Review of Real Numbers
To complete this lesson, read everything on these pages and follow the instructions that you find.
Note that there is a symbol of a CD under the title. This tells you that the CD that came with the text book has a tutorial lesson associated with this section.
Student's Opportunity to Ask Questions If after first reading and studying the examples you still experience difficulty in understanding any part of the lesson, contact the instructor by e-mail. If possible, the question will be answered by e-mail. If necessary, a chat session will be scheduled. Please do not hesitate to ask questions. It is the goal of the instructor to have all students succeed in mastering the material. It is important that you understand this lesson before moving to the next—for mathematics requires a working understanding of many different concepts. If the student fails to gain this understanding, this weak skill area may adversely impact performance in later studies or employment.
A second option is to use the tutorial service offered through Smarthinking.
Throughout the lesson, remember also that there are on-line resources, such as section quizzes, available at the textbook's web site.
SECTION 1.1 - INTRODUCTION TO REAL NUMBERS
ObjectivesAfter reading the lesson and working through the exercises, you should be able to perform the following objectives.
| 1.1A | To use inequalities and absolute value symbols with real numbers |
| 1.1B | To write sets using the roster method and set builder notation |
| 1.1C | To perform operations on sets and write sets in interval notation |
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Read all of section 1.1 in your textbook, Intermediate Algebra.
Note 1: Learn the meaning of each new term.
Note 2: I can't get some of the symbols to show in the boxes below, so you will have to look at them in the textbook.
1.1A To use inequalities and absolute value symbols with real numbers
Reading Assignment
| New vocabulary | set |
New Symbols | is
an element of ( ) |
|
| elements |
is not
an element of ( ) |
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| natural numbers |
less
than ( < ) |
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| prime number |
greater
than ( > ) |
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| composite number |
absolute
value ( |...| ) |
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| whole numbers |
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| integers |
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| negative numbers |
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| positive numbers |
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| rational numbers |
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| irrational
numbers |
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| real numbers |
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| graph of a
real number |
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| variable |
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| additive inverse |
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| opposite |
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| absolute value |
Note: Distinguish between whole numbers, integers, natural numbers, rational numbers, irrational numbers, and real numbers. These can be confusing, and will result in errors if you are not clear about their meanings.
Look at Examples 1 and 2, page 6. Do "You Try It" #1 and 2. The answers can be found on page S1 at the back of the book.
1.1B To use inequalities and absolute value symbols with real numbers
Reading Assignment
New vocabulary roster method
New Symbols
Look at Examples 3 and 4, page 7. Do "You Try It" #3 and 4. The answers can be found on page S1 at the back of the book.
1.1C To perform operations on sets and write sets in interval notation
Reading Assignment
New vocabulary union of two sets
New Symbols
Look at Examples 5 - 12, pages 11 - 12. Do "You Try It" # 5 - 12 on pages 11 - 12. The answers can be found on page S1 at the back of the book.
Lesson Assignment
Do the odd numbered questions in the exercises for section 1.1 - Pages 13 -16 # 1, 3, 5, ... ,95. Check your answers in A1 at the back of the book.
If you got more than one quarter of the questions wrong under any objective, then try the even numbered questions for extra practice.
SECTION 1.2 - OPERATIONS ON RATIONAL NUMBERS
Objectives
After reading the lesson and working through the exercises, you should be able to perform the following objectives.
1.2A To add, subtract, multiply, and divide integers 1.2B To add, subtract, multiply, and divide rational numbers 1.2C To evaluate exponential expressions 1.2D To use the Order of Operations Agreement Read all of section 1.2 in your textbook.
1.2 A To add, subtract, multiply, and divide integers
Reading Assignment
Rules
Rules for Addition of Real Numbers Rules for Subtraction of Real Numbers Rules for Multiplication of Real Numbers Rules for Division of Real Numbers Properties of ZERO and ONE in Division It is extremely important to understand these rules, as they are used frequently in all Math courses and quite frequently in real life situations.
Look at Examples 1 - 3, page 19. Do "You Try It" # 1- 3. The answers can be found on page S1 at the back of the book.
1.2 B To add, subtract, multiply, and divide rational numbers
Reading Assignment
Rules
Division of Fractions Note: In a negative fraction, the negative sign is commonly written in front of the fraction line, but it is just as correct to write it in front of the numerator or the denominator. For example,
.all mean the same thing.
Look at Examples 4 & 5, page 21. Do "You Try It" # 4 & 5. The answers can be found on pages S1 - S2 at the back of the book.
1.2 C To evaluate exponential expressions
Reading Assignment
nth power of a It is extremely important to understand the difference between (-2)2 and -22. The first one has a value of 4, whereas the second one is - 4. This type of question will definitely show up on many tests.
Look at Examples 6 & 7 page 22. Do "You Try It" # 6 & 7. The answers can be found on page S2 at the back of the book.
1.2 D To use the Order of Operations Agreement
Reading Assignment
Rules
Order of Operations Agreement
It is extremely important to understand the Order of Operations Agreement. Perhaps using an acronym may help. The acronym BEDMAS stands for
B rackets
E xponents
D ivision and M ultiplication in the order they appear
A ddition and S ubtraction in the order they appear
Look at Examples 8 - 10 page 24. Do "You Try It" # 8 - 10. The answers can be found on page S2 at the back of the book.
Lesson Assignment
Do the odd numbered questions in the exercises for section 1.2 - Pages 25 - 28, # 1, 3, 5, ... ,117 . Check your answers in A1 at the back of the book.
If you got more than one quarter of the questions wrong under any objective, then try the even numbered questions for extra practice.
SECTION 1.3 - OPERATIONS ON RATIONAL NUMBERS
Objectives
After reading the lesson and working through the exercises, you should be able to perform the following objectives.
| 1.3A | To use and identify the properties of the real numbers |
| 1.3B | To evaluate a variable expression |
| 1.3C | To simplify a variable expression |
Read all of section 1.3 in your textbook.
1.3A To use and identify the properties of the real numbers
Reading Assignment
| New vocabulary |
Commutative Property of Addition |
|
|
Commutative Property of Multiplication |
| Associative Property of Addition |
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| Associative Property of Multiplication |
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| Addition Property of Zero |
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| Multiplication Property of Zero |
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| Multiplication Property of One |
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| Inverse Property of Addition |
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| Inverse Property of Multiplication |
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| Distributive Property |
| Review vocabulary |
additive inverse |
|
|
multiplicative inverse |
| reciprocal |
Note that Multiplicative Inverse = Reciprocal
Look at Examples 1 and 2 page 30. Do "You Try It" # 1 and 2. The answers can be found on page S2 at the back of the book.
1.3B To evaluate a variable expression
Reading Assignment
Note: When the coefficient in front of a term is 1, we normally do not write it.Look at Examples 3 and 4 on page 31. Do "You Try It" # 3 and 4. The answers can be found on page S2 at the back of the book.
1.3 To simplify a variable expression
Reading Assignment
| New
vocabulary |
like
terms |
| combine
like terms |
Note: Adding like terms is like adding apples or oranges. Simply add the coefficients of the like terms (fruit).
Look at Examples 5 and 6 on page 32. Do "You Try It" # 5 and 6. The answers can be found on page S2 at the back of the book.
Lesson Assignment
Do the odd numbered questions in the exercises for section 1.3 - Pages 33 - 36, # 1, 3, 5, ... 89 . Check your answers in A11 at the back of the book.
If you got more than one quarter of the questions wrong under any objective, then try the even numbered questions for extra practice.
SECTION 1.4 - VERBAL EXPRESSIONS AND VARIABLE EXPRESSIONS
Objectives
After reading the lesson and working through the exercises, you should be able to perform the following objectives.
| 1.4A | To translate a verbal expression into a variable expression |
| 1.4B | To solve application problems |
1.4A To translate a verbal expression into a variable expression
Reading Assignment
| New vocabulary |
Different
ways of translating verbal expressions into Math expressions - See
P. 37 |
Look at Examples 1 - 4 page 39. Do "You Try It" # 1 - 4. The answers can be found on page S2 at the back of the book.
1.4B To solve application problems
Reading Assignment
| New
vocabulary |
none |
Look at Examples 5 - 7 on page 40. Do "You Try It # 5 - 7" . The answers can be found on page S3 at the back of the book.
LESSON ASSIGNMENT
Do the odd numbered questions in the exercises for section 1.4 - Pages 41 - 42, # 1, 3, 5, ... 27. Check your answers in A12 at the back of the book.
If you got more than one quarter of the questions wrong under any objective, then try the even numbered questions for extra practice.
LESSON TEST
You have now completed lesson 1 based on sections 1.1, 1.2, 1.3, and 1.4 and should be ready to write a 20-mark test on all four sections. I would suggest that before you write the actual Lesson 1 test, you do the following:
Read the Chapter 1 summary, Page 46
Write the Chapter 1 Review Exercises, Page 50 - Answers on Page A2
Write the Chapter 1 Test, Page 53 - Answers on Page A2
For more practice on writing tests, try the practice tests prepared by the publisher of the textbook. You can find it on the internet, accessed through the link below. These tests are for practice only and do not count towards your BMCC grade.
When you write the Lesson Test, the results are sent to Mr. Turco. He will grade it and then forward the test to you,along with the correct answers. Look over any wrong answers to see where you went wrong. If there are any that you still do not understand, then please email Mr. Turco to have him explain the answer.
Click below for the appropriate tests.