# Study sets matching "algebra 1 axioms equality"

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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

a + b is a unique real number.

ab is a unique real number.

a + b = b + a

ab = ba

Closure axiom of addition

Closure axiom of multiplication

Commutative Axiom of Addition

Commutative Axiom of Multiplication

a + b is a unique real number.

Closure axiom of addition

ab is a unique real number.

Closure 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

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

a ( b c) = ( a b ) c

a +b = b + a

a b = b a

Associative Property of Addition

Associative Property of Multiplication

Commutative Property of Addition

Commutative Property of Multiplication

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

Associative Property of Addition

a ( b c) = ( a b ) c

Associative Property of 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…

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

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…

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

Associative Property of Addition

Associative Property of Multiplication

Commutative Property of Addition

Commutative Property of Multiplication

When three or more numbers are added, the sum is the same rega…

When three or more numbers are multiplied, the product is the…

When two numbers are added, the sum is the same regardless of…

When two numbers are multiplied together, the product is the s…

Associative Property of Addition

When three or more numbers are added, the sum is the same rega…

Associative Property of Multiplication

When three or more numbers are multiplied, the product is the…

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

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