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Algebraic Identities

Algebraic identities for addition and multiplication.
a data set by gandrew
created November 20, 2016
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FAMILY TREE
ExpressionIdentityNameFull IdentityExample
a+0aAdditive Identitya+0=05+0=5
a+(-a)0Additive Inversea+(-a)=04+(-4)=0
(a+b)+ca+(b+c)Associativity of Addition(a+b)+c=a+(b+c)(1+2)+3=1+(2+3)=5
a+bb+aCommutativity of Additiona+b=b+a6+8=8+6=14
a x 1aMultiplicative Identitya x 1=a7 x 1=7
a x (1/a) if a is not 01Multiplicative Inversea x (1/a)=1 if a is not 09 x (1/9)=1
a x 00Multiplication by 0a x 0=02 x 0=0
(a x b) x ca x (b x c)Associativity of Multiplication(a x b) x c=a x (b x c)(3 x 6) x 2=3 x (6 x 2)=36
a x bb x aCommutativity of Multiplicationa x b=b x a3 x 5=5 x 3=15
a x (b+c)(a x b)+(a x c)Distributive Lawa x (b+c) = (a x b)+(a x c)2 x (2+7)=(2 x 2)+(2 x 7)=18
a/ba x (1/b)Definition of Divisiona/b=a x (1/b)9/3=9 x (1/3)=3
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