# Basic Laws of Algebra

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