# Properties of equality

We will show 8 properties of equality. When appropriate, we will illustrate with real life examples of properties of equality. Let x, y, and z represent real numbers.

Reflexive property: x = x

Example:

2 = 2

I am equal to myself

-1020 = -1020

Symmetric property: If x = y, then y = x

Example:

If fish = tuna, then tuna = fish

If x + 8 = -6, then -6 = x = 8

transitive property: If x = y and y = z, then x = z

Example:

If John's height = Mary's height and Mary's height = Peter's height, then John's height = Peter's height

If 2x + 8 = -12 and -12 = x - 2, then 2x + 8 = x - 2

Addition property: If x = y, then x + z = y + z

Example:

If John's height = Mary's height, then John's height + 2 = Mary's height + 2

If 5 = 5, then 5 + 3 = 5 + 3

If x + -2 = 5, then x + -2 + 2 = 5 + 2

Subtraction property: If x = y, then x − z = y − z

Example:

If John's height = Mary's height, then John's height − 5 = Mary's height − 5

If 8 = 8, then 8 − 3 = 8 − 3

If 2y + 4 = 10, then 2y + 4 - 4 = 10 - 4

Multiplication property: If x = y, then x × z = y × z

Example: Suppose Jetser's weight = Darline's weight, then Jetser's weight × 4 = Darline's weight × 4

Or suppose 10 = 10, then 10 × 10 = 10 × 10

Division property: If x = y, then x ÷ z = y ÷ z

Example: Suppose Jetser's weight = Darline's weight, then Jetser's weight ÷ 4 = Darline's weight ÷ 4

Or suppose 20 = 20, then 20 ÷ 10 = 20 ÷ 10

Substitution property: If x = y, then y can be substituted for x in any expression

Example: x = 2 and x + 5 = 7, then 2 can be substituted in x + 5 = 7 to obtain 2 + 5 = 7

Any questions about the properties of equality, let me know.

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