Transcript Ch 2 Alg 1 07 08 LA

Adding, subtracting, multiplying, and dividing real numbers.
Section 2.1
The Real Number Line
• Real numbers can be graphed as points on a line called a real number line.
•All real numbers are positive, negative, or zero.
Section 2.1
The lowest level is -3 meters in 2008 and the highest level is 4 meters
in 2005.
Section 2.2
Absolute 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)
•Identity property: a+0=a
-5+0=-5
• Inverse property: a+ (-a) = 0
5+(-5)=o
(-5+6)+2=-5+(6+2)
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
Change (in)
Sunday Monday Tuesday Wednesday Thursday Friday Saturday
-5
3
2
10
-1
300 + (-5) + 3 + 2 + 10 + (-1) + (-5) + 0 = 300 + (-2) + 9 + (-5)
= 300 + 2 = 302
The pool is 302 inches on Saturday
-5
0
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 2.7
Combining 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 2.8
Dividing 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
2X½=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-8
The End