Multiplication Property of Equality

Properties of Equality

1. MULTIPLICATION PROPERTY: If A = B is true then A · C = B · C is true.

a) If x = 2 then x · 5 = 2 · 5

b) If x + 3 = 5 then (x + 3) · (- 3) = 5 · (- 3).

2. TRANSITIVE PROPERTY: If A = B and B = C is true then A = C is true.

The transitive property is also called the “substitution” property.

We sometimes say that “Quantities equal to the same thing are equal to each other.”

a) If x = 7 · 5 and 7 · 5 = 35 then x = 35

b) If 2x = 4 · 9 and 4 · 9 = 36 then 2x = 36

We will also apply the Basic Number Properties. In particular,

Use the “Inverse” Property of Multiplication (reciprocal)

This will be referred to by a “code”: Multiply Recip

Definition of Division:

To divide: → Change to MULTIPLY by the reciprocal

a ÷ b  →