identity property of __________

Inverse property of __________

a + b = b + a

(a + b) + c = a + (b + c)

a + 0 = a

a + -a = 0

Commutative property of __________

a + b = b + a

Associative property of __________

(a + b) + c = a + (b + c)

Real Numbers

Rational

Irrational

Integers

All rational and irrational numbers

Integers, fractions that consist of integers(Terminating or r…

Any radical that cannot be simplified... Any non terminating or…

Whole Numbers, their opposites and 0

Real Numbers

All rational and irrational numbers

Rational

Integers, fractions that consist of integers(Terminating or r…

Commutative property of addition

Commutative property of multiplication

Associative property of addition

Associative property of multiplication

a + b + c = c + b + a

a x b = b x a

a + (b + c) = (a + b) + c

a x (b x c) = (a x b) x c

Commutative property of addition

a + b + c = c + b + a

Commutative property of multiplication

a x b = b x a

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

a+b=b+a... ex: 3+2=2+3

a x b= b x a... ex: 4 x 3=3 x 4

(a+b)+c= a+(b+c)... ex: (2+3)+5= 2+(3+5)

(a x b)x c= a x(b x c)... ex: (2 x 1)x 4= 2 x (1 x 4)

Commutative Property of Addition

a+b=b+a... ex: 3+2=2+3

Commutative Property of Multiplication

a x b= b x a... ex: 4 x 3=3 x 4

Rational Number

Irrational Numbers

Integers

Whole Numbers

any number written as a ratio; if it is a decimal, it stops o…

Roots that are not perfect; if it is a decimal, it continues

Positive and negative non-decimal numbers and zero

Positive non-decimal numbers and zero

Rational Number

any number written as a ratio; if it is a decimal, it stops o…

Irrational Numbers

Roots that are not perfect; if it is a decimal, it continues

Identity Property of Multiplication

Multiplicative Property of Zero

Multiplicative Property of -1

Property of Opposites in Products

a**1 = a and 1**a = a

a**0 = 0 and 0**a = 0

a(-1) = -a and (-1)a = -a

...

Identity Property of Multiplication

a**1 = a and 1**a = a

Multiplicative Property of Zero

a**0 = 0 and 0**a = 0

Matter

Volume

Menisus

Mass

anything that has volume or mass

The amount of space taken up, or occupied, by an object is kn…

The curve that you see at the liquid's surface

the amount of matter that something is made of

Matter

anything that has volume or mass

Volume

The amount of space taken up, or occupied, by an object is kn…

solution set

coordinate system

Elimination Method

Substitution Method

point (x,y) that solves the system

(x,y): values that can be graphed

solving for one variable by cancelling (eliminating) another…

solving for 1 variable then substituting its' value in to the…

solution set

point (x,y) that solves the system

coordinate system

(x,y): values that can be graphed

absolute value

compound inequality

counterexample

formula

a number's distance from zero on the number line

two inequalities joined by the word "and" or "or"

a specific case that shows that a statement is false

a mathematical sentence that expresses the relationship betwe…

absolute value

a number's distance from zero on the number line

compound inequality

two inequalities joined by the word "and" or "or"

commutative property of addition

commutative property of multiplication

associative property of addition

associative property of multiplication

a+b=b+a

a•b=b•a

a+(b+c)=(a+b)+c

a•(b•c)=(a•b)•c

commutative property of addition

a+b=b+a

commutative property of multiplication

a•b=b•a

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

a + b = b + a ... 2 + 3 = 3 + 2

a • b = b • a ... 2 • ( 3 ) = 3 • ( 2 )

a + ( b + c ) = ( a + b ) + c ... 2 + ( 3 + 4 ) = ( 2 + 3 ) + 4

a • ( b • c ) = ( a • b ) • c ... 2 • ( 3 • 4 ) = ( 2 • 3 ) • 4

Commutative Property of Addition

a + b = b + a ... 2 + 3 = 3 + 2

Commutative Property of Multiplication

a • b = b • a ... 2 • ( 3 ) = 3 • ( 2 )

First difference

Solution

Intersection point

Solution of an inequality

determined by calculating the difference between successive p…

any value that makes an equation true

an ordered pair that satisfies both functions

any value that makes the inequality true

First difference

determined by calculating the difference between successive p…

Solution

any value that makes an equation true

Commutative Property of Addition

Associative Property of Addition

Identity Property of Addition

Inverse Property of Addition

the order in which you add two numbers does not change the sum

the way you group three numbers in a sum foes not change the…

the sum of a number and 0 is the number

the sum of a number and its opposite is 0

Commutative Property of Addition

the order in which you add two numbers does not change the sum

Associative Property of Addition

the way you group three numbers in a sum foes not change the…

Commutative Rule on Addition

Associative Rule on Addition

Commutative Rule on Multiplication

Associative Rule on Multiplication

a + b + c = b + c + a

(a+b)+c = a+(b+c)

abc = bac

(ab)c = a(bc)

Commutative Rule on Addition

a + b + c = b + c + a

Associative Rule on Addition

(a+b)+c = a+(b+c)

Absolute Value

Additive Inverse

Associative Property of Addition

Associative Property of Multiplication

The distance a number is from zero on a number line

A pair of numbers whose sum is zero

Changing the grouping of three or more addends does not chang…

Changing the grouping of three or more factors does not chang…

Absolute Value

The distance a number is from zero on a number line

Additive Inverse

A pair of numbers whose sum is zero

coordinate plane

exponent

linear function

quadratic function

A plane that is divided into four regions by a horizontal lin…

A mathematical notation indicating the number of times a quan…

a function with a power of 1 on the x-variable, forming a str…

a function with a power of 2 on the x-variable, forming a par…

coordinate plane

A plane that is divided into four regions by a horizontal lin…

exponent

A mathematical notation indicating the number of times a quan…

opposite

reciprocal

numerical expression

power

the opposite, or additive inverse, of any number b is -b

the reciprocal, or multiplicative inverse, of any nonzero num…

consists of numbers, operations, and grouping symbols.

An expression formed by repeated multiplication of the same f…

opposite

the opposite, or additive inverse, of any number b is -b

reciprocal

the reciprocal, or multiplicative inverse, of any nonzero num…

absolute value of a real number

absolute value

additive inverse

algebraic expression

A numbers distance from zero on the number line.

A number's distance can't be negative because it indicated ho…

The additive inverse of any number a is -a.

An expression that contains one or more variables

absolute value of a real number

A numbers distance from zero on the number line.

absolute value

A number's distance can't be negative because it indicated ho…

Standard Form of a Quadratic Function

Parabola

Vertex Form

Intercept Form

The form ax^2+bx+c=0 when a is not zero.

The set of all points equidistant from a point called the foc…

The form y=a(x-h)^2+k, where the vertex of the graph is (h, k…

The form y=a(x-p)(x-q), where the x-intercepts of the graph a…

Standard Form of a Quadratic Function

The form ax^2+bx+c=0 when a is not zero.

Parabola

The set of all points equidistant from a point called the foc…

real numbers

rational numbers

irrational numbers

whole numbers

R... --numbers you see in everyday life... --correspond to exactly…

Q... A number that can be in the form p/q, where p and q are int…

I... An irrational number is a number that cannot be expressed a…

W... Counting numbers and zero.

real numbers

R... --numbers you see in everyday life... --correspond to exactly…

rational numbers

Q... A number that can be in the form p/q, where p and q are int…

equivalent equations

identity

literal equation

proportion

Equations with the same solutions.

An equation that is true for all values of... the variables.

An equation that contains two or more... variables.

A statement that two ratios are equal

equivalent equations

Equations with the same solutions.

identity

An equation that is true for all values of... the variables.