Today’s Objective: To understand and use properties to write and solve expressions and equations.

Why is it important? Using properties makes it easier to work complicated problems.

A property is something that is true for all situations.

1. Distributive

2. Commutative

3. Associative

4. Identity properties of one and zero

Look at this problem:2(4 + 3)

Through your knowledge of order of operations, you know what to do first to evaluate this expression.

2(7)14

Now, look what happens when I do something different with the problem.

2(4 + 3) = 8 6+ = 14No difference.This is an example of the distributive property.

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Now why would one ever use the distributive property to solve 2(4 + 3)?

The answer is generally,

“You wouldn’t! Just use the order of operations.”

One place this is going to become very important is when we have an expression in the parenthesis which can not be simplified, like:

2(4 + x)

You need to be able to recognize and use the distributive property throughout all of Algebra.

This is one property you need to know by name, forwards, and backwards!

EXAMPLE: Use the distributive property to find each product.a. 7 * 98 b. 8(6.5)

EX1EX1β

First break down (decompose) the number 98:

7(90 + 8)

Then distribute.

630 + 56

Finally, add.

686

How can we decompose 6.5? Hint: How do we read the decimal?

8(6 + 0.5)

Then distribute.

48 + 4

Finally, add.

52

The distributive property can make large calculations easier for using mental math.

A(B + C) = AB + AC

4(3 + 5) = 4(3) + 4(5)

Order doesn’t matter

A x B = B x A

A + B = B + A

Associative Property of multiplication

(a · b) · c = a · (b · c)

Example: (6 · 4) · 3 = 6 · (4 · 3)

Associative Property of addition

(a + b) + c = a + (b + c)

Example: (6 + 4) + 3 = 6 + (4 + 3)

If you add 0 to any number, the number stays the same.

A + 0 = A or 5 + 0 = 5

If you multiply any number times 1, the number stays the same.

A x 1 = A or 5 x 1 = 5