Question

Compare and contrast the Multiplication Property of Equality and the Division Property of Equality and explain why they can be considered the same property.

Answer 1

Multiplicative property states that if a = b, then ac = bc
Division property states that if a = b, then a/c = b/c

Multiplication is the inverse of division and vise-versa, so the multiplicative property can be expresses as division property (i.e. ac = bc can be written as a/(1/c) = b/(1/c)) and division property can be expressed as multiplicative property (i.e. a/c = b/c can be written as a x 1/c = b x 1/c)