Math 300

Fraction Unit

Dr. Wilson

 

Corollary: (The cancellation property of integer multiplication) If a, b, and c are integers with a not zero and ab = ac, then b = c.

 

Proof: Assume that ab = ac but a is not 0. Then

 

ab - ac = 0

 

Factor out an a from both terms.

 

a(b - c) = 0

 

We now use the fact that if a product is 0 then one of the factors is 0. We have assumed that a is not 0, so we must conclude that

 

b - c = 0

or

b = c