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1. Mathematical Properties

Mathematical Properties

Reflexive Property- if something is equal to its identical twin

Symmetric Property- if something flipped sides of the equal sign

Transitive Property- if two items are equal to a third item, the two are equal

Commutative Property- if you reversed the order of addition or multiplication

Associative Property- if you changed a grouping rearranged parenthesis, but kept everything else in the same order

Addition Property- if you added the same non-zero number to both sides

Multiplicative Property- if you multiplied the same non-zero number to both sides you have used

Additive Identity- if you added 0 to get the same number back

Multiplicative Property- if you multiplied by 1 to get the same number back

Property of Oppositesif you added opposite numbers and ended with 0

Property of Reciprocals- if you added by a reciprocal to get 1

Distributive Property- if you multiplied a number into or pulled a number out of the parenthesis

Multipicative Property of 0- if you multiplied by 0 and got 0

Multiplicative Propertt of -1- if you multiplied -1 and got the opposite of what you started with

Comparison Property- if you have stated that a<b, a=b, a>b

1st Multiplication Property of Order- if you multiplied an inequality by a positive number and maintained the inequality

2nd Multiplication Property of Order- if you multiplied an inequality by a negative number and reversed the inequality

Cancellation Property of Addition- if you cancelled hte same quantity from both sides of an equation (by subtracting)

Cancellation Property of Multiplication- If you cancelled the same nonzero quantity from both sides of an equation (by division) 


Zero Product Property- If a product is zero, so you know that one of the factors has to be zero

Defnition of Division- if you changed a division to a multiplication by a reciprcal

Definition of Subtraction- if you have switched from adding a negative to just subtraction, or vice versa

Definition of Exponents- if you have either broken apart exponents or created an exponent by multiplying a number by itself

Substitution Property- if you have replaced one statement with an equivalent one and no other property or definition works






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