September 10, 2012Properties and Integers

Warm-up: Order of Operations

1. Simplify 10 + 2(3 – 5) – 4 32

2. (Optional) Challenge: Your objective is to use the digits 1, 2, 3, 4 ONLY ONCE and arrange them using addition, subtraction, multiplication, exponents, and parentheses (NOT division), so that they equal a specific number. You may also make a two digits to make one number, such as 12 or 34. EXAMPLE: An expression equal to 43.

43 = 42 + 13

A Block

• Finish Property Notes• Classwork: 1.4-1.6 Distributive Property WS• Quiz Thursday

The Commutative Property says the order in which two numbers are added or multiplied does not affect the answer.

a • b = b • a x + (y + z) = (y + z) + x

The Associative Property says the sum or product of any three numbers is the same, no matter how they are grouped using parentheses and the order of the numbers always stays the same.

(a + b) + c = a + (b + c) x • (y • z) = (x • y) • z

The Inverse Property of Addition says the sum of a number and its opposite equals 0.

a + (-a) = 0 -x + x = 0

The Inverse Property of Multiplication says any number multiplied by its reciprocal equals 1.

11

a

a 11

xx

The Additive Identity: 0 added to any number will always equal the same number.

a + 0 = a0 + x = x

The Multiplicative Identity: any number multiplied by 1 will always equal the same number.

a • 1 = a 1 • x = x

The Distributive Property multiplies the expression outside parentheses to the expression inside.

a(x + y) = ax + ay(a + b)(x + y) = ax + ay + bx + by

Identify the property that goes with the following expressions.

1. 3(x + y) = 3x + 3y 2. a + (b + c) = (a + b) + c

3. -10 + 10 = 0 4. 5. 4 + 0 = 4 1

4

14

Simplifying expressions and using the Distributive Property

Example 1: 3(2x – 5)

Example 2: 4 – 3(x – 2)

Example 3: 2(x + 9) + 7(5x – 4)

The Real Number Line

Graph the following numbers on the number line:

-8.5 6

4

3

positivenegative

origin

Comparing Integers (positive and negative numbers)

Use < or > to compare the numbers.

1) 5.5 ____ -6 2) -3.2 _____ -3.8

3) -100 ____ 0 4)

3

4____

1

5

-4 -2 0 2 4-3 1 5-1-5 3

5) Rewrite in increasing order

3.6, 3.0, -3.2, 0, -3.5, 3.2, 2.0

Opposite − ( )

The negative sign outside parentheses means “opposite”.

- ( girl ) = - ( hot ) =

-( positive ) =

Examples: Evaluate.

6. -(100) 7. -(-6.2)

Absolute Value │x│The Absolute Value of a number is the distance

from the given number to zero.

│-4│ “How many steps from -4 to zero?”

8. │100│ 9. │-45.8│

10. │0│+ │-6│ 11.

12. Determine < or > │-6│____ |5|

9

2