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KU 122 Unit #7 Seminar
Kirsten Muller, M. A., M. Ed.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 7- 1
What’s going on this week?
Please remember to complete the following activities:
o Reading
o Practice Problems
o 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
7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
Introduction to Real Numbers
and Algebraic Expressions
Introduction to Algebra
The Real Numbers
Addition of Real Numbers
Subtraction of Real Numbers
Multiplication of Real Numbers
Division of Real Numbers
Properties of Real Numbers
Simplifying Expressions; Order of Operations
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
5 a
x
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.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Translating to Algebraic Expressions
Addition
Subtraction
Multiplication
Division
added to
subtracted from
multiplied by
divided by
sum
difference
product
quotient
plus
minus
times
divided into
more than
less than
twice
ratio of
increased by
decreased by
of
per
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 7- 5
Example
Translate each phrase to an algebraic expression.
Phrase
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
Algebraic Expression
x + 8, or 8 + x
1
x
x, , or x / 4
4
4
4x + 2, or 2 + 4x
n–8
ab – 5
0.25n
3w – 7
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Natural Numbers
The set of natural numbers = {1, 2, 3, …}.
These are the numbers used for counting.
Whole Numbers
The set of whole numbers = {0, 1, 2, 3, …}.
This is the set of natural numbers with 0
included.
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Integers
The set of integers = {…, 5, 4, 3, 2, 1,
0, 1, 2, 3, 4, 5, …}.
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5 units from 0 5 units from 0
Absolute Value
The 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.
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|
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Subtraction a  b
The difference a  b is the number c for
which a = b + c.
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Example
Subtract.
1. 15  (25)
2. 13  40
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Objective
Multiply real numbers.
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Example
Multiply.
1. (7)(9)
2. 40(1)
3. 3  7
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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 C
Multiply.
1. 9  3(4)
2. 6  (3)  (4)  (7)
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The product of an even number of negative numbers
is positive.
The product of an odd number of negative numbers
is negative.
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Example
40 x
.
Simplify: 
24 x
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Example
Multiply.
1. 8(a – b)
2. (b – 7)c
3. –5(x – 3y + 2z)
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Example
Factor.
a. 6x – 12
b. 8x + 32y – 8
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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 Terms
Terms 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.
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Example
Combine like terms. Try to write just the answer.
1. 8x + 2x
2. 3x – 6x
3. 3a + 5b + 2 + a – 8 – 5b
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Example
Remove parentheses and simplify.
(8x + 5y – 3)  (4x – 2y  6)
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Example
Remove parentheses and simplify.
(3a + 4b – 8) – 3(–6a – 7b + 14)
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Example
Simplify. 5(3 + 4) – {8 – [5 – (9 + 6)]}
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Example
Simplify. [6(x + 3) – 4x] – [4(y + 3) – 8(y – 4)]
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Example
Simplify.
1. 20 12  4  2
3
(

3)
 9  6(3)
2.
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Example
63  9
.
Simplify:
2
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Project Review
-5+5=
b.
4 + (-3) =
c.
-6∙7=
d.
- 6 (-7) =
e.
76 + (-15) + (-18) + (- 6) =
Translate each phrase:
a.
Seven more than a number
b.
Three multiplied by a number
c.
Three times a number plus seven
a.
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Questions??
Email me: [email protected]
Address me in “Course Questions.”
Office Hours: Tuesday 7:00-9:00 PM EST
Cell phone: 816-591-2070
Have a great week!
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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