# 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

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 o…

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 o…

x(y +z) = xy + xz

Common Factor

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

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**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 t…

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 t…

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 con…

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. That…

Definition of a property

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

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

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

Addition Property of Equality

Subtraction Property of Equality

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 proper…

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... Symm…

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 o…

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 o…

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