Algebra Pinkston

Review: Prove that is a rational number.

Algebraic evaluation Algebraic expressions consist of variables, constants, and mathematical symbols. We substitute numbers for the variables when we evaluate.

Example 1: Evaluate for x = 3 and y = 5. Example 2: Evaluate for x = -7. Example 3: Evaluate for x = 15 and y = -10.

Try This, p. 15

Properties of Numbers In Algebra County

Commutative Property

We commute when we go back and forth from work to home.

Algebra terms commute when they trade places

This is a statement of the commutative property for addition:

It also works for multiplication:

Associative Property

To associate with someone means that we like to be with them.

The tiger and the panther are associating with each other. They are leaving the lion out.

In algebra:

The panther has decided to befriend the lion. The tiger is left out.

In algebra:

This is a statement of the Associative Property: The variables do not change their order.

The Associative Property also works for multiplication:

Distributive Property

Sometimes executives ask for help in distributing papers.

The distributive property only has one form.

Identity Property

The identity property makes me think about my identity.

The identity property for addition asks, “What can I add to myself to get myself back again?

The identity property for multiplication asks, “What can I multiply to myself to get myself back again?

Inverse Property

A statement of the inverse property for addition is:

A statement of the inverse property for multiplication is:

Some examples of the inverse property for multiplication are:

Closure

The above set of numbers is the set we will work with for this problem. If we add any two numbers in the set, do we always get a number in the set? If so, it has the property of closure. We also say the set is closed. Is it? No, because = 2

Is the above set closed over multiplication? Yes: 1 X 1 = 1 1 X 0 = 0 0 X 0 = 0

Is the set of natural numbers closed over subtraction? No: 4 – 6 = -2

Determine which property of numbers is illustrated: Commutative for mult. Identity for addition Distributive Associative for multiplication Commutative for addition Identity for multiplication

Determine which property of numbers is illustrated: Assoc for addition Inverse for addition Distributive Inverse for multiplication

SAT Question: Which of the following number sets has the property that the sum of any two numbers in the set is also in the set? I.Even integers II.Odd integers III. Composite numbers A.I B.II C.III D.I and II E.I and III I is correct. The sum of any two even numbers is an even number. II is not correct. The sum of any two odd numbers is an even number. III is not correct. The sum of some composite numbers is prime. Ex = 29

Get ready for a “Small Quiz” to be written on your grade sheet.

1. Evaluate for 2. Evaluate for Quiz. Copy the problems and write the answer. Put your grade paper on the front of your row, quiz side down.

The End