KU 122 Unit #7 Seminar Kirsten Muller, M. A., M. Ed. Slide 7- 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

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


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


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


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


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


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.


IntegersThe set of integers = {…, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, …}.


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


Example Find the absolute value of each number.

a. |5| b. |36|

c. |0| d. |52|


Subtraction a bThe difference a b is the number c for which a = b + c.


Example

Subtract.1. 15 (25) 2. 13 40


Objective

Multiply real numbers.


Example Multiply.1. (7)(9) 2. 40(1) 3. 3 7


The Product of Two Negative Numbers

To multiply two negative numbers, multiply their absolute values. The answer is positive.


Example CMultiply.1. 9 3(4) 2. 6 (3) (4) (7)


The product of an even number of negative numbers is positive.

The product of an odd number of negative numbers is negative.


Example

Simplify:

40.

24

x

x


Example

Multiply. 1. 8(a – b) 2. (b – 7)c 3. –5(x – 3y + 2z)


Example

Factor.a. 6x – 12 b. 8x + 32y – 8


Example

Factor. Try to write just the answer, if you can.a. 7x – 7y b. 14z – 12x – 20


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.


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.


Example Combine like terms. Try to write just the answer.1. 8x + 2x 2. 3x – 6x3. 3a + 5b + 2 + a – 8 – 5b


Example

Remove parentheses and simplify. (8x + 5y – 3) (4x – 2y 6)


Example

Remove parentheses and simplify.(3a + 4b – 8) – 3(–6a – 7b + 14)


Example

Simplify. 5(3 + 4) – {8 – [5 – (9 + 6)]}


Example

Simplify. [6(x + 3) – 4x] – [4(y + 3) – 8(y – 4)]


Example Simplify.

1. 2.

20 12 4 2 3( 3) 9 6( 3)


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


Questions??

Email me: [email protected] me in “Course Questions.”Office Hours: Tuesday 7:00-9:00 PM ESTCell phone: 816-591-2070

Have a great week!


Documents

KU 122 Unit #7 Seminar Kirsten Muller, M. A., M. Ed. Slide 7- 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley