View
218
Download
3
Category
Preview:
Citation preview
KU 122 Unit #7 Seminar
Kirsten Muller, M. A., M. Ed.
Slide 7- 1Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
What’s going on this week?
Please remember to complete the following activities:o Readingo Practice Problemso Seminar o Discussion—Pay close attention to the feedback to
your classmates!o Project All assignments are due Tuesday, November 3, 2009,
by 11:59 PM EST.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Introduction to Real Numbers and Algebraic Expressions
7.1 Introduction to Algebra7.2 The Real Numbers7.3 Addition of Real Numbers7.4 Subtraction of Real Numbers7.5 Multiplication of Real Numbers7.6 Division of Real Numbers7.7 Properties of Real Numbers7.8 Simplifying Expressions; Order of Operations
77
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Algebraic Expressions
An algebraic expression consists of variables, constants, numerals, and operation signs.
x + 38 19 – y
When we replace a variable with a number, we say that we are substituting for the variable.
This process is called evaluating the expression.
5a x
y
Slide 7- 5Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Translating to Algebraic Expressions
per of decreased by increased by
ratio of twice less than more than
divided into times minus plus
quotient product difference sum
divided bymultiplied bysubtracted from added to
DivisionMultiplicationSubtractionAddition
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Example
Translate each phrase to an algebraic expression.
Phrase Algebraic Expression
Eight more than some number
One-fourth of a number
Two more than four times some number
Eight less than some number
Five less than the product of two numbers
Twenty-five percent of some number
Seven less than three times some number
x + 8, or 8 + x
4x + 2, or 2 + 4x
1, , or / 4
4 4
xx x
n – 8
ab – 5
0.25n
3w – 7
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Natural NumbersThe set of natural numbers = {1, 2, 3, …}. These are the numbers used for counting.
Whole NumbersThe set of whole numbers = {0, 1, 2, 3, …}. This is the set of natural numbers with 0 included.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
IntegersThe set of integers = {…, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, …}.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Absolute ValueThe absolute value of a number is its distance from zero on a number line. We use the symbol |x| to represent the absolute value of a number x.
5 units from 0 5 units from 0
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Example Find the absolute value of each number.
a. |5| b. |36|
c. |0| d. |52|
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Subtraction a bThe difference a b is the number c for which a = b + c.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Example
Subtract.1. 15 (25) 2. 13 40
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Objective
Multiply real numbers.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Example Multiply.1. (7)(9) 2. 40(1) 3. 3 7
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
The Product of Two Negative Numbers
To multiply two negative numbers, multiply their absolute values. The answer is positive.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Example CMultiply.1. 9 3(4) 2. 6 (3) (4) (7)
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
The product of an even number of negative numbers is positive.
The product of an odd number of negative numbers is negative.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Example
Simplify:
40.
24
x
x
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Example
Multiply. 1. 8(a – b) 2. (b – 7)c 3. –5(x – 3y + 2z)
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Example
Factor.a. 6x – 12 b. 8x + 32y – 8
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Example
Factor. Try to write just the answer, if you can.a. 7x – 7y b. 14z – 12x – 20
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
A term is a number, a variable, a product of numbers and/or variables, or a quotient of two numbers and/or variables.
Terms are separated by addition signs. If there are subtraction signs, we can find an equivalent expression that uses addition signs.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Like TermsTerms in which the variable factors are exactly the same, such as 9x and –5x, are called like, or similar terms.
Like Terms Unlike Terms
7x and 8x 8y and 9y2
3xy and 9xy 5a2b and 4ab2
The process of collecting like terms is based on the distributive laws.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Example Combine like terms. Try to write just the answer.1. 8x + 2x 2. 3x – 6x3. 3a + 5b + 2 + a – 8 – 5b
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Example
Remove parentheses and simplify. (8x + 5y – 3) (4x – 2y 6)
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Example
Remove parentheses and simplify.(3a + 4b – 8) – 3(–6a – 7b + 14)
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Example
Simplify. 5(3 + 4) – {8 – [5 – (9 + 6)]}
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Example
Simplify. [6(x + 3) – 4x] – [4(y + 3) – 8(y – 4)]
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Example Simplify.
1. 2.
20 12 4 2 3( 3) 9 6( 3)
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Example
Simplify: 6 3 9
.2
Project Review
a. - 5 + 5 =b. 4 + (-3) =c. - 6 ∙ 7 =d. - 6 (-7) =e. 76 + (-15) + (-18) + (- 6) =Translate each phrase:a. Seven more than a numberb. Three multiplied by a numberc. Three times a number plus seven
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Questions??
Email me: kmuller@kaplan.eduAddress me in “Course Questions.”Office Hours: Tuesday 7:00-9:00 PM ESTCell phone: 816-591-2070
Have a great week!
Slide 7- 32Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Recommended