Basic Laws of Algebra

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The Basic Laws of Algebra are the associative, commutative and distributive laws. They help explain the relationship between number operations and lend towards simplifying equations or solving them.

Property Name Definition Example
Commutative Law For Addition
The arrangement of addends does not affect the sum.
If , then
Commutative Law For Multiplication
The arrangement of factors does not affect the product.
If , then
Associative Law For Addition
The grouping of addends does not affect the sum.
If , then
Associative Law For Multiplication
The grouping of factors does not affect the product.
If , then .
Distributive Law
Adding numbers and then multiplying them yields the same result as multiplying numbers and then adding them.
If , then