Basic Laws of Algebra

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	$a+b=b+a$ The arrangement of addends does not affect the sum.	If $2+3=5$, then $3+2=5$
Commutative Law For Multiplication	$a*b=b*a$ The arrangement of factors does not affect the product.	If $(2)(3)=6$, then $(3)(2)=6$
Associative Law For Addition	$(a+b)+c=a+(b+c)$ The grouping of addends does not affect the sum.	If $(2+3)+4=5+4=9$, then $2+(3+4)=2+7=9$
Associative Law For Multiplication	$(a*b)*c=a*(b*c)$ The grouping of factors does not affect the product.	If $(2*3)*4=(6)4=24$, then $2*(3*4)=2(12)=24$.
Distributive Law	$a(b+c)=(a*b)+(a*c)$ Adding numbers and then multiplying them yields the same result as multiplying numbers and then adding them.	If $2(3+4)=2(7)=14$, then $2(3)+2(4)=6+8=14$