# Important Laws and Identities

(*a*) ** CommutativeLawofAddition:**a+b=b+a

(*b*) ** AssociativeLawofAddition:**(a+b)+c=a+(b+c)

(*c*) ** AdditiveIdentity–“0”:**a+0=a

(*d*) ** AdditiveInverse:**a+(–a)=0.-a is the additive inverse of a and vice versa.

(*e*) ** Commutative Law of Multiplication: **a × b = b a

(*f*) ** Associative Law of Multiplication: **(a × b) c = a × (b × c)

(*g*) ** MultiplicativeIdentity–“1”:**a×1=a

(*h*) ** MultiplicativeInverse:**a×(1/a)=1.1/a is the multiplicative inverse of a and vice versa.

(*i*) ** Distributivelaw:**(a+b)×c=ac+bc

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*j*)

**a×0=0**

*Multiplicativepropertyof“0”:*(*k*) ** Multiplicative property of “–1”: **(–1) × a = –a

(*l*) a×1/b=a/b,whereb≠0.

(*m*) a/b÷c=a/b×1/c=a/bc,whereb,c≠0 (*n*) a/b÷c/d=a/b×d/c=ad/bc,whereb,c≠0