Properties of Equality

The properties of equality are basic algebraic facts that help us solve equations.  We are already using these, we just haven't put names to them yet.  So in this video this teacher puts the name with the concept.  You will cover this again in 9th grade and refresh it in 10th and 11th grade.  So you might as well learn it now so that it's faster in 9th grade and an old concept in 11th grade.

To see this concept in more detail, watch this video.

The major takeaway are the properties of equality for the operations.  Used in conjunction with the additive and multiplicative identities and inverses, we can solve for variables.

Here is the list of properties:

Additive identity: a + 0 = a (or 4 + 0 = 4, etc)

Multiplicative identity:  a * 1 = a  (or 4 * 1 = 4, etc)

Additive inverse: a + -a = 0 (or 4 + -4 = 0, etc)

Multiplicative inverse a * 1/a = 1 (or 4 * 1/4 = 1, etc)

Addition property of equality: if a = b, then a + c = b + c  (if 4 = 4, then 4 + 2 = 4 + 2)

Subtraction property of equality: if a = b, then a - c = b - c (if 4 = 4, then 4 - 2 =  4 - 2)

Multiplication property of equality: if a = b, then a * c = b * c (if 4 = 4, then 4 * 2 = 4 * 2)

Division property of equality: if a = b, then a / c = b / c (if 4 = 4, then 4 / 2 = 4 / 2)

Using these properties, we can solve any equation with 1 variable.  We can simplify any equation with 2 variables.  Understanding these properties will help you write equations for word problems, or pick the correct equation out of a list.