# 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 or I am equal to myself

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

Example: Suppose fish = tuna, then tuna = fish

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

Example: Suppose John's height = Mary's height and Mary's height = Peter's height, then John's height = Peter's height

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

Example: Suppose John's height = Mary's height, then John's height + 2 = Mary's height + 2

Or suppose 5 = 5, then 5 + 3 = 5 + 3

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

Example: Suppose John's height = Mary's height, then John's height − 5 = Mary's height − 5

Or suppose 8 = 8, then 8 − 3 = 8 − 3

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.

## Recent Articles 1. ### How to Write an Inequality

Dec 12, 19 07:51 AM

Learn how to write an inequality quickly with this easy to follow math lesson.

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius! Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.