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commutative axiom for addition

commutative axiom for multiplication

associative axiom for addition

associative axiom for multiplication

x+y = y+x

xy = yx

x+(y+z) = (x+y)+z

x(yz) = (xy)z

commutative axiom for addition

x+y = y+x

commutative axiom for multiplication

xy = yx

commutative axiom for addition

commutative axiom for multiplication

associative axiom for addition

associative axiom for multiplication

x+y = y+x

xy = yx

x+(y+z) = (x+y)+z

x(yz) = (xy)z

commutative axiom for addition

x+y = y+x

commutative axiom for multiplication

xy = yx

Substitution Principle

Commutative Axiom(+)

Commutative Axiom(*)

Associative Axiom (+)

If a = b, then a can be substituted for b in any expression.

a + b = b + a

ab = ba

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

Substitution Principle

If a = b, then a can be substituted for b in any expression.

Commutative Axiom(+)

a + b = b + a

Substitution Principle

Commutative Axiom(+)

Commutative Axiom(*)

Associative Axiom (+)

If a = b, then a can be substituted for b in any expression.

a + b = b + a

ab = ba

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

Substitution Principle

If a = b, then a can be substituted for b in any expression.

Commutative Axiom(+)

a + b = b + a

Multiplication Property of equality

factors

multiplicative identity axiom

definition of division

x=y,xz=yz

parts of an expression that are multiplied or divided

x*1=x

multiplication by the reciprocal x/y = x*1/y

Multiplication Property of equality

x=y,xz=yz

factors

parts of an expression that are multiplied or divided

Closure Axiom of Addition

Commutative Axiom of Addition

Associative Axiom of Addition

Identity Axiom of Addition

For all real number, a and b, a+b is a real numer

For all real number a and b, a+b = b+a

For all real numbers a,b, and c, (a+b)+c = a+(b+c)

For all real numbers a, a+0=a and 0+a=a

Closure Axiom of Addition

For all real number, a and b, a+b is a real numer

Commutative Axiom of Addition

For all real number a and b, a+b = b+a

Distributive Axiom for Multiplication…

Common Factor

Multiplication Property for 0

Multiplication property for -1

x(y +z) = xy + xz

The factor that's the same in each term in an expression

0 * x = 0

-1 * x = x

Distributive Axiom for Multiplication…

x(y +z) = xy + xz

Common Factor

The factor that's the same in each term in an expression

Substitution Principle

Commutative Axiom of Addition

Commutative Axiom of Multiplication

Associative Axiom of Addition

If a = b, then a can be substituted for b in any expression.

a + b = b + a

ab = ba

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

Substitution Principle

If a = b, then a can be substituted for b in any expression.

Commutative Axiom of Addition

a + b = b + a

Substitution Principle

Commutative Axiom(+)

Commutative Axiom(*)

Associative Axiom (+)

If a = b, then a can be substituted for b in any expression.

a + b = b + a

ab = ba

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

Substitution Principle

If a = b, then a can be substituted for b in any expression.

Commutative Axiom(+)

a + b = b + a

Substitution Property of Equality

Commutative Axiom of Addition

Commutative Axiom of Multiplication

Associative Axiom of Addition

If a = b, then a can be substituted for b in any expression.

a + b = b + a

ab = ba

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

Substitution Property of Equality

If a = b, then a can be substituted for b in any expression.

Commutative Axiom of Addition

a + b = b + a

x + y = y + x

x ** y = y ** x

(x + y) + z = x + (y + z)

(x ** y) ** z = x ** (y ** z)

Commutative Axiom of Addition

Commutative Axiom of Multiplication

Associative Axiom of Addition

Associative Axiom of Multiplication

x + y = y + x

Commutative Axiom of Addition

x ** y = y ** x

Commutative Axiom of Multiplication

Axiom

Axioms of closure of additions

Communative Property Axiom of Addition

Associate Property Axiom of Addition

An accepted truth, that doesn't require evidence

A+B is a real number and a unique number

A+B=B+A ... the order doesn't matter

(A+B)+C= A+(B+C) ... again the order doesn't matter

Axiom

An accepted truth, that doesn't require evidence

Axioms of closure of additions

A+B is a real number and a unique number

Reflexive Property

Symmetric Property

Transitive Property

Substitution Principle

For all real numbers, a=a. ... "Every number equals itself"... 7=7…

For all real numbers, if a=b, then b=a.... x=2, 2=x

For all real numbers, if a=b, and b=c, then a=c.... 6+1=7, and 7…

An expression may be replaced by another expression that has…

Reflexive Property

For all real numbers, a=a. ... "Every number equals itself"... 7=7…

Symmetric Property

For all real numbers, if a=b, then b=a.... x=2, 2=x

Reflexive Property

Symmetric Property

Transitive Property

Substitution Principle

For all real numbers, a=a. ... "Every number equals itself"... 7=7…

For all real numbers, if a=b, then b=a.... x=2, 2=x

For all real numbers, if a=b, and b=c, then a=c.... 6+1=7, and 7…

An expression may be replaced by another expression that has…

Reflexive Property

For all real numbers, a=a. ... "Every number equals itself"... 7=7…

Symmetric Property

For all real numbers, if a=b, then b=a.... x=2, 2=x

Definition of a property

Definition of an axiom

Definition of Subtraction

Definition of Division

A property of a mathematical system is a fact that is true co…

An axiom is a property that forms the basis of a mathematical…

Subtracting a number means adding its oppostite. That is, x-y…

Dividing by a number means multiplying by its reciprocal. Tha…

Definition of a property

A property of a mathematical system is a fact that is true co…

Definition of an axiom

An axiom is a property that forms the basis of a mathematical…

commutative axiom for addition

commutative axiom for multiplication

associative axiom for addition

associative axiom for multiplication

x+y=y+x

xy=yx

(x+y)z = x(y+z)

(xy)z = x(yz)

commutative axiom for addition

x+y=y+x

commutative axiom for multiplication

xy=yx

Axioms of Closure (p. 53)

Commutative Axioms (p. 53)

Associative Axioms (p. 54)

Axioms of Equality (p. 55)

For all real numbers a and b:... a + b is a unique real number.…

For all real numbers a and b:... a + b = b + a... ab = ba

For all real numbers a, b, and c:... (a + b) + c = a + (b + c)…

For all real numbers a, b, and c:... Reflexive Axiom: a = a... Sym…

Axioms of Closure (p. 53)

For all real numbers a and b:... a + b is a unique real number.…

Commutative Axioms (p. 53)

For all real numbers a and b:... a + b = b + a... ab = ba

Reflexive Property of Equality

Symmetric Property of Equality

Transitive Property of Equality

Addition Property of Equality

Anything equals itself: 3 = 3

If 3y = 9, then 9 = 3y

If 2x = 8 and 8 = 2^3 (to the third power), then 2x = 2^3

Kerry is solving the one-step equation x - 8 = 10. This prope…

Reflexive Property of Equality

Anything equals itself: 3 = 3

Symmetric Property of Equality

If 3y = 9, then 9 = 3y

Communative Property

Associative Property

Additive Identity

Additive Inverse

Numbers can be multiplied or divided in any order. ... Ex. a + b…

Numbers that can be grouped together in any order when added…

Zero is added to any number; the number stays the same.... Ex. 7…

Adding a number to its opposite gives a sum of zero. ... Ex. 7 +…

Communative Property

Numbers can be multiplied or divided in any order. ... Ex. a + b…

Associative Property

Numbers that can be grouped together in any order when added…

*what is multiplicative identity prope…

*what is additive identity property

*what is multiplicative property of zero

*what is multiplicative inverse property

the product of any number and 1 is the number

the sum of any number and 0 is the number itself

the product of any number and 0 is 0

any number times its reciprocal is 1

*what is multiplicative identity prope…

the product of any number and 1 is the number

*what is additive identity property

the sum of any number and 0 is the number itself

Transitive Axiom of Equality

Symmetric Axiom of Equality

Reflective Axiom of Equality

Addition Property of Equality

for all real numbers x, y, and z... if x=y and y=z, then x=z

if x=y then y=x... 14=x+3 then x+3=14

x=x... 5=5

x=y the x+z=y+z... x-4=20 is also x-4+4=20+4

Transitive Axiom of Equality

for all real numbers x, y, and z... if x=y and y=z, then x=z

Symmetric Axiom of Equality

if x=y then y=x... 14=x+3 then x+3=14

**** If a=b, c=d, then a+c = b+d

If a=b, ac=bc

If a = b, then a can be substituted fo…

If a=a

Addition Property

Multiplication Property

Substitute Property

Reflexive Property

**** If a=b, c=d, then a+c = b+d

Addition Property

If a=b, ac=bc

Multiplication Property

Commutative Axiom for Addition

Commutative Axiom for Multiplication

Associative Axiom for Addition

Associative Axiom for Multiplication

x + y = y + x

x•y = y•x

(x + y) + z = x + (y + z)

(x•y) •z = x•(y •z)

Commutative Axiom for Addition

x + y = y + x

Commutative Axiom for Multiplication

x•y = y•x

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

Add in any order;... 12 + 5 + 8 = 12 + 8 + 5

Multiply in any order;... 5 x 8 x 2 = 5 x 2 x 8

Add by regrouping;... 8 + (2 + 3) = (8 + 2) + 3

Multiply by regrouping:... (8 x 5) x 6 = 8 x (5 x 6)

Commutative Property of Addition

Add in any order;... 12 + 5 + 8 = 12 + 8 + 5

Commutative Property of Multiplication

Multiply in any order;... 5 x 8 x 2 = 5 x 2 x 8

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

Add in any order;... 12 + 5 + 8 = 12 + 8 + 5

Multiply in any order;... 5 x 8 x 2 = 5 x 2 x 8

Add by regrouping;... 8 + (2 + 3) = (8 + 2) + 3

Multiply by regrouping:... (8 x 5) x 6 = 8 x (5 x 6)

Commutative Property of Addition

Add in any order;... 12 + 5 + 8 = 12 + 8 + 5

Commutative Property of Multiplication

Multiply in any order;... 5 x 8 x 2 = 5 x 2 x 8

Commutative Property of Addition

Commutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

Add in any order;... 12 + 5 + 8 = 12 + 8 + 5

Multiply in any order;... 5 x 8 x 2 = 5 x 2 x 8

Add by regrouping;... 8 + (2 + 3) = (8 + 2) + 3

Multiply by regrouping:... (8 x 5) x 6 = 8 x (5 x 6)

Commutative Property of Addition

Add in any order;... 12 + 5 + 8 = 12 + 8 + 5

Commutative Property of Multiplication

Multiply in any order;... 5 x 8 x 2 = 5 x 2 x 8

Power

Exponent

Base

Simplify

A number produced by raising a base to an exponent

A mathematical notation indicating the number of times a quan…

a number that is multiplied repeatedly

to write an expression in a simpler form

Power

A number produced by raising a base to an exponent

Exponent

A mathematical notation indicating the number of times a quan…

variable

algebraic expression

numerical expression

sum

A letter that stands in place of a value

a phrase (or expression) that includes one or more variables

a phrase (or expression) that only includes numbers and opera…

variable

A letter that stands in place of a value

algebraic expression

a phrase (or expression) that includes one or more variables

The distributive axiom

Commutative axiom for addition

Commutative axiom for multiplication

Associative axiom for addition

X(Y+Z)=XY+XZ/TDA Abbreviation.

X+Y=Y+X/CAFA Abbreviation

XY=YX/CAFM Abbreviation

(X+Y)+Z=X+(Y+Z)/AAFA Abbreviation

The distributive axiom

X(Y+Z)=XY+XZ/TDA Abbreviation.

Commutative axiom for addition

X+Y=Y+X/CAFA Abbreviation

variable

algebraic expression

numerical expression

sum

A letter that stands in place of a value

a phrase (or expression) that includes one or more variables

a phrase (or expression) that only includes numbers and opera…

variable

A letter that stands in place of a value

algebraic expression

a phrase (or expression) that includes one or more variables

conclusion

conditional

conjugates

converse

the part following **then** in a conditional.... EX: If I have tw…

an **if-then** statement.... EX: If I have two apples, then I hav…

expressions that are the same but have opposite signs.

like a conditional, but when you switch the conclusion and th…

conclusion

the part following **then** in a conditional.... EX: If I have tw…

conditional

an **if-then** statement.... EX: If I have two apples, then I hav…

bias

bivariate

box-and-whisker plot

element

a survey question that contains assumptions that may or may n…

a set of data that uses two variables.

a graph that summarizes a set of data by displaying it along…

a number or variable within a matrix.

bias

a survey question that contains assumptions that may or may n…

bivariate

a set of data that uses two variables.

algebraic expression

base

coefficient

coordinate system

An expression consisting of one or more numbers and variables…

In an expression of the form x^n, it is the x.

The numerical factor of a term.

The grid formed by the intersection of two number lines, the…

algebraic expression

An expression consisting of one or more numbers and variables…

base

In an expression of the form x^n, it is the x.

Algebraic Expression

Coefficient

Compound Inequality

Compound Statement

is an expression that contains at least one variable.

is the numerical factor of a variable term.

is formed by combining two or more simple inequalities.

is formed by combining two or more simple statements.

Algebraic Expression

is an expression that contains at least one variable.

Coefficient

is the numerical factor of a variable term.