# Study sets matching "algebra 1 axioms equality"

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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

x + y = y + x

xy = yx

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

(xy)z = x(yz)

commutative axiom for addition

commutative property for multiplication

associative axiom for addition

associative axiom for multiplication

x + y = y + x

commutative axiom for addition

xy = yx

commutative property for multiplication

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

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

Additive identity

Multiplicative property of zero

Multiplicative inverses

Multiplicative identity

For any number a, a + 0 = 0 + a = a

The solution of the equation is 0. The product of any number a…

Two numbers whose product is 1

For any number a, a ∙ 1 = 1 ∙ a = a

Additive identity

For any number a, a + 0 = 0 + a = a

Multiplicative property of zero

The solution of the equation is 0. The product of any number 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

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

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

Commutative Property... Hint: Change need…

Associate Property... Hint: You associate…

Identity Property... Hint: Stay who you a…

Inverse Property... Hint: N/A

Order doesn't matter when you add or multiply. ... Ex. a + b = b…

The way numbers are grouped doesn't matter when you add/multip…

The value of the number stays the same. Adding zero/multiplyin…

Addition: Adding a numbers inverse makes the value zero/ Multi…

Commutative Property... Hint: Change need…

Order doesn't matter when you add or multiply. ... Ex. a + b = b…

Associate Property... Hint: You associate…

The way numbers are grouped doesn't matter when you add/multip…

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

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

Complex Numbers

Real numbers

Imaginary numbers

Zero

A combination of a... Real Number and an Imaginary Number - 7+3i

Have points on the number line

Square roots of negative numbers. Have no points on the number…

neither positive or negative

Complex Numbers

A combination of a... Real Number and an Imaginary Number - 7+3i

Real numbers

Have points on the number line

closure

commutativity

associativity

distributivity

{real numbers} is closed under addition and under multiplicati…

addition and multiplication of real numbers are commutative op…

addition and multiplication of real numbers are associative op…

Multiplication distributes over addition; that is, if x, y, an…

closure

{real numbers} is closed under addition and under multiplicati…

commutativity

addition and multiplication of real numbers are commutative op…