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Commutative of addition

add in any order

Commutative of multiplication

multiply in any order

Associative of addition

add by regrouping

Associative of multiplication

multiply by regrouping

identity of addition

sum of a number and zero=the number

Identity multiplication

product of a number and 1 equals the number

Inverse property of zero for addition

adding a number to its opposite equals zero

Inverse Property of Multiplication

The product of a nonzero number and its multiplicative inverse, or reciprocal, is 1.

Multiplication property of zero

a number multipied by zero=zero

Property of opposites

a number multiplied by -1 is the opposite of the number

Addition Property of Equality

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

Multiplication Property of Equality

For all real numbers x, y, and z, if x = y, then xz = yz.

Substitution Property of Equality

For all real numbers x and y, if x = y , then y can be substituted for x in any expression and vice versa.

a=a

Reflexive Property of Equality

Symmetric Property of Equality

For all real numbers x and y, if x = y, then y = x.

Transitive Property of Equality

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

a+b=b+a

Commutative Property of Addition

ab=ba

Commutative Property of Multiplication

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

Associative Property of Addition

(AB)C = A(BC)

Associative Property of Multiplication

a+0=a

Identity Property of Addition

1a=a

Identity Property of Multiplication

a+(-a)=0

Inverse Property of Addition

a(1/a)=1

Inverse Property of Multiplication

a(b+c)=ab+ac

Distributive Property

Closure Property of Addition

If a and b are real numbers, then the sum of a+b is a real number

Closure Property of Multiplication

If a and b are real numbers, then the product of "a" times b is a real number

x-y=x+(-y)

Definition of Subtraction

x÷y=x(1÷y)

Definition of division

0(x)=0

multiplicative property of 0

-1(x)=-x

multiplicative property of -1

1/xy=1/x(1/y)

reciprocal of a product

multiplication prop of fractions

ab/xy= a/x(b/y) x≠0, y≠0

Closure property- A set is closed under an operation if and only if...

the operation on two elements of the set produces another element of the set. If an element outside the set is produced, then the operation is not closed.

Trichotomy

For any a and b, exactly one of the following is true:

Converse APE

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

Prop of opp of sum

For all real number a and b:

Cancellation property of additive inverses

for all real numbers a, -(-a)=a

(-a)b=-ab

Property of opp in products

Reflexive Property of Equality

Any number equals itself. x = x

Transitive Property of Equaity

*the property that states if a = b and b = c, then a = c