Properties+of+Numbers

Now, we will use what we learned about breaking down unknown words to learn about 5 different properties of numbers.


 * DIRECTIONS: Read through the information below on the 5 Properties of Numbers. At the end of each section there is a Task in purple . Copy and paste the task into a Word document and complete it. At the end of the assignment, save your document and email it to your teacher (Tegan - teganolympus@gmail.com or Jeph - olympusjeph@yahoo.com) **


 * 1. Distributive Property -** Even without knowing what the distributive property is, we could use the root word "distribute" to learn something about what the property is. Using the root words can also be useful in triggering our memories to remember what the property is after we've learned it.

The word "distribute" means "to give out." This can remind us that in the distributive property we are going to be giving a number out to the other numbers in the problem. For example:

3(x + 4) = 3(x) + 3(4) = 3x + 12

In this example, we "gave out" the 3 to the "x" and the 4 using **multiplication.**

Using what we know about the word "distribute" and what we see in the example, we can define the distributive property as: multiplying a number and a quantity in parentheses by multiplying the number by each term in the parentheses.

Here's another example: (x + 2)(x - 3) = x(x) + x(-3) + 2(x) + 2(-3) = x__//2//__ - 3x + 2x - 6 = x__//2//__ - x - 6

An important fact about the distributive property is that it is used to **get rid of parentheses.** Also, **if there's no number outside the parentheses, we can put a 1** because multiplying by 1 doesn't change the problem.

**TASK: Explain in your own words why the Distributive Property is called the Distributive Property.**

The word "commute" means to travel back and forth between home and work or school. When you think about going back and forth from school and home, you go the same distance regardless of which direction you're going (home to school or school to home). This is exactly what the commutative property tells us about multiplication and addition! Here's an example:
 * 2. Commutative Property**

1 x 2 x 3 = 3 x 2 x 1 1 x 2 x 3 = 2 x 1 x 3

6 + 10 = 10 + 6

This property **only works for Multiplication and Addition**!


 * TASK: Using what we know about the word "commute" and the examples given above, define the commutative property. **

The word "identity" means who you are. When we're talking about the identity property of addition, we want to know what we can add to a number that won't change it's identity (won't change what number is it). What number can we add to any other number that won't change the original number?
 * 3. Identity Property of Addition**

4 + 0 = 4 -2 + 0 = -2 174 + 0 = 174

** TASK: Using what we know about identity and the examples given above, define the Identity Property of Addition.**

Try this one on your own! Think about what the word "identity" means and how that could be applied to multiplication.
 * 4. Identity Property of Multiplication**

**TASK: U****sing what you know, define the Identity Property of Multiplication and provide an example.**

Try this one on your own too! Think about what the word "associative" means and look at the example provided below.
 * 5. Associative Property**

Example: (1 + 2) + 3 = 1 + (2 + 3)

**TASK: Using what you know, define the Associative Property. Will this property work for all operations? If so, give an example of each. If not, which operations does it work for?**

**TASK: Open the document below and complete the practice problems. Turn your work in during class.**