Algebra Know-It-ALL

134 Irrational and Real Numbers

Multiplicative inverse (reciprocal)

For every nonzero real number x,

x(1/x)= 1

and

(1/x)x= 1

Commutative law for addition

For all real numbers x and y,

x+y=y+x

Commutative law for multiplication

For all real numbers x and y,

xy=yx

Associative law for addition

For all real numbers x, y, and z,

(x+y)+z=x+ (y+z)

Associative law for multiplication

For all real numbers x, y, and z,

(xy)z=x(yz)

Distributive laws

For all real numbers x, y, andz,

x(y+z)=xy+xz

and

(x+y)z=xz+yz