Algebraic Properties By: Emma Lucken

The Commutative Property The Commutative Property stats that the order in which you add/multiply (cannot subtract or divide) does not change the sum or product of the problem. For example: For example:1+2=2+11*2=2*1 Addition and Multiplication only

The Associative Property The Associative Property stats that the grouping of the numbers (what’s inside the parenthesis) does not change the sum or product of the problem. (It’s only addition or subtraction) For example: 1+(2+3)=(1+2)+3- All addition 1*(2*3)=(1*2)*3- All multiplication To remember this property think or the word associate. Associate means to hang out together. Parenthesis make the numbers grouped together like they’re hanging out.

The Multiplicative Identity The Multiplicative Identity stats any number times 1 is itself. The Multiplicative Identity stats any number times 1 is itself. For example: 1*2=21*7,890=7,890 Only multiplication

The Additive Identity The Additive Identity stats that any number added to 0 is itself. For example: 1+0=19,876+0=9,876 Only addition

The Distributive Property The Distributive Property stats that if you have one number outside of two numbers in parenthesis you must multiply the outside factor by the inside factors. For example: 1(2+3)=2+31(2-3)=2-3 Addition or subtraction only

The Subtraction Property of Equality The Subtraction Property of Equality stats whatever you do to one side you must do to the other side. 10= =2+8-3 We won’t be using this one much because, we must always switch subtraction to adding a negative. Always subtraction

The Addition Property of Equality The Addition Property of Equality stats that whatever you do to one side you must do to the other. 2=1+12+1=1+1+1 All of the Identity Properties have the same concept. Only addition

The Division Property of Equality The Division Property of Equality stats that what you do to one sid eyou must do to the other. For example: 6=3*26/2=3*2/2 Division only

The Multiplication Property of Equality The Multiplication Property of Equality stats that whatever you do to one side you must do to the other. For example: 12=4*312*2=4*3*2 Only multiplication

Inverse Operations The Inverse Operations undo each other. So when we are solving equations we try to get the variable be itself on one side. For example: 2x=102x/2=x=10/2x=5x-2= x=10 The inverse operations are almost like the equality operations.

Sources My old Math notebook My old Math notebook There are also many BrainPop movies covering these properties!