Adding, subtracting, multiplying, and dividing real numbers.

Section 2.1

• Real numbers can be graphed as points on a line called a real number line.

•All real numbers are positive, negative, or zero.

The Real Number Line

Section 2.1

The lowest level is -3 meters in 2008 and the highest level is 4 meters in 2005.

Section 2.2Absolute Value

The absolute value of a number is simply the number, disregarding its sign (positive or negative)

Example 1: What does I-6I =?

Answer is I-6I = 6

Section 2.2

Since speed is the absolute value of velocity. Find the speed of a Spiderman falling off a building at a velocity of -12 meters per second?

Solution:

I-12I = 12 thus Spiderman is falling off the building at 12 meters per second.

Section 2.3

Adding Real Numbers

When you add a negative and a positive. Place the positive first and add the negative number (to subtract)

Example: You owe your parents $100 and you earn $200 from your job. How much money do you have now?

Solution:

-100+200 =200-100= 100

You have $100 now!

Section 2.3

Properties of Addition:

• Closure property: a+b is a unique number 4+6=10

•Commutative property: a+b=b+a 3+(-2)= -2+3

•Associative property: (a+b)+c=a+(b+c) (-5+6)+2=-5+(6+2)

•Identity property: a+0=a -5+0=-5

• Inverse property: a+ (-a) = 0 5+(-5)=o

Section 2.3

8 + (-4) + 5 = 8 + (-4+5) = 8 + (1) = 9

A cars velocity begins at 8 meters/second, then slows down -5 meters/second, and speeds up 1 meter/second more. What is the velocity?

8+ (-5) + 1= 8 + (-5+1) = 8 + (-4) = 4 meters/second

Section 2.4 Subtracting Real Numbers

When subtracting two positive numbers take away the second number from the first.

7-2= 5

When subtracting a positive and a negative number add the second number to the first. (2 positives make a negative)

5- (-2) = 5+2 = 7

Section 2.4

Example

The water level in this pool rises and falls due to rain and draining ever hour. From the table find the amount of water in the pool at the beginning of Saturday if it begins at 300 in.

Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday

Change (in) -5 3 2 10 -1 -5 0

300 + (-5) + 3 + 2 + 10 + (-1) + (-5) + 0 = 300 + (-2) + 9 + (-5)

= 300 + 2 = 302

The pool is 302 inches on Saturday

Section 2.5

Multiplying Real Numbers

Rules With + or - numbers

1.) A positive times a postive is positive

2.) A negative times a negative is positive

3.) A negative times a positive is negative

Examples

5 X 6 = 30

7 X (-3)= -21

(-2) X (-2) = 4

Section 2.5

Properties of Multiplication

• Closure Property: Multiply 2 numbers and the product is different from either of the numbers you were multiplying

•Commutative Property: When you multiply numbers the order in which you multiply them does not matter.

•Associative Property: When you multiply 3 numbers the order in which you multiply does not matter.

•Identity Property: If you multiply 1 by any number the product is that number.

•Property of zero: If you multiply 0 by any number the product is 0.

•Property of Negative one: If you multiply any number by -1 the product is the opposite of that number (-)

Section 2.5

Examples: Simplify the expression

a.) -5 (-x) = 5x

b.) 7 (-x)(-x)(-x) = -7x^3

c.) -1 (-a)^2 = -a^3

Section 2.6

The Distributive Property

When you have an equation with on term multiplied by a sum or quotient. Distribute that term to each one of the terms.

a (b+c) = ab+ac or (b+c)a = ba+ ca

a(b-c) = ab-ac or (b-c)a = ba-ca

Section 2.6

You need to by cookies for your class of 15 students, 1 cookie per student. If the cookies cost .50 cents how much will you spend.

15 ( .50) = 15 (1-.50) = 15 -7.50 = $7.50

You will spend $7.50

Section 2.7Combining Like Terms

Like terms are numbers in a function that have the same variable and power.

3x is a like term of 5x

2x^5 is a like term of -8x^5

Examples:

Simplify: 6(x+5) + 4(3-x) = 6x+35+12-4x

6x-4x+35+12

2x+47

Section 2.8Dividing Real Numbers

Inverse Property of Multiplication: when you multiply a number by its reciprocal its product is one.

Division Rule: When you divide a number you multiply it by its reciprocal

The Sign of a Quotient Rule: When you multiply numbers with the same sign (positive or negative) the product is positive. When you multiply numbers with opposite signs (one positive or one negative) the product is negative.

Section 2.8

Examples:

Inverse 2 X ½ = 1

Division 3÷6 = 3 x 1/6 = 3/6 = ½

Sign -2 X -3 = 6

24 X 2 = 48

Section 2.8

Example

Simplify 12x-24

3

(12x-24) ÷ 3

(12x-24) X (1/3)

12x - 24

3 3

4x-8The End