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| Operations | |
|---|---|
| Name | Property |
| Distributive Property | a⋅(a+c)=a⋅b+a⋅c |
| Commutative Property of Addition | a+b=b+a |
| Commutative Property of Multiplication | a⋅b=b⋅a |
| Associative Property of Addition | (a+b)+c=a+(b+c) |
| Associative Property of Multiplication | (a⋅b)⋅c=a⋅(b⋅c) |
| Identities | |
|---|---|
| Name | Property |
| Additive Identity | a+0=a |
| Multiplicative Identity | a⋅1=a |
| Equalities | |
|---|---|
| Name | Property |
| Addition Property of Equality | If a=b, then a+c=b+c |
| Subtraction Property of Equality | If a=b, then a−c=b−c |
| Multiplication Property of Equality | If a=b, then a⋅c=b⋅c |
| Division Property of Equality | If a=b, then ca=cb |
| Reflexive Property of Equality | Any real number is equal to itself |
| Symmetric Property of Equality | If a=b, then b=a |
| Transitive Property of Equality | If a=b and b=c, then a=c |
| Closure Property of Real Numbers | |
|---|---|
| ∀ a,b∈R⇒a+b∈R | Closed Under Addition |
| ∀ a,b∈R⇒a−b∈R | Closed Under Subtraction |
| ∀ a,b∈R⇒a⋅b∈R | Closed Under Multiplication |
| ∀ a,b∈R⇒a÷b∈/R | Not Closed Under Division |