Algebra Know-It-ALL

Product of sums

For all real numbers w, x, y, andz,

(w+x)(y+z)=wy+wz+xy+xz

Cross multiplication

For all real numbers w, x, y, and z where neither x nor z is equal to 0,

w /x=y /z if and only if wz=xy

Reciprocal of product

For all nonzero real numbers x and y,

1/(xy)= (1/x)(1/y)

This can also be written as

(xy)−^1 =x−^1 y−^1

Product of quotients

For all real numbers w, x, y, and z where x≠ 0 and z≠ 0,

(w /x)(y /z)= (wy)/(xz)

Reciprocal of quotient

For all nonzero real numbers x and y,

1/(x /y)=y /x

This can also be written as

(x /y)−^1 =y /x

Quotient of products

For all real numbers w, x, y, and z where x≠ 0, y≠ 0, and z≠ 0,

(wx)/(yz)= (w /y)(x /z)

= (w /z)(x /y)

More Rules for Real Variables 137