Properties of Equality

Front

For real numbers x, y, and z,

If x = y, then x + z = y + z

Back

Addition Property

Front

For real numbers x, y, and z,

If x = y, then x - z = y - z

Back

Subtraction Property

Front

For real numbers x, y, and z,

If x = y, then x × z = y × z

Back

Multiplication Property

Front

For real numbers x, y, and z,

If x = y, then x ÷ z = y ÷ z

Back

Division Property

Front

For real numbers x, y, and z,

If x = y, then x + (-z) = y + (-z)

Back

Alternative Version of Subtraction
Property of Equality

Front

Back

Alternative Version of
Division Property of Equality

Front

Every real number is equal to itself. For a real number x,

x = x.

Back

Reflexive Property

Front

Order of equality does not matter. For real numbers x and y,

If x = y, then y = x.

Back

Symmetric Property

Front

Any two real numbers equal to each other can be substituted for one another in any expression. For real numbers x and y,

If x = y, then y can be substituted for x.

(lets you replace one variable with another variable or expression that is already proven to be equal to it, essentially substituting one piece of information for another within an equation or statement)

Back

Substitution Property

Front

Numbers equal to the same number are equal to each other. For real numbers x, y, and z,

If x = y and y = z, then x = z.

(allows you to conclude that two variables or expressions are equal if they are both congruent to a third variable or expression)

Back

Transitive Property