#### Study sets matching "algebra 1 axioms equality"

#### Study sets matching "algebra 1 axioms equality"

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

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

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

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 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

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

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**xCommutative 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

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

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

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

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

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

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

RATIONAL NUMBER

IRRATIONAL NUMBER

INCREASED BY

DIMINISHED BY

Real number that can be a fraction, terminating decimal or re…

A number that goes on forever. It is a non-repeating or non-t…

RATIONAL NUMBER

Real number that can be a fraction, terminating decimal or re…

IRRATIONAL NUMBER

A number that goes on forever. It is a non-repeating or non-t…

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

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.

Reflexive Axiom of Equality

Symmetric Axiom of Equality

Transitive Axiom of Equality

Addition Axiom of Equality

a=a.

If a=b, then b=a.

If a=b and b=c, then a=c (*The process of replacing a number…

If a=b, then a+c=b+c.

Reflexive Axiom of Equality

a=a.

Symmetric Axiom of Equality

If a=b, then b=a.

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…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.

Slope

Coordinate Point

Equivalent

Equation of a Line

The rate of change in a linear function. Slope is the change…

A location on the x/y coordinate plane. All coordinate points…

In math, two expressions or equations may have the same value…

A linear equation can be written in slope-intercept form (y =…

Slope

The rate of change in a linear function. Slope is the change…

Coordinate Point

A location on the x/y coordinate plane. All coordinate points…